An assessment of the advantages of using TOC pull ... · An assessment of the advantages of using TOC pull replenishment in real situations Supervisor: Miragliotta Giovanni ... principi

POLITECNICO DI MILANO

Scuola di Ingegneria Industriale e dell'Informazione

Corso di Laurea Magistrale in

Ingegneria Gestionale

An assessment of the advantages of using TOC pull

replenishment in real situations

Supervisor: Miragliotta Giovanni

Co-supervisor: Buora Carlo

Master Graduate Thesis by:

Masdea Marco ID: 820364

Academic Year 2015 - 2016

i

Index of Contents

INDEX OF FIGURES ................................................................................III

INDEX OF TABLES ..................................................................................III

INDEX OF GRAPHS ................................................................................. IV

ABSTRACT ................................................................................................. V

1. INTRODUCTION 1

1.1 - COLLECTION AND REVIEW CRITERIA ..............................................................2

1.2 - GAPS ENCOUNTERED .....................................................................................8

1.3 - RESEARCH QUESTIONS ................................................................................ 10

2. TAXONOMY OF REPLENISHMENT STRATEGIES 11

2.1.1 - Push and Pull ................................................................................... 11

2.1.2 - Statistical Inventory Replenishment .................................................. 13 2.1.3 - Time-Phased Techniques: MRP and DRP ........................................ 19

2.1.4 - Lean Philosophy in Distribution ....................................................... 22

3. TOC PRINCIPLES AND PARADIGMS 25

3.1 - TOC GLOSSARY .......................................................................................... 27

3.1.1 - Constraints....................................................................................... 27

3.1.2 - Buffers ............................................................................................. 27

3.2 - LOGISTICS PARADIGM .................................................................................. 29

3.2.1 - Five Focusing Steps ......................................................................... 29 3.2.2 - VAT Analysis .................................................................................... 30

3.2.3 - Drum-Buffer-Rope ........................................................................... 31 3.2.4 - Buffer Management .......................................................................... 33

3.3 - PERFORMANCE MEASUREMENT ................................................................... 35

3.3.1 - Throughput Accounting .................................................................... 35

3.4 - DECISION MAKING ...................................................................................... 38

3.4.1 - Thinking Processes .......................................................................... 38

3.5 - TOC IN PRODUCTION ................................................................................... 40

3.5.1 - Simplified DBR ................................................................................ 40 3.5.2 - Make-To-Availability ....................................................................... 43

4. TOC AND SUPPLY CHAIN MANAGEMENT 47

4.1 - SUPPLY CHAIN REPLENISHMENT SYSTEM ..................................................... 47

4.1.1 - Aggregate Stock ............................................................................... 48 4.1.2 - Determine Buffer .............................................................................. 48

4.1.3 - Increase Replenishment Frequency .................................................. 50 4.1.4 - Manage Flow ................................................................................... 51

4.1.5 - Dynamic Buffer Management ........................................................... 52 4.1.6 - Set Manufacturing Priorities ............................................................ 55

4.2 - LOCAL PERFORMANCE MEASUREMENT ........................................................ 55

ii

5. SIMULATIONS OF REPLENISHMENT 57

5.1 - FEATURES OF THE MODEL ............................................................................57

5.1.1 - Structure of Network ........................................................................57 5.1.2 - Assumptions and Variables ..............................................................58

5.1.3 - Recorded Parameters .......................................................................61 5.1.4 - Formulas of Performances ...............................................................62

5.2 - MODELLED POLICIES ...................................................................................63

5.3 - SIMULATIONS ..............................................................................................65

5.3.1 - Scenario 1: Stationary demand with low variability..........................66 5.3.2 - Scenario 2: Stationary demand with higher variability .....................71

5.3.3 - Scenario 3: Demand with seasonality ...............................................81

6. CONCLUSIONS 85

6.1 - FINDINGS.....................................................................................................85

6.2 - LIMITS OF THE MODEL ..................................................................................89

6.3 - FURTHER DEVELOPMENTS ...........................................................................89

REFERENCES ........................................................................................... 90

iii

Index of Figures

Fig. 1: Growth of literature on TOC ...................................................................................... 4

Fig. 2: DRP in a multi-echelon supply chain ........................................................................ 20 Fig. 3: Five Lean Principles ................................................................................................. 22

Fig. 4: TOC Elements .......................................................................................................... 25 Fig. 5: Current state of TOC ................................................................................................ 26

Fig. 6: Types of buffer (adapted from Schragenheim & Dettmer, 2001) ................................ 28 Fig. 7: Five Focusing Steps cycle ......................................................................................... 29

Fig. 8: Network Typologies in VATI Analysis ....................................................................... 30 Fig. 9: Traditional DBR (adapted from Schragenheim & Dettmer, 2001) ............................. 32

Fig. 10: Buffer Zonation ...................................................................................................... 33 Fig. 11: Planned Load ......................................................................................................... 41

Fig. 12: Estimation of Safe Due Dates ................................................................................. 42 Fig. 13: Buffer Status ........................................................................................................... 51

Fig. 14: Dynamic Buffer Management ................................................................................. 53 Fig. 15: Network Model ....................................................................................................... 57

Index of Tables

Table 1: Papers and Articles selected..................................................................................... 3

Table 2: Categorization of Papers.......................................................................................... 5 Table 3: TOC Branches researched ....................................................................................... 5

Table 4: Basic Replenishment Strategies .............................................................................. 14 Table 5: Ordering Policy (adapted from Wensing, 2011) ..................................................... 16

Table 6: Networks configurations in VAT Analysis (adapted from Lockamy, 2008) .............. 31 Table 7: Common TOC Performance metrics ....................................................................... 37

Table 8: Example of Throughput Accounting (adapted from Cox & Schleier, 2010) ............. 37 Table 9: Local Performance Measures ................................................................................. 55

Table 10: Recorded Parameters ........................................................................................... 62 Table 11: Formulas.............................................................................................................. 62

Table 12: ROP, low variability............................................................................................. 66 Table 13: ROP, low var., minimum saturation and priority to profit..................................... 67

Table 14: DBM, low variability ............................................................................................ 68 Table 15: ROP, higher variability ........................................................................................ 71

Table 16: ROP, higher var., minimum saturation and priority to profit ................................ 72 Table 17: DBM Variations - Target resize and Cooling time ................................................ 73

Table 18: DBM Variations - Enhancement to Trigger of TMR.............................................. 76 Table 19: DBM vs ROP - Target Resize 10% and Trigger TMR 90% ................................... 78

Table 20: DBM - Order Batching ......................................................................................... 79 Table 21: DBM with batch ................................................................................................... 80 Table 22: ROP, seasonality .................................................................................................. 81

Table 23: DBM Variations: Target Resize and Trigger TMR with seasonality ...................... 82

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Index of Graphs

Graph 1: Scenario 1 - ROP, low variability.......................................................................... 66

Graph 2: Scenario 1 - Loading Priority to Profitability ........................................................ 67 Graph 3: Scenario 1 - DBM vs ROP, low variability ............................................................ 68

Graph 4: Scenario 2 - ROP, higher variability ..................................................................... 71 Graph 5: Scenario 2 - Loading Priority to Profitability ........................................................ 72

Graph 6: Scenario 2 - DBM Variations: Target resize and Cooling time .............................. 74 Graph 7: Scenario 2 - DBM Variations: enhancement to Trigger of TMR ............................ 77

Graph 8: Scenario 2 - DBM vs ROP: Target resize 10% and Trigger TMR 90% .................. 78 Graph 9: Scenario 2 - DBM with batch ................................................................................ 79

Graph 10: Scenario 2 - DBM with batch vs ROP.................................................................. 80 Graph 11: Scenario 3 - ROP, seasonality ............................................................................. 81

Graph 12: Scenario 3 - DBM Variations: Target resize and Cooling time with seasonality .. 83 Graph 13: Scenario 3 - DBM vs ROP, seasonality ............................................................... 84

v

Abstract

The Theory of Constraints (TOC) solutions are not widely known in Italy. This thesis has the

objective to illustrate their advantages using simulation tools. TOC principles and solutions for

supply chain management are reviewed, with focus on distribution and replenishment

strategies. An extremely low number of articles is available in literature on these topics. Many

of them discuss how to set initial parameters of Dynamic Buffer Management (DBM), but

overlook their actual sensitiveness in real applications. Improvement of demand change

detection is an area not completely explored by researchers. DBM is studied under different

degree of variability and patterns of demand. A comparison with performances obtainable from

a Reorder Point Model (ROP) is conducted in the same scenarios. ANOVA is performed on

results. Originality/novelty of this work regards different sensitiveness of DBM parameters to

variability. Trigger of “Too Much Red”, entity of resize of inventory Target Level, cooling-

time after buffer resizing and order batching were tested. Findings show that DBM is relatively

stable on change of its parameters, only small interventions are necessary and only under certain

conditions. DBM gave good results in presence of high variability demand and proved to be

comparable or better than ROP.

Keywords: TOC, DBM, ROP, theory of constraints, reorder point, supply chain, distribution,

replenishment, simulation

Sommario

Le soluzioni offerte dalla Teoria dei Vincoli (TOC) non sono ampiamente conosciute in Italia.

Questa tesi ha l'obiettivo di illustrare i loro vantaggi utilizzando strumenti di simulazione. I

principi della TOC e le soluzioni per la gestione della supply chain sono esaminate, con

attenzione alla distribuzione e alle strategie di rifornimento. Un numero estremamente basso di

articoli su questi temi è disponibile in letteratura. Molti di essi argomentano su come impostare

i parametri iniziali del Dynamic Buffer Management (DBM), ma trascurano la loro effettiva

sensibilità in applicazioni reali. Il miglioramento della capacità di individuazione di

cambiamenti nella domanda è un’area non completamente sviluppata dai ricercatori. Il DBM è

stato studiato sotto diversi gradi di variabilità e modelli di domanda. Negli stessi scenari è stato

condotto un confronto con le prestazioni ottenibili da un modello a punto di riordino (ROP).

ANOVA è stata eseguita sui risultati. L’originalità di questo lavoro riguarda la diversa

sensibilità dei parametri del DBM alla variabilità. Test sono stati eseguiti sui trigger del

"TooMuchRed", sull’entità del ridimensionamento del livello Target delle scorte, sul tempo di

cooling dopo la modifica del buffer e sul batching degli ordini. Le scoperte mostrano che il

DBM è relativamente stabile alla modifica dei suoi parametri, solo piccoli interventi sono

necessari e solo in alcune situazioni. DBM ha dato buoni risultati in presenza di domanda con

elevata variabilità e ha dimostrato di essere comparabile o migliore di ROP.

Parole chiave: TOC, DBM, ROP, teoria dei vincoli, punto di riordino, supply chain,

distribuzione, rifornimento, simulazione

vi

1

1. Introduction

Distribution has always been critical for many industries. Availability is considered a given by

customers and today stockouts have a greater impact on reputation and customer retention than

in the past. At the same time, distribution networks have grown larger and more complex than

ever. Challenging goals like minimization of total costs and improvement of service level are

even more tough in this context. In distribution networks, transportation costs are high,

especially if they are world-wide extended. Due dates are extremely important in supply chains

and firms are often on the verge of delays, which are paid with relevant penalties.

An effective planning and replenishment strategies are vital in order to simplify these

complexities.

The aim of this thesis is to evaluate Theory of Constraints (TOC) pull replenishment strategies

and describe their advantages in real situations using simulation tools. Distribution and

replenishment management literature is constantly developing. In spite of it, this theory is not

really well known in Italy.

In order to provide the whole picture, three preliminary steps were made:

1) Determine the basis of TOC and its state of development.

2) Determine a framework of the major replenishment strategies.

3) Determine the rules of TOC Pull Replenishment for distribution.

Gaps encountered have generated some research questions. Simulation scenarios were

modelled to answer them and they were tested using the tools of Rockwell ARENA. Results

were collected in MS EXCEL for a preliminary study, while statistical analysis and ANOVA

were conducted using software ERRE.

Originality of this work regards different sensitiveness of DBM parameters to variability that

they could face in real applications of TOC replenishment solutions. DBM has many parameters

but their effects are not clearly assessed in relation to variability of demand. Possible corrections

operated by controllers will be simulated and compared.

1. Introduction

2

1.1 - Collection and Review Criteria

Literature review was conducted by following a structured and systematic approach as

suggested by (Tranfield et al., 2003). This methodology has been employed by many researches

on logistics and supply chain management; the following three-steps are a variation of those

adopted by (Mangiaracina et al., 2015).

STEP 1 - ARTICLES SELECTION

Classification context: Literature evaluated in this work is about replenishment strategies in

downstream of supply chains. Different levels of integration between distribution and

production was taken into consideration, although the focus of this thesis is only on

distribution topics. Focus is on Theory of Constraints and its related methodologies.

Definition of the unit of analysis: The main sources of the collected information were

journals and articles, considering only those peer reviewed. Conference proceedings were

not included. Citations from books and manuals of high impact were added to provide a

more solid basis to the assertions of this work and to complete information scarcity on some

topics.

Collecting publications: Articles were selected from databases like Scopus and Web of

Science or downloaded from sites of publishers Springer Link, Science Direct (Elsevier),

Wiley Online, Emerald Insight, JSTOR and other. The main journals articles come from

are:

- Journal of Operations Management (JOM)

- European Journal of Operational Research (EJOR)

- Production and Operations Management (POM)

- Manufacturing and Service Operations Management (MSOM)

- International Journal of Production Research (IJPR)

- International Journal of Production Economics (IJPE)

- International Journal of Operations and Production Management (IJOPM)

The keywords entered to filter databases were combinations of the following words:

“Supply chain”, “Theory of Constraints”, “Replenishment”, “Dynamic Buffer

Management”, “Simulation”, “Distribution”, “Inventory Management”, “Policy”. Thanks

to these filtering criteria, their presence in title and abstract have been analysed, limiting the

1. Introduction

3

search to Business, Management and Economics fields and Decision Science or those

related to Engineering.

Delimiting Fields: Documents including the words “Theory of Constraints” in title, abstract

or keywords were 1082 (searched in Scopus, August 2016), without distinction about area,

document type, specific topic or temporal restriction of sources. Some of them were written

even before 1980 and some other were not related with TOC; after their removal a total of

954 was selected. Filtering only articles and reviews from journals they were reduced to

556.

A search by keywords connected with supply chain management sorted 146 papers. A

refinement was conducted by reading titles and abstracts and selecting appropriate subject

areas, as Management and Decision Science. Ignoring those dedicated exclusively to

production or matters not directly linked to distribution, no more than 74 articles were

reputed of direct interest. Finally, those not dealing with topics of distribution,

replenishment or inventory control were excluded.

The selection highlighted 23 articles related to the topics of this thesis. Because of their

little amount, a new search was conducted on other databases (like Web of Science) relaxing

the restriction on the subject area. Other three articles were found, so a total number of 26

articles was considered.

Even in this preliminary phase, this little amount of articles was already seen as a clear

evidence of the low attention on TOC by researchers.

Document containing “Theory of

constraints” (no restrictions) 1082

Topics of TOC 954

Only articles and reviews from journals 556

Topics on SCM or related 146

Topics on SCM, distribution and TOC

replenishment 74

Core on distribution and replenishment 23

(other sources and less formal search) 3

TOTAL 26

Table 1: Papers and Articles selected

1. Introduction

4

STEP 2 – REVIEW METHOD

General characteristics of papers: First, collected papers were analysed using their titles,

abstracts (when available), year of publication and authors. Attention focused on the main

pieces of information with the aim of finding a pattern to TOC studies and popularity of its

concepts applied to supply chain management.

Temporal distribution of 146 articles on SCM (core topic or references) showed that TOC

developed these topics in the last twenty years, but that even today this is not a well-explored

field. Less than 25% of all TOC papers published on journals every year covers these

subject. This does not consider other sources like conference or books, but it is very little

given that there has been about 30 articles per year during the last decade.

Fig. 1: Growth of literature on TOC

Most of the attention of the researchers is put on production and real applications of Drum-

Buffer-Rope, the first proposal of TOC and its central core. On the other hand, the number

of articles on production systems is now very considerable.

The early papers facing problems of TOC in distribution networks appeared in the ‘90s, but

even before it had already been treated in reports and empirical cases of the real application

of the methodology. Due to a lack of literature, they were not supported by a clear branch

of TOC and were seen as a ramification of Drum-Buffer-Rope from production. Simulations

and analytical analysis with significant basis appeared only from 2003.

Research methods in reviewed papers: The analysis on 74 papers which were filtered until

now has then been deepened by a categorization on the type of approach adopted and topics

discussed. This was done with a reading of the abstract, or the entire paper when in doubt.

The types of the classified approach were:

- Theoretical: contributions to the theory and conceptual works.

- Review: frameworks and review.

1. Introduction

5

- Analytical/Quantitative: papers with quantitative analysis or proposing simulations.

- Empirical: mostly focused on a case study.

The papers selected treat supply chains with a various degree of integration between

production and distribution. They were considered of interest when replenishment in a

downstream network was explicitly cited, retailers were involved or the contribution of the

production system was lower. All the simulations and quantitative works were held, seen

the preselection of papers regarding supply chain. However, only three simulations focused

on distribution environments and compared them.

It is worth noting that only one review was completely dedicated to outbound logistics

of TOC and the low number of empirical cases on distribution. Two additional cases were

found thanks to a less structured search. Nonetheless, it is important to report that a greater

number of cases was available googling in Internet but they were not considered because

of their unknown origin.

TOC branches researched: Papers were also classified according to the TOC areas they

discussed. Only when the article contents were linked to these main areas and they were

more than just an isolated citation, have they been taken into consideration:

Papers on

SCM

On TOC

Replenishment

Theoretical 43 10

Review 8 1

Analytical 10 10 (+1)

Empirical 13 2 (+2)

TOTAL 74 23 (+3)

Table 2: Categorization of Papers

(NB. Papers have been classified under more than one research topic)

Table 3: TOC Branches researched

5FS

VA

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Bu

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Man

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DB

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(Pro

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TOC

Su

pp

ly C

hai

n

Rep

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ish

men

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Syst

em

(TO

C-S

CR

S)

Thro

ugh

pu

t

Acc

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Thin

kin

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ss

21 11 20 20 16 22 13

28% 15% 27% 27% 22% 30% 18%

PerformanceDecision

MakingLogistic ParadigmScheduling and

Control

1. Introduction

6

It seemed that articles on supply chain were well distributed between the areas of TOC.

Authors discussed the topics quite uniformly, so the modern approach on TOC problems

seems to have changed from the past. Indeed, this is not true for other systems addressed

by TOC researches: for example, a great number of empirical cases on TOC production

systems were reported during the years, but their analysis with the principles of Thinking

Process is far more recent. This is coherent with the prospected shift advocated by (K. J.

Watson et al., 2007).

Summarize Papers: Articles referring to replenishment and distribution were read and

outlined below:

(Simatupang et al., 2004) studied how TOC replenishment positively affects the collaboration

between supplier and retailer in reducing the Bullwhip Effect. Contributions on how to manage

demand peaks and buffer levels were brought by (Ronen et al., 2001), while methods of

prioritization of multiple orders in supply chain adopting TOC were studied by (Tang & Cai,

2009).

Simulation regarding TOC are numerous in literature, but most of them are about

production systems and DBR (Walker, 2002). Works that addresses TOC replenishment in

distribution are infrequent and most of them are exploratory kind of studies. One of the first

was (K. Watson & Polito, 2003) with a comparison between TOC and DRP. They created

scenarios using a field research they conducted on multi-product multi-echelon network of a

US manufacturer. The four models dealt with the situation “AS IS” and three possible ways of

its improvement. Baseline model was a decentralized DRP with a lot for lot policy; network

was structured by six retailers and a manufacturer where seasonality and lost sales were

permitted. They simulated other models using DRP under centralization of warehouse and two

implementations of TOC, one aimed to service and one to inventory reduction. Results gave

evidences of the validity of TOC models, with a general improvement of costs and profit

without losing availability.

(Kaijun & Yuxia, 2010) proposed three different TOC policies comparing them with a (s,S,T)

Min-Max policy. First of all, they warned how the model of TOC replenishment was not

formalized in literature, despite being already adopted in various forms by real firms, and the

conflict in determining the replenishment frequency and quantity in central warehouse and

plant. They tried to enhance to most widespread variant in an environment with non-stationary

demand basing on previous researches of (Yuan et al., 2003). Their conclusions showed that

1. Introduction

7

customizing the model to the context provided the better performance and it can also outperform

the Min-Max policy.

A model inspired to the classic Beer Game is proposed by (Costas et al., 2015). It is a single

product linear supply chain composed by five actors. They compared an Order-Up-To policy

(r,S) with a variant of TOC replenishment based on an agent-based approach, a branch of

artificial intelligence.

(Jafarnejad et al., 2016) studied simulation models comparing JIT, TOC and Mixed Integer

Programming (MIP) on the optimization of orders across supply chain. They tried to maximize

profit by considering ABC logic and due dates of the orders, so that the final results were an

appropriate planning for an optimized allocation.

The problem of order frequency under capacity constraint in plant or warehouses were

addressed by (Wu et al., 2010). The problem consists in the dependency of frequency and lead

time of production from order quantity when these locations are capacity constrained; however,

in TOC replenishment these parameters are considered as given in order to determine the order

quantity. The consequence is that order quantity could not be produced or replenished entirely.

This problem does not exist when plant has enough capacity, so that replenishment frequency

can be as fast as possible. Authors proposed possible solutions with an algorithm for the

simultaneous determination of both parameters. The same authors suggested prolongations of

replenishment frequency in another paper (Wu et al., 2012) and how to moderate impact of the

increment in inventory of low frequency (Jiang et al., 2013). The problem had great attention

and other procedures based on swarm particle optimization, genetic algorithm (Jiang & Wu,

2013b) and optimization models (Jiang & Wu, 2013a) were developed refining the solution.

Later, some papers formalized the knowledge on TOC in distribution and downstream of

supply chains (Souza & Pires, 2010) and new approaches emerged. (Leng & Chen, 2012) using

a genetic algorithm to improve coordination and peak management between members of the

supply chain, while (Tabrizi et al., 2012) showed the advantages of information sharing in TOC

and how contract management can benefit both vendor and retailer. (Tsou, 2013) explored

strategies of detection of demand changes with a collaborative approach and how this can

improve the efficiency of Dynamic Buffer Management.

Recently some authors developed strategies mixed with TOC and hybrid methodologies;

for example, (Puche et al., 2016) studied the integration of TOC replenishment with practices

of collaboration proposed by Viable System Model. Most of these studies are supported by

specific industries: some empirical cases were presented by (Chang, Chang & Lei, 2014) in

1. Introduction

8

semiconductor and wafer production supply chain. They analysed the characteristics of demand

and products in order to find effective grouping strategies and apply Drum-Buffer-Rope and

TOC replenishment along the supply chain. (Chang, Chang & Huang, 2014) studied the

integration of demand management through forecast with the pull-demand approach of TOC in

the same industry. (Chang et al., 2015) simulated scenarios using this hybrid and comparing

them with statistical policies. (Lawler & Murgolo-Poore, 2011) studied an application of the

theory to supply chains of the gaming industry, while (Dos Santos & Alves, 2015) its

effectiveness in home appliances segment. Other empirical study like (Oglethorpe & Heron,

2013) used tools and concepts of TOC in studying UK food supply chain next to traditional

ones and finally proposed improvement in management of downstream supply chain with TOC

replenishment. Testing of TOC replenishment with online retailers and e-commerce were

investigate by (Sun & Leng, 2013).

1.2 - Gaps Encountered

The last step of the review procedure presents the findings of readings and analysis conducted

on articles:

STEP 3 – REPORTING

1) Incoherency on the meaning of some terms.

Studying TOC sources some discrepancies were found among the definitions adopted by

researchers. This was caused by an evolution of the topic itself, but also by some misleading

interpretations accepted for years. The most evident example is the meaning of TOC

performance measurements; indeed, Throughput, Operating Expenses and Investments are

those used with a wrong meaning more frequently. TOC terms cited in this work are all and

only those referenced by TOCICO dictionary (Cox III et al., 2012). These are the terms

officially accepted today by TOC practitioners in order to give uniformity to researches.

2) Low number of study on supply chain management and on replenishment

solutions.

From the starting point, total number of papers on TOC was not so high, about one thousand.

Of those excluded it was found that most of the literature on TOC is about production, project

management or organizational change. The first two topics are the initial core of Theory of

Constraints so they are well documented and historically they are the most researched. Even

now empirical cases of DBR are reported; it has been the most promising area of TOC for a

1. Introduction

9

long time. The same can be said about project management and methodology of Critical Chain.

The reason behind the development of so many articles on organizational change management

and strategy are exactly opposite. This is chronologically the last area investigated by TOC

researchers so most of the recent papers are dedicated to these topics.

Literature on supply chain management has not received much attention and this is clearly

visible in the low number of articles. Even if it has finally had an increasing visibility, the

research on some topics are really lacking. Distribution is one of them.

3) Excessive focus on initial parameters instead of demand change detection

Researchers focused their attention on how efficiently setting initial parameters of buffer

management in order to provide quicker start-up in real implementation. Papers on this subject

are largely available in literature, because researchers consider the standard method too

simplistic. By the way, all these criteria have a limited effect and only in the initial phase of

implementation, while autoregulation of DBM can provide more benefit on long term.

Researches should focus on implementing effective criteria to detect changes in demand

pattern.

Little literature on TOC in distribution was found, but this is probably linked to the low attention

of TOC in general towards supply chain management. Excluding papers and articles, only two

books report rigorous formulas of TOC replenishment and how it detects demand change. They

are slightly different: the first is similar to classic DBR in production (Cox III & Schleier, 2010),

the other is based on cumulative penetration (Schragenheim et al., 2009). Principles and theory

supporting them do not change, but the second approach seems to have better performances in

real applications. Nonetheless, most of the papers found in literature apply the first method,

probably because it is slightly simpler and similar to the classic DBR.

4) Lack of empirical cases and quantitative analysis.

Only few empirical cases and real application of TOC distribution management were reported

and well documented in literature. Most of the studies are not available or not accepted in

academic database and those existing regard strategic analysis of firms using Five Focusing

Steps or Thinking Processes.

A limited number of simulations was found. Findings on stability of this solution with

constraints like transportation or minimum batch are missing. Reorder point models with a fixed

order quantity were not found, despite they have been the most common simulations of DBR

in a production system for a long time.

1. Introduction

10

Comparison found in a multi-echelon network were conducted with strategies like DRP, Order-

up-To and Min-Max policies. A few simulations compared TOC with JIT, but in a context

highly integrated with production system and marginal attention on distribution network. All

simulations found considered a pattern of demand quite variable, even with demand peaks, but

rarely verifying the behaviour for a pretty stable demand rate. This is one of the main hypothesis

of models like EOQ and it is the pattern of demand where they reach optimal results. Though

EOQ may perform less efficiently with variable demand, it would be interesting verify that

DBM do not degrade its performance in a stable context.

1.3 - Research Questions

The following questions were formulated studying the gaps in literature. They are considered

interesting for an investigation about TOC with simulation tools and focus the aim of the thesis

towards a definite direction:

1) How does TOC perform in a distribution network compared to a Reorder Point

policy?

2) DBM has numerous settings that guide its functioning. Which parameters have

greater influence on performances?

3) Which constraints\variables\context provides more limitations to DBM

performance?

4) What are limits and drawbacks in TOC Pull Replenishment?

11

2. Taxonomy of

Replenishment

Strategies

The following framework has the aim to trace the principal variants of replenishment strategies.

A complete classification is really difficult due to the huge quantity of articles on this subject.

A considerable number of factors influences configurations of a distribution system and

strategies adopted. They have a trade-off with qualitative variables, which multiply the possible

results and complexity of a unique framework.

Replenishment logic affects profitability and goals, like improvement of service level,

minimization of operating costs or inventory investment. A proper strategy has to customize a

standard methodology in relation to context and adapt it to its objectives determining the

variables needed in order to fit the market. Here is presented a taxonomy of standard models

for inventory control and replenishment decisions, with some of the most known variety.

2.1.1 - Push and Pull

Although push and pull systems are assigned precise definitions by APICS (Blackstone Jr.,

2013), it is also notable that many variants exist. By definition:

Push: “a system for replenishing field warehouse inventories where replenishment

decision making is centralized”. In a push logic, inventory planning is responsibility of

a unique planner and replenishments are allocated to downstream locations; centralized

forecasts and allocations to downstream warehouses are typical of push systems.

Pull: “a system for replenishing field warehouse inventories where replenishment

decisions are made at the field warehouse itself”. In a pull logic, every facility maintains

control on local planning and place orders independently from manufacturers or

distributors; a decentralized ordering and demand-driven approach are more distinctive

of pull systems.

2. Taxonomy of Replenishment Strategies

12

In distribution systems, the dividing line between these logics is put where decision making

about replenishment takes place. Other implications of adopting a pull system consist in the

possibility of each facility to choose its own ordering technique and necessity to establish a

solid channel of communication with high quality information. TOC avoids push approach

because this model has a natural predisposition to keep extra stock as close as possible to

customers without a real and manifest demand.

The advantages of a push logic are risk reduction, provided by accumulating inventory at

POS, and economies of scale. Having control on all replenishments in supply chain enables

accurate planning and optimal reorder points. On the other hand, the large amount of stock

implies higher holding costs and obsolescence. The problem firms are more sensible to is the

low flexibility and lack of responsiveness. The pre-allocated inventory cannot cope effectively

with a sudden demand peak and forecasts can prevent this only partially (if correct).

In last decades an increasing number of firms is turning to pull models. Advantages of pull

systems come from a simpler planning and higher inventory turns. Every location is responsible

for its planning, with less efforts of planners at central warehouse. Only the needed quantities

are supplied, so generally overall cost of inventory is lower and stock turnover faster.

Conversely, this decentralized approach makes critics quality of communications and feedback.

A constant monitoring of performance and status is needed for a correct application of

replenishments. Local optimizations are a concrete risk if a correct performance measurement

system is not implemented, partially reducing potential benefits of the model. Pull requires the

quality of transmitted information to be improved while push is more permissive. In a push

strategy information really needed circulating in the network are a small amount and less

essential.

Generally, supply chains use both these types of models, avoiding the consequences of a

radical shift from a pure model. Push approach is useful and preferred in upstream locations

because of a better reliability of forecasts; pull is applied downstream in order to enable

postponement strategies and avoid big amount of inventory. Decoupling points are the

connection between a push upstream and pull downstream, working as interfaces. The

positioning of these points cannot proceed separately from the identification of push/pull

features required by the market. However, once they are in place, some of these characteristics

may be changed to match different requirements. Managerial decisions can change the

behaviour of the system and move decoupling points. A change of this entity requires also a


13

different strategic view of the system. In this context every supply chain has a mix of push and

pull processes in order to assure agility (Christopher & Towill, 2000).

Push and Pull concepts are applied by numerous techniques in different ways. They are

referred indistinctly to whole systems, policies or simple features of controlling. It is not trivial

to study networks or complex systems and to determine under which direction they are moving,

because their locations can be subject to different pressures.

Despite of where orders are issued in a network and the general classification provide by

definitions, there are methodologies and tools recognized as typical of a pull system more than

others; however, they do not exclude practices and tools of the opposite strategy in the same

system. A supply chain can be temporarily unbalanced towards one of these extremes if

circumstances call for it

(Pyke & Cohen, 1990) propose a partial framework for some common control systems in

order to resolve the ambiguity of terms “push” and “pull”. Their schema follows the definitions

of APICS, studying who has decisional authority, and determines how information flow

through the network. The analysis reveals that MRP and Kanban have features that are not

completely push or pull, though they are considered the quintessential examples of respective

systems. (Hopp & Spearman, 2004) study pull production systems and offer an empirical

alternative of the meaning of these terms. They highlight that an explicit limitation to WIP is

the only feature common to all pull systems and absent in push; also distribution system respects

this observation.

2.1.2 - Statistical Inventory Replenishment

A large variety of systems is treated in literature, each of them with its own specific problems

and a different degree of attention during past years. Numerous solutions were proposed,

implementing new philosophies, hypothesis or counterintuitive algorithms.

Commonly, classifications of replenishment rules are based on review frequency and order

quantity as the two decisions that answer questions like “when” and “how much” an order

should be issued. Other classifications with a higher level of detail were proposed by

(Aggarwal, 1974), (Hollier & Vrat, 1978), (Silver, 1981), (Prasad, 1994) considering also

inventory-related costs, environmental parameters and structure of the system.

Inventory reviewing frequency splits strategies in two broad categories:

- Continuous review: monitoring in every instant trigger points.

- Periodic review: with a fixed frequency of control.


14

Strategies are classified as hybrid when they mix characteristics from these monitoring method.

Orders size can be either fixed or variable; quantity is fixed when orders are in batch of size

(Q), while it is variable if it is adjusted to make inventory position meet a predetermined

inventory target level (S), generally called base-stock level.

This provides a first partition between policies with variable cycle/fixed order quantity and

fixed cycle/variable order quantity. Inventory position (IP) includes physical inventory actually

on hand, backorders to fulfil and orders from suppliers not arrived yet. It is defined as:

𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 = 𝑆𝑡𝑜𝑐𝑘 𝑜𝑛 ℎ𝑎𝑛𝑑 + 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑂𝑟𝑑𝑒𝑟𝑠 − 𝐵𝑎𝑐𝑘𝑜𝑟𝑑𝑒𝑟𝑠

The evaluation of the strategy to adopt is based on the limitation of trade-off between

ordering/reviewing and warehousing costs. Considering demand, we can see that a continuous

approach for low demand and a periodic review for high demand items is frequent. There are

also qualitative characteristics of the supply chain that influence this decision, for example

reliability of the suppliers, the difficulties of taking a complete inventory or the possibility of

order aggregation. A continuous review is more responsive to demand variation and reduces

the level of safety stock, while periodic review has an exposition equal to order frequency

interval. A periodic review opens to some risks but it is usually less expensive and involves less

efforts thanks to the discontinued approach, enabling also a detailed planning. However, today

the cost differences have been reduced progressively because of the new tools of information

technology and results of a continuous or periodic review are very similar for short review

period.

Given the choice between fix or variable, four basic policies are possible (Ross, 2015). The

adopted notation may vary from other literature:

Q = Fixed Order Quantity S = Base stock (MAX)

r = Review Frequency s (often indicated as R) = Order Point (MIN)

Order Quantity

Fix Variable

Review

Frequency

Periodic (r,Q) (r,S)

Continuous (s,Q)

also known as (R,Q) (s,S)

Table 4: Basic Replenishment Strategies


15

(R,Q) and (s,S) replenishment rules are classified under continuous review and are also called

Reorder Point (ROP) systems. (r,S) policies has a periodic review system, while generally (r,Q)

is of low interest because it is the most rigid. Their logic is described as follows:

(r,Q): a periodic review policy with a fixed order of size Q released every r period. Note

that only order size is fixed, not number of orders, so it is possible to release N orders

of size Q. This limitation usually is related to an EOQ calculation or a transportation

constraint, so it has a low flexibility.

(s,Q) or (R,Q): continuous review policy where N orders of size Q are released every

time IP is equal or less than a minimum quantity s. It often is adopted when supplier

requires ordering in batch, so it is also denoted as (s, nQ). Number of orders depends on

the minimum quantity of batch required so that IP is at least higher than s, but the

maximum value of inventory position is always limited at IP ≤ s + Q (Axsäter, 2015);

the Order Point (OP) is met exactly in s only in a case with constant demand and

continuous review.

(r,S): a periodic review policy commonly referred to as “Order-Up-to” or “Base Stock

Policy”. Every r periods an order is released so that IP once replenished is at least equal

to a maximum value S. Note that ordering in this policy is mandatory and it is

completely independent from actual inventory position.

(s,S): also called “Min-Max” policy. A variable order of size OQ = S – IP is released

every time inventory position is equal or less than a predetermined minimum value s in

order to restore the stock to the max level S. This policy is equivalent to (s,Q) when S

= s + Q. It has a variation called (S-1,S) when it releases order immediately after one

unit is taken.

This classification is the most widely adopted in literature, but reviewing method and triggers

are somehow overlapped. Reviewing method regulates the task of determining inventory

position and how much inventory is in stock; that decides how often inventory is monitored.

On the other hand, trigger outlines how orders are placed and it is not strictly dependent on

inventory position. Indeed, an order could be mandatory because of some contractual

constraints with supplier, so the trigger would be fix. Instead, triggers are variable if linked to

a minimum inventory level (s); when inventory position is equal or less than a certain reorder

point, then an order is placed.


16

In all the policies above, the instant of identification of actual stock level is the same of

when is possible to release an order. Realistically, it is not always viable; although information

technology can make it possible for most of the products, there are also items that for some

reason record delays between these two events. Seen the importance of Buffer Management for

TOC, it is interesting to add a further distinction between these two parameters and to split the

decisions in order to provide a better comparison. Wensing studies this type of classification

(Wensing, 2011) and identifies combinations of triggers and reviewing methods that do not fit

each others:

Frequency of inventory review (HOW OFTEN)

Size of the order (HOW MUCH)

Triggers for order release (WHEN)

Given this further differentiation, policies can express some of their variants more in detail:

This classification covers the four basic rules previously identified, but analyses also their

corresponding under a different review. Not all these eight policies are logically consistent,

only five of them are usually considered rational or economically viable (see the bold ones in

Table 5). As already said, policies (r,Q) and (t,r,Q) are non-adaptive and they are not

recommended in case of stochastic demand, which is the most common case in reality. The

policy (t,r,S) does not contemplate the possibility to place an order whenever it is necessary,

else the effort of reviewing continuously would be vain. It is possible that it will have to wait r

periods until the next order, unless order interval is set equal with reviewing period. This policy

is always treated with t = r in literature, so it is always seen as a periodic review and coinciding

with (r,S) of the precedent classification. Policies (t,s,S) and (t,s,Q) are periodic review variants

POLICY

MONITORING

( 0 = Continuous )

( t = Periodic )

TRIGGER

( r = Periods )

( s = Reorder Point )

QUANTITY

( Q = Fix size )

( S = Max Level )

(t, r, Q) T R Q

(r, Q) 0 R Q

(t, s, Q) t S Q

(s, Q) 0 S Q

(t, r, S) t R S

(r, S) 0 R S

(t, s, S) t S S

(s, S) 0 S S

Table 5: Ordering Policy (adapted from Wensing, 2011)


17

where evaluation of inventory is not continuous. This difference enables the coordination of

orders processes compared to the (s,S) and (R,Q).

Numerous variants of these policies have been studied in literature, and it has been noticed

that most of them have hybrid characteristics. It has been demonstrated that under simple

assumptions optimal policies exist in a single-echelon context. (Veinott, 1965) proved

optimality of (R,Q) policy in serial systems when there are no ordering costs and order quantity

is a multiple of Q. Also (s,S) policy is optimal for serial systems, as shown by (Iglehart, 1963)

and (Zheng, 1991). These results have been extended also to assembly systems thanks to

(Rosling, 1989), who proved that serial systems are only a subcategory of them when costs are

linear.

Till this point, only single-echelon systems have been considered. However, supply chains

are formed by the interaction of more actors and warehouses. Optimality of the precedent cases

is not maintained in every multi-echelon systems. Coordination covers a particular role and new

technologies assume a vital role to get clear information. Heuristic approaches are more

common for these systems, because of the great complication of the problem. Distribution

networks may have an arborescent structure with many downstream locations, differently from

serial and assembly systems of production which have at most one successor. In TOC, a similar

research is conducted with the help of VAT analysis, explained in the following paragraphs.

The necessity of a global point of view has led to a differentiation in how stock are viewed.

In ’60s, Clark introduced the distinction between installation stock and echelon stock (Clark &

Scarf, 2004). For a distribution system where typologies of items are the same at every level,

echelon stock is equal to the sum of installation stock at a certain level plus all those

downstream. Inventory position in an installation stock policy regards only local inventory, so

facility N releases an order to N+1 location without considering the whole amount of inventory

already in downstream supply chain. This kind of policy is always nested, linking each level to

the next one. Instead, an echelon stock policy reacts only to the final demand because it

considers the total amount of the downstream stock in inventory position calculation. A problem

to face using echelon stock policy is the number of information needed; although it has a global

point of view, it requires also a constant flow of information from downstream in addition to

local information on inventory position. On the contrary, they are minimal with installation

stock but local optimizations are more likely.


18

(Axsäter & Rosling, 1993) proved the following propositions related to (R,Q) multi-echelon

policies for serial systems:

1. “An installation stock reorder point policy can always be replaced by an equivalent

echelon stock reorder point policy”.

2. “An echelon stock reorder point policy which is nested can always be replaced by an

equivalent installation stock reorder point policy”.

This means that installation stock policy is a special case of an echelon stock policy for linear

and converging supply chain, similarly to the single-echelon case. The republished work of

(Clark & Scarf, 2004) provides results regarding optimal base-stock policies in serial multi-

echelon systems. They validate this in a finite horizon periodic problem, with unlimited

capacity, no setup cost and linear transportation cost. Later, this has been extended to infinite

horizon or presence of capacity limitation and even to assembly systems, but it is not possible

to state this optimality also for distribution systems. Other results about these systems with

batching orders were brought by (Chen, 2000b).

(Axsäter & Rosling, 1993) shows that optimality of echelon stock is not assured for distribution

system, contrary to cases of serial and assembly systems:

3. “S policies based on the echelon stock are equivalent to S policies based on the

installation stock for general systems”

An optimal approach is not found out in these situations. Base Stock policies are said to be

myopic, however they can reach good results even in this context (Kogan & Shnaiderman,

2011). Generally, a (R,Q) policy offers comparable results in these cases; this is true in

particular for (S-1,S) policy, which is a special case of a (R,Q).

A problem of installation stock policy in multi-echelon system is the “Forrester effect” or

“Bullwhip effect”. The functioning of the policy does not require other information than local

one, so communication could be neglected to a low level. Synchronization and collaboration

between stages of supply chain is one of the most effective way to avoid this backstroke of

installation stock (Ciancimino et al., 2012).

In multi-echelon systems, there are at least three methodologies of common use:

(R,Q) or (s,S) installation stock policy to control each facility, each of them with their

own reorder point and inventory position.


19

(R,Q) echelon stock policy, considering that calculation of inventory position is slightly

different and require more information.

Kanban policies; they are very similar to an installation stock (R,Q) policy where

backorders are not subtracted from inventory position.

A great variety of simulations is present in literature, each of them focusing on some elements

or introducing new decision variables. (Pérez & Geunes, 2014) considered a single-stage

inventory replenishment model that includes two delivery modes, one cheaper but less reliable

while the other one more expensive and really fast in case of emergency. (E. A. Silver, H.

Naseraldin,D.P.Bischak, 2009) studied an Order-up-To under periodic and continuous review

and presented an approach to determine reorder point and target value using customer fill rate.

A variation of the same model was discussed in (Silver et al., 2012), considering negative

binomial demand. (Handfield et al., 2009) presented a model considering the attitude of

decision maker toward the risk of stocking out during the replenishment period and use a

triangular fuzzy functions for modelling the uncertainty of factors. (Grewal et al., 2015) studied

a dynamic adjustment of decision variables with seasonal demand. They recognize the

advantages of these corrections, but do not link them to Theory of Constraints.

2.1.3 - Time-Phased Techniques: MRP and DRP

A different solution from statistical calculation is to apply a time-phased demand and supply

in a multi-echelon supply chain. (Whybark, 1975) proposed Distribution Requirements

Planning (DRP) as an extension of MRP, while (Stenger & Cavinato, 1979) formalized the

logic moving the same principles of MRP from production to distribution. Their relationship

is really tight because DRP feeds Master Production Schedule, which is itself an input to

MRP. DRP uses the same backward logic of MRP, but it can be applied under either push or

pull logic. Its pull functioning requires some input data:

Inventory Status: on-hand stock available and safety stock level.

Ordering Data: minimum lot size required for an efficient process of replenishment.

Distribution Network Design: required for addressing orders to the correct facilities

and determines lead times.

Bill of Distribution: product structures and dependencies of components undergo an

“implosion” of requirements, instead of an “explosion” of Bill of Materials (BOM) like

in MRP.


20

Output of the process are:

Planned Orders: quantity necessary in order to protect the minimum safety stock level

and cover requirements.

Planned Release Date: it determines when to transmit order to parent warehouses

anticipating required lead time.

Projection of Inventory Balance: stock level status considering hypothetical orders.

The DRP grid is time-phased by periods, so it is organized in time buckets. Entities of these

buckets are decisions of the planners, depending on lead times and aggregation, but they are

usually all of the same size. Separation between in transit and planned orders is not only visual,

but a distinction of real and active orders from planned ones.

Forecasts and gross requirements are elaborated locally in a pull implementation. Every echelon

compiles a DRP grid considering its own reorder points. Resultant orders are transmitted to

suppliers, triggering replenishment operations. On the other hand, a centralized DRP operates

with a push approach. Customer demand at every retailer is communicated to a central

supplying facility. Retailers do not generate local replenishment orders. Resupply planning is

elaborated by a single grid at a central structure. Total demand of all downstream locations is

aggregated before the elaboration of DRP. Forecasts and generation of replenishments are

defined jointly. Centralized DRP decides timing and quantities of replenishments of all

downstream locations. Also, it has control on allocation of resources, defining the most

appropriate supplier to push inventory towards dependent facilities.

Fig. 2: DRP in a multi-echelon supply chain


21

DRP and MRP grids are similar in functioning. They do not calculate inputs like lot size, safety

stock or frequency of replenishment under a predetermined integrated algorithm or a certain

policy. This means that their implementation can be complementary to an existing policy, but

it can also be independent from it, applying their calculations of these inputs rather than using

another method. For example, choice of a lot size can be made by using Economic Order

Quantity, Lot for Lot or the result of a policy.

A great drawback of MRP and DRP is the large computational effort in case of thousands

of items and complex structures. Nonetheless, their logic is simple and effective. Another well-

known problem is “nervousness” of MRP output even for small change in input. A centralized

DRP has this same problem related to instability of input forecast, instead of MPS. ”Freezing”

closest orders is a solution to avoid nervousness.

Contributions to this theme are brought by (Bookbinder & Heath, 1988), with a comparison

of five lot-sizing policies in a multi-level distribution network with stochastic demand. They

find that, contrary to MRP cases in production, DPR performances are greatly influenced by

lot-sizing policies. Within their simulations, they identify the best outcome in Silver-Meal

heuristic (Silver & Meal, 1973). (Martel, 2003) studies rolling planning horizon policies,

discussing the impact of expediting actions on DRP. A complete review on rolling planning is

developed by (Sahin et al., 2013). (Wang, 2009) propose an integration artificial intelligence

and DRP, examining the field of continuous review inventory model with the introduction of a

transformation of fuzzy number into a closed interval. An effective comparison between

DRP/MRP, Reorder Point policy and Kanban is provided (Suwanruji & Enns, 2006). They

simulate multi-echelon supply chain with stochastic demand considering both production and

distribution. Their results highlight that with a seasonal demand DRP/MRP perform best,

followed by Reorder point policies and Kanban. What is more interesting for this thesis, they

argue that performance ranking depends on capacity constraints without seasonality, so they

analyse it with queueing theory: in presence of a constraint, Kanban is the best and DRP/MRP

immediately follow; without evident capacity constraints, Reorder point is the top and

DRP/MRP is even better than Kanban. Similar comparison between MRP, Kanban and Reorder

Point policies is conducted by (Axsäter & Rosling, 1994). In particular, they demonstrate that

MRP is dominant over installation stock policy for general inventory system and it is equivalent

to a reorder point policy if replenishments are instantaneous. As already said for statistical

techniques, they argue that a mere classification of MRP and DRP under the name of push and

pull is unclear. They demonstrate that:


22

1. For a general inventory system, an MRP system can give the same control as any

installation stock reorder point system.

2. For serial and assembly systems, MRP can work as any echelon stock reorder point

system.

2.1.4 - Lean Philosophy in Distribution

Today the Lean approach has a large diffusion in numerous industries and business. Its origins

dates back to Japan of post Second World War and it has been largely influenced by this context

strongly constrained by resources. Principles of Toyota Production System (Ohno, 1988)

blended Ford’s mass production and Japanese culture and was recognized as a new approach.

TPS had a great success in manufacturing and Just-in-Time concept became popular among

western companies. Lean Thinking (Monden, 1998; Womack & Jones, 1996) is one of the

responsible for the shift from a push-based production to a pull-based approach. Philosophy of

JIT expanded and was applied on other enterprise areas, until it overtook company borders with

applications on supply chains. This evolution involved even environments completely different

from manufacturing, like service operations (Swank, 2003).

Lean Principles are the key elements of Lean

philosophy. It is visible the similarity of these

principles with Five Focusing Steps of TOC, even if

they focus on different aspects: TOC controls

constraints that limit throughput, while Lean

eliminates waste and variability in order to level the

flow. Both of them are customer oriented and pull-

based, but the way chosen to achieve this is opposite:

for example, Lean focuses on balancing; on the other

hand, TOC accepts imbalance if it can maximize

throughput.

Despite developments of the theory and the presence of an incredible number of cases of

study, (Anand & Kodali, 2008) note that theoretical concepts behind Lean Supply Chain could

be furtherly developed. Lean Distribution is a logical extension of Lean Supply chain and Lean

Logistics (Zylstra, 2005), so it is not a radically new concept and could benefit of those same

studies. A definition of Lean Distribution under Lean Thinking philosophy is “minimizing

waste in the downstream supply chain, while making the right product available to the end

Fig. 3: Five Lean Principles


23

customer at the right time and location” (Reichhart & Holweg, 2007). Unfortunately, this area

of Lean has less evidence in literature, while relationships with suppliers have a predominant

role and have been deeply investigated (MacDuffie, 1997).

Compared to other branches of Lean, authors have been interested in the Supply Chain

Management only lately, facing problems of responsiveness (Fisher et al., 1994; Fisher, 1997).

(Manzouri & Rahman, 2013) investigate how supply chain management theories adapt to lean

principles. (Reichhart & Holweg, 2007) argue that contributions of Lean focusing specifically

on distribution operations and applications to downstream are really scarce in literature. They

retrieve a possible cause in the conflict between lean principle of level scheduling (heijunka)

and the excessive variability of market and demand of final customers; inevitably, a lean

distribution system collides with buffering against demand volatility. More recently (González-

R et al., 2013) discuss the slow diffusion of JIT in downstream locations in pull-based supply

chains, but highlighting an increment of studies on this subject. They propose a methodology

for implementation of short-term control in a multi-echelon supply chain with a sequential-

iterative mechanism to optimize the single-card Kanban loops. An example of a recent study

on distribution and retail sector is (Daine et al., 2011). (Martínez Jurado & Moyano Fuentes,

2014) show empirical evidence that researchers have focused on analysing ‘upstream’ Lean

principles and practices, while little work has been done on analysing how they have been

applied ‘downstream’. Despite the lack of theoretical studies on this matter, numerous cases of

study have been reported of successful implementations of JIT in distribution. Some examples

are (Kiff, 2000) about automotive dealers and their customers, (Jaca, 2012) in distribution

centres and retail sector with insight on change management and (Lehtonen & Holmström,

1998) in paper industry.

(Olhager, 2002) analyses advantages of JIT in supply chain management and potential

benefit of balancing lead times between locations. He suggests that lead-time conformity in

every stage of supply chain is more important than equivalence between processing time in

order to achieve good lead-time performance. He supports the analysis of lead-time efficiency

as key measure of a good implementation of JIT in supply chains. However, a distribution

system has to manage extreme variability and it cannot work in efficient way without a certain

amount of inventory placed strategically along the network. This trade-off is faced by

(Christopher, 2000) and (Christopher & Towill, 2000) with the proposal of a shift from Lean

Supply Chain to an Agile Supply Chain, aimed to a better availability.

Themes linked to supply chain management are growing, particularly on green practices,

but most of them are focused on the relations between suppliers and the focal company.


24

For example, (Vachon & Klassen, 2006) study how green practices are related to supply chain

characteristics, making a distinction between suppliers and customers. Downstream integration

and extensions of collaborative paradigm to customers are investigated, but they highlight that

these practices are strong only on a strategic level and less effective on a tactical level. Thanks

to surveys and empirical evidence, they find out that most firms believe it is more productive

sharing and monitoring with suppliers on environmental measures, despite the growing

attention of customers on these topics.

Lean manages buffers in a manner sharply different from TOC. In a Lean system they are

placed between every node and replenished of the quantity required by downstream location;

they absorb demand variations in order to minimize fluctuations on the flow. In contrast, TOC

places consistent buffers only in strategic locations and it uses an additional regulation

mechanism of buffer size next to normal replenishment cycle.

Kanban cards are the most common technique to trigger inventory replenishment in a Just-

in-Time implementation. Many variations of the Kanban system are present in literature.

Originally, Toyota adopted a double-card Kanban system (Sugimori et al., 1977), but numerous

alternatives have been developed in order to fit a wide range of systems and surpass its

restrictions. Their peculiarities aim to better performance, maintaining Kanban logic;

development of new communication technologies opened to a progressive evolution of Kanban.

(Lage Junior & Godinho Filho, 2010) studied 32 typologies of Kanban, from the original

double-card Kanban to E-Kanban, without physical cards circulating.

Kanban policy operates in a similar manner to a (R,Q) policy (Axsater et al., 1999; Axsäter,

2015). If we consider a system with N containers / Kanban of size Q and one container serving

per time, then N-1 containers are always full. Actual inventory position will be equal to (N-

1)∙Q plus the remaining of container serving in that moment; a new order is triggered every

time a container is empty and its Kanban released. The behaviour of this simple case is the same

of a (R,Q) policy with R = (N-1)∙Q and container size identical to order size. The real difference

between the two models is that Kanban put an explicit limit also to the total number of

outstanding orders; no more orders are released when their number reaches N, that is the

maximum number of Kanban cards in the system.

Even base-stock policies have similarity with Kanban (Veatch & Wein, 1994). (S-1,S) is a

variation of a Min-Max policy with a continuous review process that releases an order of one

unit as another item is taken away. Ideally, Kanban is reduced to a single piece when Lean

achieves the objective of One-piece-flow processes. (S-1, S) policy operates in the same manner

when they are near this upper limit.

25

3. TOC Principles

and Paradigms

In the late ‘70s, Eliyahu M. Goldratt formulated first principles and basis of Theory of

Constraints (TOC); its development started with the introduction of a scheduling and control

software known as Optimized Production Technology (OPT), but only by ‘80s the overall

concept became known as TOC (Goldratt & Cox, 2004; Spencer & Cox III, 1995).

It started as a production philosophy but gradually expanded to every aspect of business: it

refined itself from production floor and logistical system for material flow Drum-Buffer-Rope

(DBR) till a comprehensive approach called Thinking Processes (TP), which can analyse

constraints in every division of a firm. Currently, these Thinking Processes are the most

advanced paradigm of TOC.

TOC has three major interrelated components (Boyd & Gupta, 2004; Inman et al., 2009;

Rahman, 1998): a philosophy that defines the production/logistics paradigm, which covers the

continuous improvement with Five Focusing Steps, VATI analysis, Drum-Buffer-Rope

scheduling system and Buffer Management control system; a methodology to deal with problem

solving and decision making, where Thinking Processes are the key tools in order to examine

methodically complex situations; a new performance measurement system, different from

traditional cost accounting, called Throughput Accounting.

Fig. 4: TOC Elements

3. TOC Principles and Paradigms

26

In literature are present numerous frameworks that facilitate comparison with other

methodologies of operational research and management science. Refer to the work of Davies,

Mabin and Balderstone (Davies et al., 2005) for a classification of TOC and its tools in the most

known frameworks and for further comparisons with other important philosophies.

Apart these development, TOC had great numbers of critics since its first appearance. (K. J.

Watson et al., 2007) identified the most relevant of them, highlighting how most part have been

resolved nowadays. Major points are:

Results not always optimal, but nonetheless feasible and immediately viable.

Ambiguity on some basic definitions.

Lack of methodology and structure in many studies.

This philosophy is not well-known and encountered wide difficulties in its diffusion. A brief

analysis of the problem is given by (Schragenheim, 2016):

Fig. 5: Current state of TOC


27

3.1 - TOC Glossary

3.1.1 - Constraints

TOC defines “constraint” everything that prevents a firm from achieving its goal and obtaining

higher performances. A basic assumption of TOC is that every system has at least one

constraint; otherwise, it conducts to the absurd that a system would be infinitely capable

(Goldratt & Fox, 1986).

There are two large categories of constraints, internal and external; indeed, internal ones can be

further defined:

Physical (internal): they are the physical capacity limit; every resource could be a

Capacity Constrained Resource (CCR) limiting the output, while raw materials, WIP

and any other goods necessary to process are Material Constraints (MC). Usually they

are very common on shop floor in form of production bottlenecks. Physical constraints

are the simplest to solve and elevate.

Policies (internal): they are rules and restraints that a firm puts to itself to limit wrong

or maverick behaviours and make its processes and procedures respected; they also

strongly affect a good decision making and most of the time they increase bureaucracy.

Market (external): the existing system is unable to cope with demand from the market

itself, so strong and deeper improvements are necessary. It can depend on a high level

of demand and too small capacity or bad buffer management.

This means that the widely known production bottlenecks are only a particular class of

constraints, while policies are more widespread and limiting in every organization.

3.1.2 - Buffers

They may be time, stock, capacity, space or money buffers and are strategically located to

protect the system from disruption (Cox III et al., 2012). Stock Buffers are used both in MTS

and MTO environments, while Time Buffers are specific of MTO context. In DBR they are

categorized as Constraint, Assembly and Shipping Buffers. Usually, Times Buffers are time in

advance that materials are released before they are planned to be processed. The characteristic

of TOC is that this type of buffer is not used to protect a planning or respect machine schedules

during the process, but to assure that the entire system is on time for a due date. More generally,

a Time Buffer is defined as a liberal estimate of the manufacturing lead time from one control


28

point to another, which can be a material release point, a CCR or a shipping dock. They are

“liberal estimation” because this implies that both manufacturing time and a reasonable safety

time are included. For example, in case of Shipping Buffers this means that usually they are not

larger than the quoted lead time for customer in MTO context (Schragenheim et al., 2009).

Three types of buffers are identified:

Constraint Buffer: liberal estimation of the manufacturing lead time from the release

of raw materials to the site of the CCR; this typology of buffer is present only if there is

an internal CCR to the process and protects the constraint from starvation.

Assembly Buffer: liberal estimation of the manufacturing lead time from the release of

raw materials to an assembly point where CCR parts and non-CCR parts are combined.

Its presence depends on routing and bill of material of the item, it could be unnecessary.

Shipping Buffer: liberal estimation of the manufacturing lead time from the CCR to

the completion of an order. It protects from any statistical fluctuation along the process.

Time Buffers cannot be directly related with the physical presence of stock on the shop floor.

Naturally there will be more orders in the process, but they are not assigned to a specific

location. This is why Time Buffer can be computed only between two control points. The real

value of these buffers depends on time they need to be processed and the overall level of

variability of the system.

Fig. 6: Types of buffer (adapted from Schragenheim & Dettmer, 2001)


29

3.2 - Logistics Paradigm

3.2.1 - Five Focusing Steps

The following are generally known as the “Five Focusing Steps” (Goldratt, 1990), or "Process

of On-Going Improvement" (POOGI):

1. Identify the system constraints.

2. Decide how to exploit the constraints.

3. Subordinate everything else to the constraints.

4. Elevate the constraints.

5. If in the previous steps a constraint has been broken return to step 1, but beware of

inertia.

The first step requires mapping processes,

identify the weakest links of the chain and

address improvements to these constraints. In

order to accomplish this, it is necessary to

understand the real purpose of our own

organization, the goal behind every action and

how to measure the impact they have on

performances. A constraint could be a resource

with high utilization or low capacity, one which

requires a too large investment or that whose modification has a large impact on the whole firm.

The second step studies actual situation, where internal resources are not often used

efficiently. The first attempt should not be to seek externally for improvements and new

resources by buying machines or hiring workers, but a better utilization of the system.

Nonetheless, focusing efforts on not critical parts of the system is ineffective; overall long-term

performances will not improve, because system output only depends on utilization of

constraints.

Step three is a remark on ineffectiveness of excessive interventions on non-constraints

elements; every effort has to be focus on enabling the full utilization of the constraint, else it

will go wasted or its effect reduced.

The fourth step aims to eliminate actual constraints; in doing this, system overcomes its

actual limit and constraint shifts to another component. Usually, this phase is considered only

if step two and three fail or they have too light impacts, because it introduces major changes to

Fig. 7: Five Focusing Steps cycle


30

the system. Contrary to common sense, TOC views constraints as positive because their

presence establish actual performance and elevate them is a source of opportunities (Rahman,

1998). Last step completes the loop guarding from inertia; this is a cyclic process where

changing is the norm, while stopping in a steady state prevents from further improvements.

3.2.2 - VAT Analysis

VAT Analysis studies the flowing of parts, materials and work through plants and supply chain.

This mapping technique permits a good level of synthesis, but it gives also an overview on the

whole system, providing a valid support in decisions of how to exploit the constraint and

subordinate non-constraints resources through the determination of system control points

(gating, convergent, divergent, constraints and shipping points). Its application should precede

DBR and Buffer Management implementation, avoiding occasional local optimization.

This approach recognises three types of basic configurations that can be mixed and

modified to describe systems. This categorization is based upon the nature of the dominant

material flows, products routings and bill of materials; it provides information on level of

variety at each stage and how much it explodes or reduces compared to the number of

components and assembly parts. Usually, graphical representations of flows are somehow

similar to V, A, T letters:

Recognizing the type of system and its workflow permits a better study of critical points at

different levels. Originally it developed for the study of plants and facility, afterwards its scope

was expanded to the entire Supply Chain networks. Lockamy explains the actions that this

framework suggests in implementation of DBR and Buffer Management referring to divergence

and convergence points (Lockamy, 2008):

Fig. 8: Network Typologies in VATI Analysis


31

In a V-network, shipping buffers at manufacturers level should protect from relevant orders

from distributors; the efficient sharing of information with distributors and development of

effective information technology to reduce shortages and mismatches is important. In a T-

network is more likely the “stealing” of products by distributors in order to fulfil orders from

their retailers, so buffers should be placed at distributor level. Cases of A-network require a

proper use of buffers, but also attention to delivery performance and correct mix from

manufacturers.

3.2.3 - Drum-Buffer-Rope

Traditional DBR is a finite-capacity scheduling and planning method to manage an internal

constraint in a MTO production context (Goldratt & Fox, 1986). It operates in pair with Buffer

Management, that is the respective control mechanism. Here its activity will be explained in a

MTO context, where its implementation was proposed first. Afterwards, its simplified version

S-DBR will be described and they will be enlarged to MTS contexts, more common in

distribution and suited to TOC replenishment solution.

DBR can be put into practice successfully when at least an internal constraint is active. Its

components are:

Drum: CCR resource that directly influences the Master Production Schedule, it sets

the pace for the entire system. When no CCR is active, market is the Drum and it is

merely the list of shipments due to customers.

Buffers: as said above, they are the protection against uncertainty, starvation and delays.

When a CCR is active, CCR Buffer is equal to the time required to safely process

materials upstream of the Drum, making sure that it is never starved for work. A Space

Types of Network

V A T

Nu

mb

er o

f… Suppliers Few or Singular Many Many

Manufacturers Few Many Few or singular

(per each supplier)

Distributors Many Few or singular Few or singular

(per each manufacturer)

Retailers Many Few or singular Many

Critical points DIVERGENCE

(Manufacturer Level)

CONVERGENCE

(Distributor Level)

DIVERGENCE

(Distributor Level)

Table 6: Networks configurations in VAT Analysis (adapted from Lockamy, 2008)


32

Buffer is required after Drum to prevent CCR from blocking because of downstream

problems.

Rope: control mechanism that limits the flow of material into the shop at the same rate

the CCR completes its work. Its tangible form is a Material Release Schedule that is

updated on pace variations of the Drum.

From these definitions it is clear that Drum is a particular constraint influencing the level of

output, hence entire system Throughput (see ”3.3 - Performance Measurement” paragraph).

Drum behaves as a single scheduling point in the system, determining how Rope releases

material and how it synchronizes the amount of WIP with the processing rate (Bicheno, 2004).

Drum workload is so important that can be stated that “an hour of work lost on this resource is

lost for the whole system” (Goldratt & Cox, 2004). Supplying it continuously assumes a

particular relevance and in order to maintain it operative Buffer Management should be a high

priority task. The scheduling of Drum in a MTO context is made establishing the amount of

work that CCR should process to meet customer orders in a certain time period.

As said, buffers are evaluated as additional time in MTO. A problematic task in DBR is

determination of appropriate buffer sizes. A general solution identifies two extremes to this

decision: nullify Time Buffer, considering a deterministic Production Lead Time equal to the

sum of processing times and setup times, or set it to half of the interval covered by

corresponding stock buffer adopted before DBR implementation. The latter one is likely a

maximum value for Time Buffer because generally it comes from an environment where

operations are decoupled by excessive stock buffers. That protection is granted by much more

inventory necessary and it emerges as plenty of time in the passage from stock-based-Buffers

to Time Buffers. Given these extremes, a recommended value is half the precedent buffer

translated in time.

Fig. 9: Traditional DBR (adapted from Schragenheim & Dettmer, 2001)


33

The Rope mechanism is a communication process that rules over buffers, releasing material

to the Drum. It prevents the uncontrolled growth of buffers because of full utilization of non-

constrained resources, at the same time it avoids starvation pulling towards Drum only

necessary material. This mechanism has the counterintuitive effect that a non-constrained

resource would be blocked if it had no requests of material from downstream buffer; this is

coherent with the concept of efficiency for TOC, which is not referred to full utilization of every

resource, but to full utilization of the system capacity. Material Release Schedule is created by

moving backwards the due date of orders. The “length” of the Rope is equal to the Time Buffer

and gating operations are synchronized with Drum, so it will release in advance only needed

materials.

3.2.4 - Buffer Management

As just said above, due to its importance, Buffer Management should be treated very carefully.

Buffers have to be placed in strategic points of the process, depending by material flow; VAT

analysis is a valid tool for this aim. Buffer management (BM) is an execution control system,

which purpose is to help management identifying critical situations, to correctly evaluate

impacts of major changes in demand on buffers and to monitor trade-off between lead time and

protection of constraint. Its four main functions are (Cox III et al., 2012):

Prioritize tasks/orders based on buffer penetration / consumption.

Signal when to expedite individual tasks/orders that are at risk.

Provide feedback to the planning process to consider changing certain parameters.

Identify prime causes of delay to focus ongoing improvement activity.

In a MTO production context, buffers are evaluated as Time Buffers with the purpose of making

them uniform for different items. The reason is that every order has its own size, products,

different routings and other kind of specific parameters. Buffer Management calculates Buffer

Fig. 10: Buffer Zonation


34

Status for each order and assigns them a priority. Their standard time of production and due

dates are known in MTO, so it is calculated as:

𝐵𝑢𝑓𝑓𝑒𝑟 𝑆𝑡𝑎𝑡𝑢𝑠 (%) =𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑇𝑖𝑚𝑒

𝑆𝑇𝐷 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐿𝑇× 100

Buffer Status gives a measure of Time Buffer available to finish the order. Another parameter

is employed in MTS, where orders have not defined any due date.

According to Buffer Status, orders with high values have less priority meaning they have not

used much of the time available yet. Conventionally, Buffer Status divides between three zones

with a colour assigned to each order as visual reference:

Green Orders (100% - 67%): they have plenty of time still available or they were

released in advance to increase CCR utilization. Do not need attention.

Yellow Orders (66% - 34%): require monitoring at their location. Though these are

expected and should be normal situations, a sudden disruption or delay could make them

red orders.

Red Orders (33% - 0%): buffer penetration is very deep and starving risk high. They

need to be immediately located because probably they need expediting in order to meet

the due date.

Available Time is the time which remains until the order is due. It decreases Buffer Status as

time goes and makes priorities varying with time. Instead, Buffer Status is independent from

order actual location in queue and size does not affect it because of percentage expression. This

relative form makes possible direct comparison between priorities of different orders.

Expediting is not always necessary. When Buffer Management detects an excessive buffer

“hole”, the corresponding orders need to be located and monitored. It must be highlighted that

information on Buffer Status only is not completely sufficient to determine a critical situation.

It naturally diminishes with time, but this does not mean that order is not being processed by

the system and it is not advancing. For example, it could happen that two orders are both red.

Buffer Status cannot distinguish them, being independent from order location. If one has just

begun its processing, then it is critical for sure. On the other hand, if it is finishing the last

production phases, then it is urgent but near completion. Probably this order will be completed

on time and it does not need expediting. Continuous monitoring of the process is helpful to

detect real critical situations and identify causes of the disruption, providing feedbacks

necessary to evaluate corrective actions.


35

Coloured tag orders give useful information about the adequacy of Production Lead Time.

An equilibrated amount of green, yellow and also red orders is necessary. Too much Green

Orders indicate a too large batching, while predominant Red Orders are signal of too small

batch. The system will be regulated by adapting batch size to contingency, meaning it is

possible that inventory will be increased under some circumstances. This reflect precisely the

subordination of everything else to the protection of CCR.

These general indications seem in contrast with the importance of Buffer Management, but

they are coherent with the main idea of TOC that few indicators avoid conflicts and

misinterpretations, so contexts with high complexity need clearer information.

3.3 - Performance Measurement

Throughput Accounting is an area of TOC that has been exposed to critics more than others.

Definitions of new performance measurements were given confusedly and usually they mixed

Traditional Accounting terminology with TOC metrics. This problem affected a large number

of the first articles, books and papers on TOC. Today this problem has been solved establishing

a unique dictionary for TOC (Cox III et al., 2012).

3.3.1 - Throughput Accounting

Increasing complexity triggers the necessity of new metrics and performance assessments. TOC

approach is to face complexity with even simpler metrics which permit to take decisions on

clear information, otherwise data overflow can paralyze the process. Other approaches try to

get the whole range of the problem. They enlarge the scope using large performance

dashboards. Indeed, their effectiveness depends on a good design phase and continuous

maintenance. Also skills of the readers influence their success; ability in interpreting qualitative

factors, besides quantitative ones, is not a given. Such a system usually does not focus on less

than ten measures and clean data are also quite difficult to obtain for some of them (Nørreklit,

2000).

The aim of TOC is to concentrate efforts on few simple measurements avoiding the

possibility of bad behaviours or opportunism, which can be inducted by misinterpretation or

contradictory metrics. “Throughput accounting” is proposed to provide a better explanation of

financial and operative aspects, because traditional accounting methods in decision making are


36

not considered effective with such a complexity. The basic set of operational measurements

includes (Bragg, 2007):

Throughput (T): “the rate at which the system generates money through sales”; output

which is produced and sold. Pieces not sold become inventory. In calculating

Throughput, TOC accounts the part of total variable costs (TVC) that depends from sold

products. The consequence is that generally throughput measures are higher than gross

margin from traditional cost accounting. In traditional cost accounting this measurement

is a contribution margin considering only totally avoidable costs; both approaches

suggest it for a better decision making in case of product-mix definition, acceptation of

extra-orders and make-or-buy decisions (Azzone et al., 2011). TOC proposes the use of

a “Throughput per unit of constraint time” in order to respect the usage of CCR and be

effective considering the configuration of the system.

Operating expenses (OE): “all the money the system spends in turning inventory into

throughput”. It includes company costs like overhead, semi-variable and not totally

avoidable costs (e.g. direct and indirect labour, supplies, MRO, scrap…), but also costs

incurred due the passing time (e.g. depreciation, carrying cost). Today is usual hiring

workforce with a contractual form that makes workers a fixed resource; they cannot be

hired and fired following market oscillation and even if a production line is blocked they

will be paid. Piecework is a rare case where direct labour is not accounted as operating

expense, but as a truly variable cost. Direct labour would not be considered unless

employees were paid only if an item is produced.

Inventory (or investment) (I): “all the money invested in things the system intends to

sell”. It includes every physical inventory intended to be sold; so finished products,

tools, WIP, buildings, capital equipment, furnishing, but also knowledge products like

patents and technology licenses if they are going to be sold. The term “investment” has

been adopted as synonymous with inventory to solve this misunderstanding.

These three measurements are defined in a very plain and simple way in order to be the most

understandable and less arguable possible. In TOC there are only three categories of cost: total

variable costs, investments/inventory and operating expense. Investments and Operating

Expenses are defined with reference to the destination of the costs: for example, a building is

an investment and its depreciation is an operating expense. Actually, definitions of I and OE

eliminate difficulties in accounting value added, which is not purposely assessed by TOC

(Goldratt & Cox, 2004). Generally, TOC does not distinct between direct and indirect labour


37

costs. They are all accounted as OE, given that also idle time is included. This fact suggests that

should be paid more attention on improving T, while addressing efforts on OE only as last

correction (Goldratt & Fox, 1986). The rationale is that gains in costs reduction (OE and I) have

upper limits and usually they are badly tolerated by firm itself. Coherently, practical

applications apply the maximization of sales/throughput with particular attention to marketing.

The following is a brief example that compares traditional full-absorption logic and

throughput logic. It considers for simplicity a manufacturing with no initial WIP, materials and

finished goods and a final stock of 5000 units after the production of 20000 units:

Basic measurements

Throughput T = Revenue - TVC

Operating Expenses OE

Inventory I

Global measurements

Cash Flow CF = T - OE ± ∆I

Net Profit NP = T - OE

ROI ROI = NP / I

Productivity Prod = T / OE

Inventory turns ITurn = T / I

Table 7: Common TOC Performance metrics

Table 8: Example of Throughput Accounting (adapted from Cox & Schleier, 2010)

Traditional Accounting Total Per Unit Details

Direct materials 40.000$ $ 2,00 (∗) 40000 units @ $1

Var. mfg. OH 20.000$ $ 1,00 (∗) 4000 machine hours @ $5

Direct labor 25.000$ $ 1,25 (∗) 2500 hours @ $10

Total Variable product cost 85.000$ $ 4,25 (∗) Based on 20,000 units producedFixed mfg. OH 80.000$ $ 4,00 (∗) 4000 machine hours @ $20 (∗∗) Based on 15,000 units soldTotal product cost 165.000$ $ 8,25

Var. selling and admin. 30.000$ $ 2,00 (∗∗)

Fixed selling and admin. 75.000$ $ 5,00 (∗∗)

Total costs incurred 270.000$ $ 15,25

Revenues / Price 300.000$ $ 20,00 (**) 15000 units @ $20

Revenues (15000 units @ $20) 300.000$ Revenues (15000 units @ $20) 300.000$

Beginning Finished Goods (0 units) -$ Beginning Finished Goods (0 units) -$

Direct materials 40.000$ Direct materials 40.000$

Direct labor (only if piecework) -$ Direct labor 25.000$

Variable mfg. overhead 20.000$ Variable mfg. overhead 20.000$

Var. Cost of goods manifactured (20000 units) 60.000$ Fixed mfg. overhead 80.000$

Ending Finished Goods (5000 units) (**) 15.000$ Total Cost of goods manifactured (20000 units) 165.000$

Costs of Goods Sold (15000 units) 45.000$ Ending Finished Goods (5000 units) (**) 41.250$

Variable sell. and admin. 30.000$ Costs of Goods Sold (15000 units) 123.750$

Total Variable Costs 75.000$ Gross Margin 176.250$

Throughput 225.000$ Variable sell. and admin. 30.000$

Fixed sell. and admin. 75.000$

Fixed mfg. overhead 80.000$ Total sell. and admin. Costs 105.000$

Labor (considered fixed, unless piecework) 25.000$ Net Operating Income 71.250$

Fixed sell. and admin. 75.000$

Total Fixed Costs 180.000$

Net Operating Income 45.000$

THROUGHPUT INCOME STATEMENT TRADITIONAL INCOME STATEMENT

Variable Costs Costs of Goods Sold

Fixed Costs


38

Throughput is calculated directly from TVC, while Operating Expenses are all items of cost

not included. Total Investments are increased by the number of finished goods not sold this

period ($15000). Total value can be retrieved from Balance Sheet as Total Assets less Current

Liabilities, free of adjustments, revaluations, allocations etc. This is similar to Net Working

Capital. By definition, it is the difference between current assets and current liabilities, but the

metric proposed is more comprehensive.

Conventional accounting uses full-absorption costing while Throughput Accounting adopts

a form of direct costing. It is not a new concept and it is present in every accounting textbook.

Direct costing has the advantage of a higher support in managerial decision, making a

distinction between fixed and variable production costs. The key difference between these

approaches is the treatment of inventories and cost of product. TOC solution is more

conservative regards to inventory variations and it does not allocate fixed costs of

manufacturing to products. Goods are not assets until they are sold. The difference in Net

Operating Income of the precedent example is due to a part of fixed manufacturing overhead

and direct labour costs accounted as not already sustained (respectively $4,00 and $1,25 for

5000 units unsold) and allocated to finished goods in inventory (Cox III & Schleier, 2010).

There are also some qualitative differences from direct costing. Product costs itself is a

virtual cost, because this category enables more alternative allocations to products. None of

them is supported by TOC. For the same reason, TOC considers labour costs mostly fixed.

Apart particular cases such as piecework, nowadays workers have always a minimum of paid

hours, even if they do not represent a physical constraint (Draman et al., 2002). The necessity

to split value added from idle time does not exist in common applications of TOC. The only

guideline about the price is that it should be greater than the sum of Investments per unit and

Operating Expense.

3.4 - Decision Making

3.4.1 - Thinking Processes

Thinking Processes are not part of this work, but they are worth to cite because of their implicit

presence in every application of TOC. They are a tool that helps the exploration and resolution

of cause-effect problems in change processes (Scheinkopf, 1999) and answer to three questions:

What to change?

What to change to?


39

How to make the change?

They are answered using some base concepts: cause-effect relations, necessary-sufficient

conditions and a set of constructions rules. They are expressed in form of cause-effect diagrams

establishing a structured approach which pushes to verbalize the contrast:

Current Reality Tree (CRT): it discovers actual problems and undesirable effects

(called UDE). While UDE are the effects, the aim of this tree is to find out their “root

causes”. Usually, a sufficiently complete tree will lead to at least one core problem,

cause of many UDE.

Evaporating Cloud (EC): it is a conflict resolution tool. It points to the unresolved

problems in current reality tree and tries to exploit a settlement to the situation.

Future Reality Tree (FRT): it is another cause-effect diagram which studies the effects

of the solution identified. Part or all UDE will be eliminated, but there is the possibility

that it will generate new UDE; the new problem is called “Negative branch reservation”

and it should be trimmed changing the original solution or adding another correction.

Prerequisite Tree (PRT): it is made by intermediate objectives that are necessary to

resolve UDE. It highlights conflicts and obstacles that can arise during the transition

from Current Reality Tree to Future Reality Tree. The output of this tree is a sequence

of objectives. It discloses which ones can be achieved independently or in parallel and

which are strictly subsequent to others. Sometimes these intermediate goals are

unfeasible, precluding the resolution.

Transition Tree (TRT): it guides the implementation, unlike Prerequisite Tree. This

tree analyses the action that should be taken. It is like a road map, while Prerequisite

Tree is focused only on results of actions. It helps to identify which actions are sufficient

to achieve the results and which one are only collateral.

The CRT, FRT and TRT are based on a sufficiency logic, while EC and PRT are based on

necessary logic. The validity of the sufficiency-based trees is tested by a set of rules called

“categories of legitimate reservation”, which proves the robustness of entities, relationships and

additional or insufficient causes


40

3.5 - TOC in Production

3.5.1 - Simplified DBR

DBR can be furtherly improved under some circumstances. From DBR to simplified DBR (S-

DBR) there is an inversion of the basic assumptions. DBR holds mandatory due dates for orders

and it can simply check if CCR schedule assures a margin of safety after it is generated. Instead,

Simplified DBR provides a method to estimate Safe Due Dates before a customer order is

issued.

Particular cases are possible in CCR identification while following the Five Focusing Steps.

One of them is to identify more active constraints or even market itself as a constraint. DBR

does not perform at its best in these situations, but with some modifications it can accomplish

even better results. The following planning method is generally accepted as a preferable

solution to DBR in MTO context.

Implementation and functioning are made easier by these developments, so it has been called

Simplified-DBR (S-DBR). Range of adoption is wider, but it is not a solution in all situations

because it has some unresolved limitations from DBR. In S-DBR there are two more underlying

assumptions than DBR (Schragenheim & Dettmer, 2001):

1. Market is always the constraint: even if an internal CCR were to emerge, it would be

considered avoidable. This means that market is always the Drum of the system.

2. A small change to the actual processing sequence at an internal constraint does not have

much impact on overall system performance.

The reason behind first assumption is the direct impact on future demand that a firm will suffer

if today it does not comply needs of its customers. The damage of lose a customer is not

acceptable compared to the additional cost of keeping capacity buffers. It is considered as a loss

in value of a long-term relationship. Whenever a new CCR becomes active there would be

strong routing problems in a normal DBR implementation. This is due to unwanted interactions

between the constraints. When this event occurs, it is complex to determine which CCR should

have priority in expediting orders. Conflicts between resources emerge, but S-DBR overcomes

this complication introducing a qualitative difference between constraints. Indeed, only market

is always a constraint so all internal CCR should be fully subordinated. Some additional

capacity is necessary in order to avoid multiple internal constraints, but subordination to market

avoids excessive monitoring and detailed scheduling, in favour of the only real critical point.


41

The absence of detailed CCR scheduling requires the second hypothesis. S-DBR does not

perform at its full capabilities with sequence-dependent setups. Routing and sequences impose

to BM more constrictions on priorities (Schragenheim et al., 2009). However, S-DBR would

be still applicable if flexibility were assured and difficulties would be lesser than using DBR.

Capacity management deserves a particular care in S-DBR and attention on load is stressed. In

S-DBR another monitoring tool is adopted alongside Buffer Management.

Simplified DBR provides planning only for short-term, not for medium or long-term.

Useful schedules and buffers are only those that protect market, so Shipping Buffer is the focal

point. This buffer is renamed Production Buffer and defined as a liberal estimate of the amount

of time required to reliably complete production of the work orders (Cox III et al., 2012). This

is the only relevant Time Buffer in order to promise reliable due dates to customer orders. The

Drum schedule simply corresponds to the list of orders, while other Constraints Buffers or CCR

schedule are unnecessary in S-DBR. The potentially critical resources should have some

additional capacity in order to cope with demand from the Drum/market and prevent the

activation of internal constraints. They will be held back from full utilization, in order to avoid

emerging of other CCR.

“Load Control” prevents this from happening and replaces detailed schedules of CCR.

Material Release and CCR schedules should be recalculated whenever a new order is issued in

traditional DBR. Three buffers do not grant flexibility and new schedules are not always

immediate. Planned Load simplifies the alerting system, so that impact of a new order is directly

visible. Rope is no longer tied to CCR schedule, but directly to market. Material and Order

Release are ineffective if this condition is managed by a rigid Time Buffer like in DBR. Also

dynamic corrections from BM are too slow.

Planned Load is a tool used to prevent any

emerging CCR and to quote reliable due

dates in advance. It is the sum of the derived

load on the CCR from all production orders

already released, but not yet processed by

CCR. It compares the required capacity of a

new order and the current derived load; if

load of the probable CCR exceeds a safe

limit, the order that is going to be added

Fig. 11: Planned Load


42

probably will be late. Adequate actions should be taken immediately. General advice is to

preserve replenishment time without exceeding 80% of full capacity.

BM cannot stop an order in advance, before it is released. It can only change its priority.

Instead, Planned Load avoids also quotation of unfeasible lead time. Horizon has to include all

orders issued by customers, but the interval to monitor with attention is roughly equal to the

standard lead time of the market. This instrument supplies less information than a finite-

capacity schedule, which can be more accurate and can warn about orders lateness during

processing. Indeed, the aim of Planned Load is to eliminate emerging CCR without time-

consuming recalculations. It needs only a fast comparison in order to highlight a critical issue,

like more sophisticated tools.

Estimation of Safe Due Dates to customers is a useful marketing capability of Planned Load

for production and even more for distribution. It guarantees more flexible plans and less

recalculations if a change happens. For simplicity, now we will assume that size of the order is

quite stable and Processing Time is really small compared to Queuing Time. The potential CCR

splits Production Buffer in two parts. Their size depends on how much time an order takes from

when it is released on shop floor until it reaches CCR and to end of the production cycle.

A Safe Due Date for the order is the sum of current Planned Load Date and Production Buffer

remaining after CCR. Consequently, Material Release date can be safely considered as current

Planned Load Date minus the Production Buffer before CCR, so that new order has a whole

Production Buffer available:

𝑆𝑎𝑓𝑒 𝐷𝑢𝑒 𝐷𝑎𝑡𝑒 = 𝑃𝑙𝑎𝑛𝑛𝑒𝑑 𝐿𝑜𝑎𝑑 𝐷𝑎𝑡𝑒 + 12⁄ ∙ 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐵𝑢𝑓𝑓𝑒𝑟(𝐴𝑓𝑡𝑒𝑟 𝐶𝐶𝑅)

𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑅𝑒𝑙𝑒𝑎𝑠𝑒 = 𝑃𝑙𝑎𝑛𝑛𝑒𝑑 𝐿𝑜𝑎𝑑 𝐷𝑎𝑡𝑒 − 12⁄ ∙ 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐵𝑢𝑓𝑓𝑒𝑟(𝐵𝑒𝑓𝑜𝑟𝑒 𝐶𝐶𝑅)

Fig. 12: Estimation of Safe Due Dates


43

Generally, half of the Production Buffer is a recommended value whatever the position of the

potential CCR. This avoids problems during the first identification of CCR. Anyway, it can be

refined after identification of CCR position. Moreover, this interval should be sufficient for BM

to correct priorities and eventually to give precedence to late orders. This formulation is

preferable to a Production Buffer time ahead of the due date, as it is calculated in DBR. This

value avoids idle time at CCR. If Safe Due Date is shorter than the Standard Lead Time quoted

by the market also for new orders, then no critical situations are present at the time of calculation

of Planned Load. This is not a guarantee that received orders will be on time, because probably

they need to be processed from other resources after CCR. A strong limitation of Planned Load

is that it assumes all precedent due dates as given.

BM is the only control once an order is released. Its functioning is not different from DBR,

but it is more critical. Priorities have to be well defined because production is more flexible

than in S-DBR.

Differences between the two models are visible and tangible. S-DBR requires only

Shipping Buffer to be maintained. Assembly and Constraint Buffers are unnecessary without a

CCR. Shop floor control is simplified using directly Master Production Schedule and not CCR

schedule. This translates in a shorter lead time and higher responsiveness.

Implementation and control of S-DBR are surely easier than DBR, too. A complex situation

does not require more detailed schedules, but a simpler approach. S-DBR performs well in this

cases, while traditional DBR is not suited due to the calculation of many schedules. The same

goes for a system with multiple CCR or worse cases where they move along the system.

Stability of schedules is a critical point in traditional DBR. New or deleted orders affect Master

Production Schedule, which implies a probable recalculation of various schedules. This

problem is minimized (but not eliminated) in S-DBR because it is based on Master Production

Schedule. Also CCR schedules are subordinated to it. Moreover, S-DBR can anticipate capacity

problems with Planned Load.

3.5.2 - Make-To-Availability

TOC describes Make-To-Availability (MTA) as Make-To-Stock with a marketing message. It

commits to the perfect availability of an item at a specific location (Cox III et al., 2012).

MTA is definitely a subset of MTS, but it can grant a competitive edge if the commitment to

availability is correctly communicated to customers. In order to accomplish this, TOC modifies

furtherly DBR model and applies it to a MTS context. MTA is not a substitute of MTS. Make-


44

to-stock is necessary in situations like producing in advance, levelling load before a demand

peak or when lead time requests by customer is shorter than Production Lead Time.

MTA is very near and similar to TOC Replenishment solution and can be considered its

precursor in a production environment. In a broad meaning also Vendor Managed Inventory

(VMI) is a type of MTA, where stock is at customer location.

Schragenheim highlights five points that guide the correct implementation of MTA

(Schragenheim et al., 2009):

1. Inventory and replenishment time are closely correlated.

2. Work-in-process supplements protection of availability.

3. Tomorrow will be similar to today.

4. Status of finished inventory dictates production floor priorities.

5. Stagnation is undesirable.

The first and second observations are just a reformulation of the “Little’s Law”. They point out

that if an increase in stock were to happen in order to maintain availability, then an equivalent

enlargement of Replenishment Time would be necessary. This operation of stock increment is

the corresponding of an elongation of Production Buffer in DBR if due dates are not met.

Buffers are evaluated using quantities instead of time, but they have the same purpose they had

in MTO. The meaning of Production Buffer is not changed; it is still a protection. The difference

is that in a context like MTA there are not explicit due dates, but commitment on availability.

It has to cope with the interval between the sale of an item and the arrival of the replenishment:

𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝐵𝑢𝑓𝑓𝑒𝑟 = 𝐹𝑖𝑛𝑖𝑠ℎ𝑒𝑑 𝐺𝑜𝑜𝑑𝑠 + 𝑊𝐼𝑃

WIP is a protection to availability, too. MTA imposes a limit to the value of Production Buffer,

given that both finished goods and what is in the pipeline assures availability. This limit is

called Target Level. Two simple methods are employed for the selection of initial Target

Levels: “Paranoia Factor” and “Reliable Replenishment Time”. The first method is simple, but

quite subjective and it is not safe in case of sequence-dependent setup; on the other hand, the

second approach is generally better, but it needs at least 6-12 months of data. These methods

are explained below, in paragraph dedicated to distribution.

The hypothesis of having day by day similar demand makes the system stable on the short

term, ensuring validity of Little’s Law. In absence of any evidence of changes, MTA will

continue to produce only what was consumed in the precedent period. Total quantity of stock


45

does not change significantly. When a product is consumed, a production order is generated. In

this manner replenishment quantities are known, making it a pull system. They do not change

the overall level of stock. TOC avoids every form of long-term forecast with this assumption

and adapts the model to short-term characteristics of DBR. MTA is not interested in what is

sold on average in a period, but in what might be sold if a peak were to happen in that period.

Forecasts should try to individuate the maximum value of sales, not a probable mean.

Differently from a push MTS, order quantities are not just an estimation of consumption during

a certain period. It is different also from MTO, where they are precisely defined by customer

orders.

Deviations from the Target Level of each item define orders priorities. Orders are released

without any due date in MTA, so BM cannot establish priorities looking at Time Buffers. Lack

of due dates limits performance measurements concerning time in MTS. In fact, availability is

a better indicator. A system similar to BM assigns a priority to each order that is going to be

released in production. MTA adopts a modified version of Buffer Status. Priorities depends on

the quantity of stock positioned downstream the order, between its position and Production

Buffer:

𝐵𝑢𝑓𝑓𝑒𝑟 𝑆𝑡𝑎𝑡𝑢𝑠(%) =𝑂𝑛 𝐻𝑎𝑛𝑑 + 𝑃𝑖𝑝𝑒𝑙𝑖𝑛𝑒

𝑇𝑎𝑟𝑔𝑒𝑡 𝐿𝑒𝑣𝑒𝑙× 100

The division in three coloured zones provides a visual reference about urgency even before

releasing orders. The number of orders entering in shop floor is tied to the current value of

Planned Load, like in S-DBR.

The last guideline supports a new element of control system for MTA. It is an improvement

to Buffer Management, called Dynamic Buffer Management (DBM): an intervention is

necessary to resize Target Levels when too much orders are constantly in red or green zone.

This allows the system to get a new balance with a gradual adaptation and to avoid disruption

in the short-term. This mechanism will be explained extensively later, because it is central for

TOC Replenishment.

Two important premises before the adoption of the MTA solution should be noted. The

first is that initial Target Level set with the methods explain above is only temporary. Those

values are proxies before MTA is stabilized. They will be monitored and adapted by DBM in

order to face actual demand. The second is that finished goods buffer should be full since the

initial implementation of MTA, otherwise DBM could cause problems with wrong adjustments.


46

The biggest risk for MTA is a growing market (Cox III & Schleier, 2010). In MTO is possible

to quote longer lead time in order to avoid an overwhelming demand, but MTA cannot do this.

It is in contrast with the principle of MTA itself. Capacity Management and the correct use of

Planned Load is a key element to maintain some idle capacity. Preserve a little more capacity

than what CCR is capable to handle is required.

Similar studies to this thesis have been already brought to the attention of researchers during

last decades, but most of them is concentrated on production side. These works are a start point,

providing ideas and methodology in a new field of research as distribution networks.

Comparisons of DBR with other scheduling systems are numerous. (Mabin & Gibson, 1998)

sustains the synergies with Linear Programming. (Chakravorty, 2001) examines performance

of DBR on shop floor comparing it with two workload control policies. Results highlight the

effectiveness of DBR if CCR is protected adequately with some extra capacity. (Steele et al.,

2005) perform a simulation supported by a real case of transition from MRP to DBR. Although

DBR surpasses MRP on the field, they modify MRP with a DBR-like policy that greatly

improves classic performance and argue the importance of a pull policy. A great number of

studies on Just-in-Time and DBR is available in literature, using any kind of simulation,

hypothesis and industry. (K. J. Watson & Patti, 2008) corroborates evidences that under the

same conditions JIT requires a greater quantity of inventory in order to achieve the same level

of output as DBR. They show a greater stability of DBR in presence of system variation.

A comprehensive review and a deeper analysis can be retrieved in (Gupta & Snyder, 2009).

They study literature that compares MRP, JIT and DBR. Their work argues the lack of empirical

and analytical articles and proposes a more methodical approach in future researches.

Nonetheless, they recognize that these researches bring interesting achievements that need to

be investigated with applications in real world. A new impulse to cases of study has been

launched following these suggestions. One of the most recent implementation is in (Darlington

et al., 2015), that show how TOC and DBR can perfectly complement Lean and Kanban.

47

4. TOC and Supply

Chain Management

Theory of Constraints philosophy aims to a systemic perspective in supply chain management.

Local optimizations are not effective, especially in contexts subject to high variability. Supply

chains are not always coordinated, so excess of stock and stockout are possible in the same

location as results of the “Forrester effect”.

4.1 - Supply Chain Replenishment System

The official TOCICO Dictionary (Cox III et al., 2012) defines TOC replenishment solution as:

Replenished stock usually is a quantity roughly equal to the actual sales of previous period. It

is based on the effective depletion of inventory. The most part of stock is held in a central

warehouse at the manufacturer. Only a small quantity is at regional warehouses (Schragenheim

et al., 2009). More frequent deliveries increase transportation cost, but this is more than

compensated by additional Throughput given by the high availability of items at retailers.

This definition is complied with six main decisions that help the shift from the former

replenishment system (Cox III & Schleier, 2010):

1) Aggregate stock at the highest level in the supply chain.

2) Determine stock buffer sizes for all chain locations based on demand, supply and

replenishment lead time.

3) Increase the frequency of replenishment.

4) Manage the flow of inventories using buffers and buffer penetration.

“A pull-distribution method that involves setting stock buffer sizes and then

monitoring and replenishing inventory within a supply chain based on the actual

consumption of the end user rather than a forecast. Each link in the supply chain

holds the maximum expected demand within the average replenishment time,

adjusted for the level of unreliability in replenishment time. Each link generally

receives what was shipped or sold, though this amount is adjusted up or down when

buffer management detects changes in the demand pattern”

4. TOC and Supply Chain Management

48

5) Use Dynamic Buffer Management (DBM).

6) Set manufacturing priorities according to urgency in stock buffers at Plant

Warehouse.

4.1.1 - Aggregate Stock

The principle behind TOC Supply Chain Replenishment System (SCRS) is the “Law of large

numbers”. Statistical fluctuations of supply and demand are sharply reduced aggregating stock

closest as possible to the source/plant. This is a result already known since the studies of Maister

on effects of stock centralisation and the so-called “Root Law” (Maister, 1976). Further

refinements on total cost reduction due to risk pooling were proposed by Eppen (Eppen, 1979).

The first step is identification of divergence points in supply chain. Tools like VAT analysis

can be useful to analyse the flow and find critical points where variety explodes or inventory is

excessive. Aggregation of inventory in these locations and establishing central warehouses

provides a notable reduction of variability. Plant Warehouses (PWH) and Central Warehouses

(CWH) replenish retailers keeping stock at acceptable levels. Indeed, the effect of this

aggregation is a reduction of stock level in the whole supply chain. These locations guarantee

the lowest level of inventory possible, as demonstrated. Their position is not always favourable

in order to meet Point of Sales (POS) requests. Other Regional Warehouses (RWH) would be

necessary closer to final consumption point if transportation time were excessive or lead times

were a strong qualifier to the market (Cox III & Schleier, 2010).

A change to distribution network is not required in a first implementation, SCRS can be adapted

to the actual structure. These are strategic considerations that are bound to Distribution Network

Design. They can be developed later, when also continuous improvement and other concepts

will be accepted.

4.1.2 - Determine Buffer

Buffers provide protection to Throughput. Their most important task is to secure it from every

disruption. Firstly, it is influenced by demand rate, supply and Replenishment Lead Time (RLT)

in a supply chain. Stock buffer size is connected directly to the level of safety desired and it

varies by item and location. As said for production, initial values of buffers size are not critical

decisions. They do not need a precise value to grant the success of implementation, because

DBM process will correct Target Level of each item driven by effective demand.


49

TOC suggests two methods to determine initial buffers size, also adopted in production (Cox

III & Schleier, 2010):

Paranoia Factor: it consists in multiplying average demand rate during a certain period

and the corresponding Replenishment Time for a “Paranoia Factor”, usually 1.5 or 2, in

order to avoid peak of sales or blockage. This factor reflects the anxiety of a possible

stockout and adds a certain quantity of stock as additional safety.

Reliable Replenishment Time: it is called “reliable” because an order has a really high

probability (90%-95%) of arriving to destination within this time. It is different from

standard replenishment time, which is calculated on average. Reliable Replenishment

Time is greater than average and more similar to a maximum value. This method needs

historical time series of sales to evaluate the maximum peaks in the last year.

A good base for initial target value can be obtained using “Paranoia Factor” method, but it is

only a suggested cautious criterion to avoid a more complicated procedure.

Although demand and supply can be affected by actions of the firm, these imply external

interactions with market and supplier. TOC prefers controlling replenishment frequency in

order to influence Replenishment lead time. Its definition is slightly different from the

traditional one, deeply affecting system behaviour. APICS defines RLT as the “total period of

time that elapses from the moment it is determined that a product should be reordered until the

product is back on the shelf available for use” (Blackstone Jr., 2013). This definition refers to

the moment when the perception of need emerges. An order is placed only when it reaches

some type of trigger point that depends on the policy adopted. It can be a reorder level, a

minimum of stock or also a certain review frequency. RLT(TOC) is quite different because it

starts when an item is sold or consumed, so it includes the time that replenishment policy

requires to identify the need. RLT(TOC) comprises four different lead times:

𝑅𝐿𝑇(𝑇𝑂𝐶) = 𝑂𝑟𝑑𝑒𝑟𝐿𝑇 + 𝑃𝑟𝑒𝑟𝑒𝑙𝑒𝑎𝑠𝑒𝐿𝑇 + 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝐿𝑇 + 𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛𝐿𝑇

Order LT: time from the consumption until a replenishment order is placed.

Prerelease LT: time between the acceptance of the order and its release to production.

Production LT: time from order release until it is ready for shipment or storing.

Transportation LT: time it takes to transport order to the point of sales/consumption.

An implementation of SCRS tries to reduce drastically replenishment lead time. The first

component of RLT is intrinsic in the replenishment model adopted. Monitoring frequencies and


50

order points decide responsiveness of the system. Part of this component is not considered

explicitly by the APICS definition and it contributes to extend the risky interval with a non-

perfect availability. Improvements of Order LT are limited by economies of scale and also by

technologies, although nowadays this is no more a problem considering the advancements in

IT.

Prerelease and Production LT components are bounded to manufacturing environment.

Prerelease LT ends when rope signal is received by DBR or S-DBR and it is pulled in the

productive cycle. The ideal situation would be an instantaneous release into shop floor, but in

order to avoid overload a prerelease time is necessary. This lead time depends on actual load,

number of orders in queue and urgency. In a push system an order might be released to

production with less regard to the work in process. Pull solutions and capacity control can

provide a better reduction of Production LT. They grant also a continuous flow, with benefit on

capacity and Prerelease LT. S-DBR and Buffer Management are TOC pull solutions, but these

results are achievable following different ways, like Lean Production and Kanban.

The very limit of RLT is Transportation LT. The natural limit of RLT will be the distance and

transportation time between locations once a replenishment model, sufficient capacity and an

effective production cycle are in place.

4.1.3 - Increase Replenishment Frequency

Replenishment frequency is directly linked to responsiveness of the system. TOC tries to

unbalance the trade-off between inventory and transportation cost with the adoption of a new

set of measurements and a strong attention on availability instead of cost. Increased frequency

provides some benefits, like less amount of safety stock and more flexibility on shipments. TOC

suggests to increase the number of transportations, even more deliveries per day if necessary.

Improvements in Transportation LT are the most difficult to achieve. TOC suggests to exploit

them using faster transports, even if their cost is considerably higher. The higher transportation

costs are justified if studied with the measurements of Throughput Accounting. Cost of an

additional shipment is for the most part a TVC if the vehicle is owned. This cost is less than

marginal increment obtainable in Throughput in almost any case. The rationale is that

Throughput increment fully covers these additional costs. Moreover, inventory costs decrease

at the consumption points because stock is smaller for a shorter lead time. TOC recommends to

invest in variety when this happens, given that availability is at good level. Order LT is heavily


51

reduced thanks to this replenishment model, because it delays an order for a shorter time before

the next shipment.

Batching orders to meet the right volume or benefit of big discounts are behaviour

discouraged by TOC. It suggests to create mixed orders so that all variety can be replenished

more frequently. Discounts from suppliers can be obtained in other way, like redefinition of

contracts regarding annual quantities, not single purchases.

4.1.4 - Manage Flow

Managing flow simply means to keep consistent buffers in every location of supply chain.

Number of buffers in a supply chain tends to explode with the enlargement of distribution

network. Different buffers for the same item are maintained in every location, even for slow-

moving articles. Small quantities scattered in various places are difficult to monitor and subject

to big oscillations. Aggregation at CWH achieves great results and makes controlling simpler.

SCRS uses Buffer Management as control mechanism. It monitors inventory level and

penetration with a measurement similar to Buffer Status, but considering buffer by unit of stock.

Buffer Status alone, as it is defined in

production, does not provide complete

information about stock in a distribution

network. Every local inventory is

associated to a specific Buffer Status

measurement. Hence, it provides only

partial data about a specific place and does

not consider supply chain as whole.

However, in supply chains there are stock along pipeline and some other in downstream

locations. A measure so location-dependent does not take in consideration precedent

replenishment actions and what is happening in other sites. Moreover, different buffers of a

same item are managed separately and not seen as connected.

This problem emerges when two or more orders from different locations are placed. Orders

priorities cannot be influenced only on Buffer Status at the stocking points. They could even

have a similar penetration or ignore a precedent replenishment. TOC defines Virtual Buffer

(VB) in order to coordinate items priorities in supply chain:

𝑉𝐵(%) =𝐴𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒𝑑 𝑆𝑡𝑜𝑐𝑘(𝑃𝐼𝑃𝐸𝐿𝐼𝑁𝐸 + 𝐿𝑂𝐶𝐴𝐿)

𝑇𝑎𝑟𝑔𝑒𝑡 𝐿𝑒𝑣𝑒𝑙(𝐿𝑂𝐶𝐴𝐿)× 100

Fig. 13: Buffer Status


52

It is calculated for every item, considering aggregated stock of what is on the pipeline, headed

to the next site, and stock already available locally. Stock varies with the closeness to the

customer, so a value of VB for an item is valid only until the next stocking point (Cox III &

Schleier, 2010). VB of an item is related to the local target level, but at the same time its urgency

reflects also precedent replenishment orders and all stock that is already on-hand.

Priorities are coordinated and changed dynamically with the same rules of buffer

management. They are defined by VB status in the next downstream location and not related to

the status of upstream inventory. They consider only what has been requested by point of sales.

Priorities of a same item are coordinated with the actual demand, providing full visibility on

the overall level of stock in the system.

Availability should take in account also stock in-transit, which is not yet arrived to destination.

It cannot be ignored as a form of protection. This measurement avoids replenishment

overreactions of the system. In fact, red zone will be reached locally in some sites, but VB can

monitor the overall level of stock. It highlights when this alarm needs interventions or if it has

been already replenished with a precedent order that is on the pipeline.

4.1.5 - Dynamic Buffer Management

TOC does not specify an optimal level for buffers and does not push necessarily towards an

inventory reduction. Dynamic Buffer Management (DBM) regulates buffers size on actual

demand and variations of the context. These adjustments are natural corrections of Buffer

Management mechanism, taking part in a finer tuning of its zones. Initial level of stock has an

impact only in early phase of a Buffer Management implementation, while the process is

warming up. When the process reaches a steady state, buffer size will be adjusted with DBM

algorithm as time goes. In a first time, buffers can be safely initialized on higher quantities in

order to avoid all disruptions. The above cited methods of Paranoia Factor and Reliable

Replenishment Time are of common use in SCRS applications. Their simplicity is suited for

the great number of buffers in a distribution network, proportional to number of items and

locations.

DBM modifies size of buffers under the condition of continuous high or low buffer

penetration. It works in reaction to actual level of inventory and has the advantage of being

responsive both to lowering and increasing in demand. When the irregular situation is stable for

a certain number of periods, it corrects the excess or shortage changing buffer size. DBM

identifies two categories of corrections:


53

“Too much Green” (TMG): if buffer penetration is in green zone or above for a long

period. Size of buffer is excessive and inventory are accumulating, so DBM contrasts

overstocking with a reduction of buffer Target Level.

“Too much Red” (TMR): opposite to green. Here the risk is stockout, not overstocking.

DBM increases buffer size in order to stabilize buffer penetration in yellow zone.

A rule of common sense for BM and distribution is “report daily and transport frequently”

(Schragenheim et al., 2009). Longer intervals in placing orders requires more inventory, so a

check period of at least twice the replenishment time is considered conservative in order to

avoid TMG. If buffer is persistently in green zone for such a long time, then a reduction of its

size is necessary.

The opposite intervention is activated when a buffer remains regularly in red zone.

Replenishment is considered urgent following the rules of Buffer Management and it needs to

expedite orders immediately. Differently from TMG, entity of penetration is a relevant

information. It signals how much critical is situation.

Two algorithms are documented for identification of TMR in literature. The first is similar to

the mechanism applied in production and it is simply triggered by the amount of time on-hand

inventory remains below red level (Cox III & Schleier, 2010). The other one is more recent and

it is believed more effective, though it requires some more information. An increment of size

is recommended only if the cumulative sum of units below red zone during an interval equal to

replenishment time reaches the size of red zone itself (Schragenheim et al., 2009).

Finally, DBM does not operate if a steady state is achieved with a buffer penetration

between green and yellow zone. In this case Buffer Management is working correctly and

demand is pretty stable. Intervention of DBM is not even necessary in such a situation because

Fig. 14: Dynamic Buffer Management


54

it could introduce an artificial disruption. Only minor corrections should be applied in order to

avoid stagnation. Further actions would be aimed at inventory reduction.

DBM adjusts stock level on contingency, so its corrections vary their intensity from item

to item. The suggested standard correction is a 33% increment/decrement of Target Level, but

it is influenced by importance of the product, strategic value of location where buffer is placed

and managerial decisions that support strong reactivity of DBM. These adjustments depend

entirely on the type of algorithm chosen. It can be a simple instruction as the suggested one or

taking in consideration other parameters. At the same manner, width of buffer zones is not an

unchangeable decision. DBM can adapt itself to greater complexity by working on simple rules

that control its functioning. However, these parameters can also be treated separately from

buffer size in more advanced applications. The key point is to study their penetrations

consistently with demand rate of the downstream sites.

A certain “cooling period” is required after every adjustment acted by DBM. The next

correction check should be delayed at least the time necessary for replenishment delivery to

reach the buffer, in order to stabilize it. Twice the replenishment time is the suggested value in

literature. It is more than conservative and avoids nervousness in adjustments.

This mechanism provides good results with gradual demand shifts, but it can introduce

some nervousness in case of sudden changes. DBM makes corrections very quickly and reacts

immediately to demand, but placement or removal of inventory are not instantaneous. This is

due to the natural adjustments of buffer level and to long transportation lead time. They cannot

be removed completely, but DBM can still be applied without worries if replenishment lead

time is not extremely long.

A similar problem is created by seasonality. If demand pattern assumes a steep and rapid

peak or a product is affected by strong seasonality, then DBM can support wrong or delayed

adjustments. In these cases, anticipation of demand is the only way to help a gradual shift

towards the peak. Seasonality could be caused by actions of the firm itself. Most common

explanations are promotions, an announced price adjustment or concentrated purchases at the

end of financial periods (for B2B firms). Nonetheless, if the reason of the disruptive events are

environmental variables, firms can only face them, being independent from their decisions.


55

4.1.6 - Set Manufacturing Priorities

Five Focusing Steps are valid also in supply chain. Walker discusses the importance of the

correct identification of which partner in a supply chain should be the drum (Walker, 2002).

Subordination of a not CCR in production has a respective in a distribution network.

The problem is a coherent assignment of priorities with both production and distribution.

Urgency of an order should not be different between manufacturing and transportation,

otherwise it cannot flow smoothly through the system. Supply chain has to assume a point of

view that regards all actors and does not encourage local efficiency. VB is extended to

production in order to accomplish this, synchronizing S-DBR with the rest of the network. The

most reliable point for setting this mechanism is at the Plant Warehouse, which generally is the

highest level of aggregation. In this point VB can react to every variation in supply chain and

has a complete view on all downstream locations. If priority of production order depends on

VB, then it is influenced by all other stock remaining in the whole network, until the last emitted

order of the same item. This mechanism is not limited to shop floor, but includes orders from

all downstream locations.

4.2 - Local Performance Measurement

TOC supports global measurements, but they do not provide an immediate push to improvement

on local level. The three main measures are shifted on operative level:

(Simatupang et al., 2004) described how these measures should be used to manage supply chain

network performance. Reliability and effectiveness in each link of supply chain can be assessed

with Throughput-value-days (TVD) and Inventory-value-days (IVD). Suppliers can use IDV to

evaluate stock at retailer, while retailer can assess reliability of supplier using TDD. These

measures have not a correspondence in reality. They cannot be compared with other real

quantity, but only between them. Their sole purpose is to launch a clear signal and trigger

attention of the controller.

Local

level

Throughput-value-days TVD

Inventory-value-days IVD

Local Operating Expenses LOE

Table 9: Local Performance Measures


56

(Schragenheim et al., 2009) reflected upon the usefulness of this measures when due date

performances are already close to 100%. A correct implementation of DBR leads to a marginal

role of these measures. Initial stages of model implementation or system with really high

variability can benefit of their value. However, it seems they are progressively made redundant.

(Gupta & Andersen, 2012) sustained the same conjecture and presented also a case where these

measurements push towards organizational changes. At the same time, they observed that

management seems to refuse this metrics because they have not a correspondence in reality.

Throughput-Value-Days

It is the potential Throughput generated by an order multiplied for the number of days late that

order accumulated before shipping. It is a measure of reliability of supply chain, an estimation

of the impact of late orders. The best achievement is to maintain this value to zero, because it

grows rapidly with every late order.

The assumption behind TVD is that customers have perception of damage and uncertainty the

more they wait. However, a correct value of this perception is not possible and every

measurement is unreliable. Taken this assumption, TOC tries to estimate the potential

improvement of the system. It shifts focus on supply chain itself. The losses suffered are safely

assumed higher than the value of throughput, so lost Throughput is seen as an opportunity cost.

The more an order has to wait before delivery, more it implies a deficiency of the system.

Inventory-Value-Days

IVD is computed as the sum of all current inventory on hand valued at the original purchase

price multiplied for the number of days since the inventory was received and it remains unsold.

It is a measure of effectiveness. Inventory should be set to the minimum required level in order

to maintain TVD at an acceptable level, ideally near zero. A growth of IVD value is sign of a

push behaviour and an accumulation of inventory not required. This metric is proven to be

effective at retailers and in levels of supply chain in direct contact with the market.

Local Operating Expense

It is equal to amount of operating expense that is directly under control of the local manager. It

is the least relevant between the three. Its purpose is to provide a simple measurement of

variations between real and planned expenses.

57

5. Simulations of

Replenishment

Models and simulated scenarios are discussed in this chapter. Two models were developed and

tested under various conditions, influenced by environmental variables and policy of the firm.

They were studied under different value of parameters in order to establish the robustness of

results. Validity of the analysis was supported by statistical tools.

5.1 - Features of the Model

5.1.1 - Structure of Network

Modelled supply chain is a distribution network with a divergent structure. Three retailers

(RET) are replenished by a central warehouse (CW), which is supplied by a plant (PL).

Plant has infinite capacity; in this manner limits of production do not restrain replenishments.

Stocking points are placed at every retailer and at central warehouse.

Retailers are identical and sell the same three products (P1, P2, P3) to their customers. Demand

is aggregated on daily basis to simplify the model; however, this does not change the nature of

the continuous review policy and how orders are placed. Shipments move between locations

and transport products to points of sale. These direct deliveries can load different products at

the same time. Replenishment lead time are deterministic.

Fig. 15: Network Model

5. Simulations of Replenishment

58

5.1.2 - Assumptions and Variables

Demand Generation

Simulations are conducted under stationary demand with low and high variability and then with

seasonality. The process of demand generation is slightly different.

Formula is based on that from (Chen, 2000a) and (Lee, 2000), but modified in order to introduce

a certain degree of instability. Original formula was:

𝐷𝑡 = 𝑘 + 𝜌 ∗ 𝐷𝑡−1 + 𝜀

𝐷𝑡 = Demand in period t

𝑘 = Not-negative constant

𝜌 = Correlation factor

𝜀 = White noise, Normal distribution N(0,1)

Demand generated by this formula is stable after a warm-up period. For great value of K, it is

almost flat and white noise is strongly reduced. Simulation of a greater variability is introduced

by using a Normal distribution with 𝜎2 ≠ 1 for the generation of white noise.

Without losing generality, it is modelled as:

𝐷𝑡 = 𝑚𝑎𝑥(𝑁(𝑘, 𝜎2) + 𝜌 ∗ 𝐷𝑡−1; 0)

This is nearly equivalent to the precedent for 𝜎2 = 1. It requires less calculation to the simulator

and, if necessary, can introduce a higher level of variability when it normally would reach

steady state. Also, high values of K do not limit variability and it oscillates around a certain

value at steady state.

Seasonality is introduced using a multiplicative component. Correlation is set to 0 in order

to avoid divergence and parameters of Normal is set with the values of steady state. It gradually

grows so that demand is two times the original value when it reaches its peak. Products do not

have peak at the same time, they are equally distributed along the year.

All simulations generate the same demand values thanks to the implementation of identical

seed generators in ARENA. This way, results are completely independent from random value,

though randomly generated.

𝑆1(𝑡) =1

2∗ sin (

2𝜋

300∗ 𝑡 +

𝜋

2) + 1.5

𝑆2(𝑡) =1

2∗ 𝑠𝑖𝑛 (

2𝜋

300∗ 𝑡 −

𝜋

6) + 1.5

𝑆3(𝑡) =1

2∗ 𝑠𝑖𝑛 (

2𝜋

300∗ 𝑡 −

5𝜋

6) + 1.5

NB: 300 days = 1 Year


59

Stockout and Backorder

Stockout are recorded each time retailers or CW cannot meet demand. At retailers, every order

not entirely satisfied is recorded as a stockout. Available pieces are sold while the rest of the

order is considered lost. In this manner retailers cannot have backorders.

Indeed, backorders are allowed at Central Warehouse: available part of the order is delivered,

while the remaining is put in a queue until stock is replenished from plant. Stockout is recorded

in any case.

Ordering Costs

Demand is aggregated daily, so every day only one order for each product can be placed. Costs

under this category are:

- Costs of preparation and emission

- Administration costs

- Costs of receiving and control

- Transportation costs

The first three costs are considered as an aggregate in these models. Personnel in charge of

receiving and controlling goods at arrival of replenishments is not saturated, so accounting of

this cost is done for every order emission. Orders are placed independently for each product, so

a logic of joint replenishments optimization is not implemented.

Transportation costs are treated separately, paying a fee for every truck sent from supplier or

adopting a pay-per-use tariff.

Holding Costs

Typical components of this cost are listed here. Not all of them are considered in these models:

- Capital costs: interests on working capital or opportunity cost of the money

invested in the inventory.

- Storage costs: building and facility maintenance.

- Inventory Services costs: IT, personnel and physical handling of inventory,

Insurance and Taxes.

- Inventory Risk costs: damage, shrinkage, administrative errors, theft.

By hypothesis, they are set at 30 % for retailers and at 20% for central warehouse on annualized

basis (Creazza et al., 2010). Studies have reported that generally 5% - 15% are capital costs,

while the rest is split between the others (Richardson, 1995).

Products are considered not perishable, damageable or subject to theft; otherwise, inventory

risk is one of the most relevant cost in retail industry.


60

Products

Products have a final price addressed to customers and their value increases while flowing down

the supply chain. They are assigned a cost of production at plant, which is considered equal to

purchase cost for warehouse. CW can sell/transfer goods to retailers adding a mark-up to the

purchase cost. This is dependent on various factors in real world; for example, postponement

of value added operations can take place in these locations or an external distributor owns

warehouse. By default, CW does not apply any mark-up in the following models. Products

belong to the same family of goods, so they can be considered three variants. Their final prices

are identical, but purchase costs are different from each other. This means that mark-up and

profitability are different, so retailers can decide to prioritize replenishment of one type over

another.

Purchase cost Price to customer

P1 50 € 100 €

P2 60 € 100 €

P3 75 € 100 €

Transportation

Trucks travel between warehouse and retailers and from plant to warehouse. There are no limits

to the number of trucks, but they have a limited capacity. In particular, only two sizes of truck

are allowed in these simulations. Mixed deliveries are allowed, so every item is assigned a

coefficient of occupation, making possible to calculate load value and compare goods:

Max

Capacity [unit]

Max

Capacity [coef]

Lead

Time [days]

R1 400 4000 2

R2 400 4000 2

R3 400 4000 2

CW 700 7000 5

Coefficient

[coef/unit]

P1 10

P2 10

P3 10

Aiming to availability, it is reasonable to assume that number of vehicles does not represent a

constraint to deliveries. A quantity can be delayed waiting for a minimum saturation of the truck

or backordered due to stockout, but outsourcing of transportation service to an external carrier

is also a possibility. Renting a truck or using a groupage service have different costs. Tariffs of

these services are decisional variables of the models.


61

Loading Priorities

Mixed deliveries need a set of rules to define priorities between orders. Though capacity limit

of trucks can be overcome with multiple deliveries, goods are loaded with different priorities.

Deliveries with low priority or a low saturation can be avoided, but it is necessary a policy to

determine their status. Common policies consider either availability or profitability; DBM uses

a policy integrated with the rest of the methodology and based on Buffer Status.

All simulations are conducted aiming to full availability. In presence of order batching and

minimum saturation also mechanisms prioritizing the most profitable items are implemented.

Minimum Batch

Every product has a minimum order quantity to meet. This is an important limitation to the

effectiveness of replenishment policies if it is a constraint imposed by a supplier. ROP models

do not consider such a situation in these simulations, setting minimum order equal to EOQ.

Instead, this can be a policy constraint that greatly affects DBM, because order quantity is

supposed to adapt itself to demand. This is far from being an optimal reorder, but some batching

can improve cost performance of DBM without compromising it. By default, batch is set to 1

in the following DBM models, eliminating this effect.

Minimum Saturation

The same logic is applied to deliveries. Orders are loaded on one or more trucks; if an order

exceeds capacity limit of the vehicle, then a second truck is loaded. Naturally this imply to start

two deliveries and so an extra cost. Setting a minimum saturation partially avoids this situation,

stopping the second vehicle if it does not meet a requisite. A minimum saturation of truck

capacity has to be meet in order to start journey of a vehicle, otherwise the part of order

exceeding is backordered and has to wait until a sufficient load.

In this manner, the number of deliveries is reduced and a small cost optimization is done. An

internal policy can impose this limitation in real world, aiming to increase saturation of

deliveries.

5.1.3 - Recorded Parameters

Every replication records the same indexes for each product, both at retailers and CW. They are

collected in form of matrix 3x4 for simplicity, where the meaning of the first number is type of

goods (P1, P2, P3) and the other stays for the location (R1, R2, R3, CW): for example,

#Stockout(2,4) is the index for number of stockout of P2 at CW. The complete list of indicators:


62

Total Demand Sum of units requested by customers

CumQ_Sold Sum of units sold to customers

NB: for CW, sum of units available

CumQ_PartialSold Sum of units sold to customers, when a stockout happened

NB: for CW, sum of units available during stockout

#Stockout Number of stockout

CumQ_Stockout Sum of units lost, not sold

#Reorder Number of reorders done

CumQ_Reorder Sum of units reordered

CumQ_Loaded Sum of units sent from supplier

Pipeline Stock (f) Actual units in pipeline

#Replenishment Number of replenishments completed

CumQ_Replenishment Sum units received and replenished

CumQ_WAY Sum of inventory in pipeline at the end of every period

CumQ_INV Sum of inventory in stock at the end of every period

OnHand Stock (f) Actual units in stock

Time_Reorder Mean time between consecutive reorders

Service Level [orders] % of orders without stockout over those received

Service Level [quantity] % of units sold over total demand received

Table 10: Recorded Parameters

It is important to know the behaviour of ARENA during warm-up period; in fact, no parameter

is recorded during this amount of time.

5.1.4 - Formulas of Performances

Scenarios are evaluated on Total Cost of network, Total Profit and achieved Service Levels.

Performances are calculated with different levels of aggregation, like single products, single

location and whole network. Replications are conducted on more years, so performances are

calculated on the whole length of simulation and then annualized.

Total Cost of Network

Components of this indicator are calculated following these formulas:

(NB: 300 days = 1 year)

Revenue 𝑃𝑟𝑖𝑐𝑒𝑆𝑒𝑙𝑙 ∗ (𝐶𝑢𝑚𝑄𝑆𝑜𝑙𝑑 + 𝐶𝑢𝑚𝑄𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑆𝑜𝑙𝑑)

Value of Sold 𝑃𝑟𝑖𝑐𝑒𝐵𝑢𝑦 ∗ (𝐶𝑢𝑚𝑄𝑆𝑜𝑙𝑑 + 𝐶𝑢𝑚𝑄𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑆𝑜𝑙𝑑)

Carrying Cost (𝐶𝑢𝑚𝑄𝐼𝑁𝑉

300) ∗ 𝑃𝑟𝑖𝑐𝑒𝐵𝑢𝑦 ∗ (%𝐶𝑜𝑠𝑡𝐶𝑎𝑝𝑖𝑡𝑎𝑙 + %𝐶𝑜𝑠𝑡𝑆𝑡𝑜𝑟𝑎𝑔𝑒,𝑒𝑡𝑐)

Pipeline Cost (𝐶𝑢𝑚𝑄𝑊𝐴𝑌

300) ∗ 𝑃𝑟𝑖𝑐𝑒𝐵𝑢𝑦 ∗ %𝐶𝑜𝑠𝑡𝐶𝑎𝑝𝑖𝑡𝑎𝑙

Ordering Cost #𝑅𝑒𝑜𝑟𝑑𝑒𝑟 ∗ 𝐶𝑜𝑠𝑡𝐴𝑑𝑚𝑖𝑛,𝐶𝑜𝑛𝑡𝑟𝑜𝑙

Travel Cost #𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡 ∗ 𝐶𝑜𝑠𝑡𝑇𝑟𝑎𝑣𝑒𝑙

Table 11: Formulas


63

Other two components are considered, but not included by defaults:

Pay-per-Use Cost 𝐶𝑢𝑚𝑄𝐿𝑜𝑎𝑑𝑒𝑑 ∗ 𝐶𝑜𝑒𝑓𝑈𝑛𝑖𝑡 ∗ 𝐶𝑜𝑠𝑡𝑃𝑎𝑦𝑈𝑠𝑒

Stockout Penalties 𝐶𝑢𝑚𝑄𝑆𝑡𝑜𝑐𝑘𝑜𝑢𝑡 ∗ 𝐶𝑜𝑠𝑡𝑃𝑒𝑛𝑎𝑙𝑡𝑦

Network Profit

It considers revenues of all products sold to final customer at retailers:

𝑇𝑜𝑡𝑎𝑙𝑃𝑟𝑜𝑓𝑖𝑡𝑁𝑒𝑡𝑤𝑜𝑟𝑘 = (∑ 𝑅𝑒𝑣𝑒𝑛𝑢𝑒𝑅𝑒𝑡,𝑃𝑟𝑜𝑑

) − 𝑇𝑜𝑡𝑎𝑙𝐶𝑜𝑠𝑡𝑁𝑒𝑡𝑤𝑜𝑟𝑘

Service Level

As seen from the indexes, there are two types of service performances. They evaluate units sold

and orders without stockout, which at retailer level is equivalent to the percentage of days

without stockout or backorder due to the construction criteria of the model (LREP is replication

length, WarmUp is time excluded from recording). Even though the overall evaluation is given

by performance of the network, measurements are calculated at different levels:

(i = product)

(j = location) Service [Order] Service [Quantity]

Product 𝑆𝑂𝑖𝑗 =(𝐿𝑅𝐸𝑃 − 𝑊𝑎𝑟𝑚𝑈𝑝) − #𝑆𝑡𝑜𝑐𝑘𝑜𝑢𝑡𝑖,𝑗

(𝐿𝑅𝐸𝑃 − 𝑊𝑎𝑟𝑚𝑈𝑝) 𝑆𝑄𝑖𝑗 =

(𝐶𝑢𝑚𝑄𝑆𝑜𝑙𝑑 + 𝐶𝑢𝑚𝑄𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝑆𝑜𝑙𝑑)𝑖,𝑗

𝑇𝑜𝑡𝑎𝑙𝐷𝑒𝑚𝑎𝑛𝑑𝑖,𝑗

Retailer (j=1,2,3) 𝑆𝑂𝑗 =

∑ 𝑆𝑂𝑖𝑗3𝑖

3 𝑆𝑄𝑗 =

∑ 𝑆𝑄𝑖𝑗3𝑖

3

CW (j=4)

𝑆𝑂4 =∑ #𝑅𝑒𝑜𝑟𝑑𝑒𝑟𝑖,123𝑖𝑗 − ∑ #𝑆𝑡𝑜𝑐𝑘𝑜𝑢𝑡𝑖,4𝑖

∑ #𝑅𝑒𝑜𝑟𝑑𝑒𝑟𝑖,123𝑖𝑗 𝑆𝑄4 =

∑ (𝐶𝑢𝑚𝑄𝐴𝑣𝑎𝑖𝑙 + 𝐶𝑢𝑚𝑄𝑃𝑎𝑟𝑡𝑖𝑎𝑙𝐴𝑣𝑎𝑖𝑙)𝑖,4𝑖

∑ 𝑇𝑜𝑡𝑎𝑙𝐷𝑒𝑚𝑎𝑛𝑑𝑖,4𝑖

Network 𝑆𝑂𝑇𝑜𝑡 =∑ 𝑆𝑂𝑗

3𝑗

3 𝑆𝑄𝑇𝑜𝑡 =

∑ 𝑆𝑄𝑗3𝑗

3

5.2 - Modelled Policies

Dynamic Buffer Management

One of the assumption on which is based DBM is that demand oscillation between two periods

are always limited. Thus, minimum requisite of DBM is the capacity to cope with the maximum

variation in short term and gradually adapt itself.

The first goal is achieved with normal replenishment cycle: every period an order roughly equal

to actual demand is emitted. It is calculated as the difference required to reach Target Buffer

considering inventory in stock, on the pipeline and backorders.


64

Adjustment of Target Buffer to the new level of demand is modelled monitoring penetration of

Red Zone for a period equal to a replenishment time. Values are saved in a vector of RLT

elements. It is continuously overwritten and the parameter checked for the activation of TMR

is the sum of its values. On the opposite, every time inventory on-hand is over Yellow Zone

(2/3 of Target) a counter is updated. When it reaches a values equal to 2 times the replenishment

period, then TMG is activated. Target Level is adjusted by a settable parameter, where +/-33%

is the standard. A lower value of this parameter can avoid violent reactions of DBM. The

following periods are treated in two different manners:

1. After “TooMuchGreen”: new orders are blocked until level of on-hand stock reaches

Target Level.

2. After “TooMuchRed”: new adjustments are blocked for at least a full replenishment

time. If supplier is stockout, then it waits another full replenishment time.

Reorder Point

An order is emitted every time Inventory Position is equal or below Reorder Point. Order

quantity is an EOQ calculated optimizing costs incurred along a time span of one year.

Hypotheses of EOQ are not completely verified, like in majority of real cases. Even so, this

quantity remains a useful benchmark. Some of them are validated in simulated scenarios:

Deterministic Lead Time

Not perishable goods

No dimensional limit at warehouse/retailer

Constant purchase cost

Proportional Costs

Others are not realistic or only partially checked:

Constant demand rate

Stockout not allowed

Infinite capacity of supplier

Ordering and holding costs completely proportional to inventory and placed orders.

Inventory position considered inventory in stock, on the pipeline and backordered.


65

5.3 - Simulations

A simulated year last 300 days, about the equivalent of a retailer opened 6 days per week. Every

simulation run last 690 days, where the first 90 are not recorded and intended for warm-up.

Each scenario has 50 replications so that statistical analysis can use solid a database.

All simulations aim to reach the highest service level and availability, considering that every

unit lost creates a loss greater than possible savings.

Demand generation in ARENA uses the same seeds, so independent demand of customers is

the same for every model if it is set with identical parameters. DBM model logic was validated

using software Elucidate with data obtained by real cases of implementation guided by NOUS

Srl. Validation regarded only logic on one level, with a perfect supplier and one product.

ROP and DBM are simulated under different levels of demand variability. ROP models are

the base cases and they are compared with simulations of DBM in the same context. Parameters

of demand are set in order to obtain two types of demand:

1. Stationary: two variants, one quite stable while the other with a certain variability.

2. Seasonal: with a peak every year.

For stationary demand, the correlation between periods as set at 0,7. Parameters adopted in

these simulations are:

RETAILER

LEVEL Mean

(IN) ST. Dev.

(IN) Correlation

(IN) Mean (OUT)

ST. Dev. (OUT)

PATTERN 1

(“Low Var.”) 3 1 0,7 ~10 ~1,5

PATTERN 2

(“High Var.”) 3 4 0,7 ~10 ~5,5

Characteristics of generated demand are collected and used to set parameters of ROP. Data

showed in the previous table are demand as seen by each retailer.

A few runs with infinite capacity of CW are simulated in order to get the behaviour of demand

at the upper level:

CENTRAL WAREHOUSE

LEVEL Mean (OUT)

ST. Dev. (OUT)

PATTERN 1

(“Low Var.”) ~30 ~60

PATTERN 2

(“High Var.”) ~30 ~60

Forrester effect is perfectly visible: demand variability at retailer causes standard deviation of

demand for CW to be many times higher than that at the point of sales.


66

Initial targets of DBM are set using paranoia factor criteria, while initial stock is set at

slightly superior values both for ROP and DBM.

5.3.1 - Scenario 1: Stationary demand with low variability

Case 1: ROP

The following are the results using ROP with the first pattern. Uncertainty of demand is limited

so safety stock is very little in this simulation. As expected, it minimizes total costs providing

optimal results with stationary demand. Demand rate is almost constant so replenishments are

regular and transportation reduced. Levels of safety stock, reorder points and EOQ are

calculated with the standard formulas proposed in literature, imposing a service level of 97%:

NETWORK (n=50)

Mean

(�̅�)

ST. Dev. (𝝈)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

ST. Dev. (𝝈)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

With tariff-per-unit With cost-per-vehicle

Profit € 974.261 4487 +/- € 1.275 € 964.078 4471 +/- € 1.271

Revenue € 2.702.639 11192 +/- € 3.181 = = =

Total Cost € 1.728.378 7019 +/- € 1995 € 1.738.561 7062 +/- € 2.007

Value of sold € 1.666.480 6971 +/- € 1.981 = = =

Carrying € 39.437 153,1 +/- € 43,5 = = =

Pipeline € 3.863 21,2 +/- € 6,03 = = =

Ordering € 828 5,44 +/- € 1,55 = = =

Transport € 17.770 121,3 +/- € 34,48 € 27.953 300,7 +/- € 85,5

Service [Ord] 99,95% 0,05% +/- 0,013% = = =

Service [Q] 99,97% 0,04% +/- 0,010% = = =

Table 12: ROP, low variability

Service level is nearly perfect, with average values over 99,9% in orders and quantities. These

tables report results of simulations in two manners, with a different treatment of transportation

costs: one pays a tariff per delivered unit, the other has a cost per sent vehicle. In the following

Graph 1: Scenario 1 - ROP, low variability


67

paragraph will be explained the reasons of this choice. All comparisons will consider tariff-per-

unit from here on.

Previous outcome is the result of a loading priority based on urgency at the downstream

level. This criterion is similar to that proposed by DBM and is aimed to ensure availability.

Testing is conducted also prioritizing the most profitable items under a constraint of minimum

saturation:

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Min 5% Sat. - Profit priority Min 10% Sat. - Profit priority Min 20% Sat. - Profit priority

Profit € 974.229 +/- € 1.273 € 973.706 +/- € 1.281 € 973.033 +/- € 1.315

Revenue € 2.702.503 +/- € 3.175 € 2.700.185 +/- € 3.199 € 2.697.159 +/- € 3.376

Total Cost € 1.728.274 +/- € 1.991 € 1.726.479 +/- € 2.006 € 1.724.126 +/- € 2.152

Value of sold € 1.666.384 +/- € 1.975 € 1.664.657 +/- € 1.993 € 1.662.419 +/- € 2.128

Carrying € 39.426 +/- € 43,48 € 39.350 +/- € 46,33 € 39.215 +/- € 48,42

Pipeline € 3.866 +/- € 6,10 € 3.887 +/- € 6,75 € 3.926 +/- € 8,85

Ordering € 828 +/- € 1,56 € 827 +/- € 1,50 € 826 +/- € 1,55

Transport € 17.771 +/- € 34,70 € 17.757 +/- € 32,25 € 17.740 +/- € 32,90

Service [Ord] 99,94% +/- 0,014% 99,85% +/- 0,025% 99,72% +/- 0,046%

Service [Q] 99,97% +/- 0,010% 99,88% +/- 0,023% 99,77% +/- 0,043%

Table 13: ROP, low var., minimum saturation and priority to profit

Low priority deliveries are avoided thanks to a minimum threshold. Saturation of vehicles

increases, but part of demand is lost due to this policy. It has an effect of cost reduction, but it

is counterbalanced by lost revenue. In these simulations the aim is availability. Setting loading

priorities on profitability has mainly drawbacks. It does not let deliveries to bring at retailers

what is really needed. Restraining the load to even higher minimum saturation deteriorates

performances even more.

Graph 2: Scenario 1 - Loading Priority to Profitability


68

Case 2: DBM

Simulation of DBM is conducted exactly with the same customer demand generated for ROP.

DBR is set with increment/decrement of 33% as suggested by theory. Detection of change in

demand is monitored using cumulated quantity that penetrates in Red Zone during

replenishment time:

NETWORK (n=50)

Mean

(�̅�)

ST.

Dev. (𝝈)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

Mean

(�̅�) ST.

Dev. (𝝈)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

With tariff-per-unit With cost-per-vehicle

Profit € 993.690 4355 +/- € 1.238 +2,0%

€ 816.546 4425 +/- € 1.257

Revenue € 2.703.400 11056 +/- € 3.142 +0,03% = = =

Total Cost € 1.709.710 7018 +/- € 1.994 -1,1% € 1.886.854 6946 +/- € 1.974

Value of sold € 1.666.925 6921 +/- € 1.967 +0,03% = = =

Carrying € 3.060 97,0 +/- € 27,57 -92,2% = = =

Pipeline € 3.888 16,1 +/- € 4,57 +0,6% = = =

Ordering € 17.981 5,2 +/- € 1,47 +2071,6% = = =

Transport € 17.855 73,3 +/- € 20,84 -0,5% € 195.000 0,0 +/- € 0,00

Service [Ord] 100,00% 0,006% +/- 0,002% +0,05% = = =

Service [Q] 100,00% 0,001% +/- 0,000% +0,03% = = =

Table 14: DBM, low variability

Results in tables show the difference between accounting transportation cost with a tariff-

per-unit or cost-per-vehicle. It is evident that DBM would not be convenient if it had to pay

transportation basing on sent vehicles. Daily deliveries make costs grow rapidly, while fall in

profit is disastrous. Growth of ordering and travelling costs is proportional to number of orders

and trucks delivered. EOQ minimizes total costs, so orders are generally quite large and full

trucks are preferred. This operation of batching is in disaccord with DBM basics. TOC adopts

replenishment of small lots with high frequency deliveries. These deliveries are daily at their

limit and they replenish about what was sold in the precedent period. Rationally, small lots

Graph 3: Scenario 1 - DBM vs ROP, low variability


69

cannot be delivered with the same vehicles of ROP, otherwise trucks would be highly

unsaturated.

A similar reasoning is applied to ordering costs. Their reduction is achievable in different

manners. TOC pushes in particular towards a strong collaboration with supplier. Calculation of

virtual buffer requires a relevant sharing of information. It is reasonable to think of a reduction

in ordering costs when this system is already in place. DBM operates at its best when it is

integrated with other actors of the supply chain, while ROP can be applied stand-alone. A

relationship of collaboration can bring some improvements to these costs, even if in the long

term. These considerations are valid also for ROP, but certainly they have a greater impact in a

context where communication and ordering are on daily basis, like DBM.

Impact of transportation cost is huge if compared with ROP. Smaller vehicles travelling on

daily basis would be the ideal solution, but this decision requires a strategic planning that

usually is not achievable or realized in short term. Service of an external carrier is a way to

solve this problem. A tariff per delivered unit can be introduced in order to simulate a realistic

solution and rational values. Costs of transportation are completely different considering a tariff

per unit at least equal to the cost per unit of a full truck:

(Approx: all products) DBM ROP

Vehicles delivered ~1200 trucks ~170 trucks

Quantity delivered ~54048 units ~53763 units

Mean Saturation 7,5% (Ret) –12,9% (CW) 55,2% (Ret) – 79,7% (CW)

Travels Cost (trucks) € 195.000 € 27.953

Travels Cost (quantity) € 17.855 € 17.770

Saturation of vehicles is at an extremely low level in simulations of DBM. Even higher tariffs

per unit are convenient to DBM. Transported quantities are roughly equal to two times the

received annual demand in both pull models, considering also transportation from Plant to CW.

From now on transportation costs will be accounted considering a tariff-per-quantity in both

models. No corrections will be applied to ordering costs.

Increment of ordering costs is not significant considering low level of inventory at retailer.

The most relevant effect is on carrying costs. Average value of on-hand stock is really low

compared to ROP. It determines a drastic reduction in held units at retailers.

Even if ROP and DBM have similar financial performances, their operative functioning is

deeply different. Space occupation is not considered in these models, but it can be a critical

constraint for local warehouses. Potentially, handling and operations of control require more


70

efforts and they are far more complex in ROP than those managing small batches for DBM.

This is especially true when many large batches of EOQ size arrive at retailer at the same time.

(Approx.: all products) DBM ROP

Retailer

Average Mean Stock 55,1 units 358,6 units

Average Inventory Value 3400,2 € 21828,9 €

Inventory Turns 163,4 25,4

Central Warehouse




Inventory reduction is clearly visible. This implies 1,84 days of inventory stocked at retailers

and 11,8 days for ROP. At central warehouse situation is even better under DBM: 5 days of

inventory versus 17,86 days. These values are a direct consequence of replenishments without

delays and no batching in emission of orders. Lead time of replenishment is reduced to the pure

time of deliveries in an ideal application of DBM, while ROP has to wait until inventory

position reaches reorder point.

One-way ANOVA analysis on total cost and profit sustain these observations. Normality of

every sample is tested with Kolmogorov-Smirnov test, while homogeneity of variances

(homoscedasticity) with Bartlett test. Comparisons between ROP and DBM give these results:

TOTAL COST:

PROFIT:

Both ANOVA are statistically significant. Null hypotheses are rejected: DBM has minor total

cost and higher profits.


71

5.3.2 - Scenario 2: Stationary demand with higher variability

Case 1: ROP

The only difference is given by the level of demand variability. This simulation uses exactly

the same parameters of the precedent, exception for level of safety stock. Standard deviation of

demand changes from 1,5 to 5,5, with a slightly increment in mean value due to the correlation

factor. In order to maintain the same level of service of the precedent scenario, safety stock of

ROP model is increased. The weight of safety stock is now more relevant, triple than before. It

induces a 50% increment in reorder point level:

NETWORK (n=50)

Mean

(�̅�)

ST. Dev. (𝝈)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Profit € 994.747 17087 +/- € 4.856

Revenue € 2.760.294 42960 +/- € 12.209

Total Cost € 1.765.547 26861 +/- € 7.634

Value of sold € 1.701.464 26643 +/- € 7.572

Carrying € 41.046 362,2 +/- € 102,9

Pipeline € 3.964 66,3 +/- € 18,83

Ordering € 849 13,7 +/- € 3,89

Transport € 18.224 301,9 +/- € 85,81

Service [Ord] 99,87% 0,06% +/- 0,016%

Service [Q] 99,93% 0,04% +/- 0,013%

Table 15: ROP, higher variability

Behaviour of ROP is pretty the same as before. Radical shifts are not visible. Profit is higher

than precedent scenario due to a little increment in annual demand. It changes from 3000 annual

units for single retailer to about 3050 in this scenario. This is due to a side-effect of correlation

factor, but it has nearly no impact on EOQ size or reorder point. However, variability makes

confidence of these results a little lower and subject to more oscillations.

Graph 4: Scenario 2 - ROP, higher variability


72

Variability is covered by ROP with additional safety stock; nonetheless service levels show the

presence of a little number of not satisfied orders and that lost units increases. This drop of

service is infinitesimal. It does not impact customer perception nor performance of ROP.

It is important to note that setting of DBM is done in the most accurate possible way.

Results highlight how a correct regulation of parameters can stabilize performances also in

context with high variability.

This model is tested also giving higher loading priority to the most profitable items. The

results are similar to those with stable demand. A minimum saturation of 5% and priority to

profitable items have only marginal effects:

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Min 5% Sat. - Profit priority Min 10% Sat. - Profit priority Min 20% Sat. - Profit priority

Profit € 994.701 +/- € 4.847 € 993.949 +/- € 4.852 € 993.200 +/- € 4.862

Revenue € 2.760.176 +/- € 12.178 € 2.757.162 +/- € 12.186 € 2.754.070 +/- € 12.204

Total Cost € 1.765.475 +/- € 7.612 € 1.763.213 +/- € 7.596 € 1.760.870 +/- € 7.613

Value of sold € 1.701.394 +/- € 7.552 € 1.699.212 +/- € 7.520 € 1.696.991 +/- € 7.544

Carrying € 41.042 +/- € 100,75 € 40.966 +/- € 91,99 € 40.828 +/- € 103,99

Pipeline € 3.966 +/- € 18,79 € 3.984 +/- € 19,12 € 4.017 +/- € 20,03

Ordering € 849 +/- € 3,85 € 848 +/- € 3,85 € 847 +/- € 3,98

Transport € 18.225 +/- € 85,18 € 18.204 +/- € 85,58 € 18.188 +/- € 88,88

Service [Ord] 99,86% +/- 0,017% 99,76% +/- 0,033% 99,65% +/- 0,043%

Service [Q] 99,92% +/- 0,014% 99,81% +/- 0,036% 99,70% +/- 0,046%

Table 16: ROP, higher var., minimum saturation and priority to profit

Graph 5: Scenario 2 - Loading Priority to Profitability


73

Case 2: DBM

DBM parameters are tested under different regulations. Initially, effects of two parameters are

studied:

- Target increment/decrement of 33% is reduced to 10%.

- Cooling time of DBM is increased by 1 day.

These parameters affect how DBM reacts to change in demand rate. Higher variability will

compromise DBM if its reactions are too much violent:

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

33% and Cooling=RLT 33% and Cooling=RLT+1

Profit € 992.171 +/- € 4.908 -0,26%

€ 991.016 +/- € 4.919 -0,37%

Revenue € 2.710.374 +/- € 12.515 -1,81% € 2.707.153 +/- € 12.636 -1,93%

Total Cost € 1.718.203 +/- € 7.916 -2,68% € 1.716.137 +/- € 8.021 -2,80%

Value of sold € 1.670.663 +/- € 7.768 -1,81% € 1.668.658 +/- € 7.881 -1,93%

Carrying € 9.455 +/- € 65,77 -77,0% € 9.379 +/- € 61,80 -77,1%

Pipeline € 3.900 +/- € 18,38 -1,61% € 3.895 +/- € 18,53 -1,75%

Ordering € 16.269 +/- € 27,22 +1817,3% € 16.312 +/- € 25,85 1822,4%

Transport € 17.915 +/- € 84,31 -1,70% € 17.893 +/- € 84,13 -1,82%

Service [Ord] 95,57% +/- 0,101% -4,3% 95,33% +/- 0,119% -4,5%

Service [Q] 98,12% +/- 0,062% -1,8% 98,00% +/- 0,075% -1,9%

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

10% and Cooling=RLT 10% and Cooling=RLT+1

Profit € 1.001.201 +/- € 4.874 +0,65%

€ 1.000.324 +/- € 4.873 +0,56%

Revenue € 2.735.202 +/- € 12.361 -0,91% € 2.732.506 +/- € 12.376 -1,01%

Total Cost € 1.734.001 +/- € 7.788 -1,79% € 1.732.182 +/- € 7.807 -1,89%

Value of sold € 1.685.975 +/- € 7.653 -0,91% € 1.684.282 +/- € 7.671 -1,01%

Carrying € 8.856 +/- € 51,71 -78,4% € 8.739 +/- € 51,68 -78,7%

Pipeline € 3.934 +/- € 18,15 -0,76% € 3.930 +/- € 18,20 -0,86%

Ordering € 17.163 +/- € 18,04 +1922,6% € 17.176 +/- € 18,56 +1924,2%

Transport € 18.073 +/- € 82,93 -0,83% € 18.055 +/- € 83.04 -0,93%

Service [Ord] 97,26% +/- 0,079% -2,6% 97,01% +/- 0,080% -2,9%

Service [Q] 99,02% +/- 0,037% -0,9% 98,92% +/- 0,040% -1,0%

Table 17: DBM Variations - Target resize and Cooling time


74

Increasing cooling time is ineffective here, or even negative. Likely it is more useful when lead

times of replenishment are not deterministic, but in these models they are sure and reliable.

Cooling off DBM after TMR is necessary to stabilize new target level. Order quantity consists

of what is consumed last period and an additional quantity to rise inventory position to the new

target level. If supplier is unreliable or requested quantity is not available, then one more day

of cooling is definitely useful in order to prevent from rising target again. Stockout happens in

that case, but further damages are avoided keeping target at the new level, without another

increment. Even if slightly, performances of DBM are affected negatively from this correction.

It is not needed in these simulations. The final effect is just the opposite; it slows down ability

of reaction of DBM.

Little adjustments of target prove to be effective in this context. Though 33% of increment

gives good results, 10% is able to improve performances. It emits more orders because of a

more frequent correction of the threshold value, but thanks to this it is able to sell more units.

At the same time a finer tuning of target reduces carrying cost, even more than the case with

standard parameters. These conclusions are motivated comparing the combined effects of the

parameters: when little adjustments and increased cooling time are combined, their results are

inferior to a simulation adopting only 10% increment/decrement of target.

One-way ANOVA analysis on profit of the four groups is performed in order to verify these

observations. Normality of every sample is tested with Kolmogorov-Smirnov test, while

homogeneity of variances (homoscedasticity) with Bartlett test. After a successful test, a post-

Graph 6: Scenario 2 - DBM Variations: Target resize and Cooling time


75

hoc test investigates differences in deep. HSD-Tukey test (“Honestly Significant Difference”)

is evaluated. ANOVA purpose is to determine if groups differ, but it cannot highlight which

groups in the sample are different. HSD represents the minimum distance between two group

means that must exist before the difference between the two groups is to be considered

statistically significant:

PROFIT:

P-value is less than 0,05, so ANOVA is considered statistically significant. Average profit of at

least one of the groups is different. HSD-Tukey test showed these results:

HSD-Tukey test:

This test confirms precedent observations: a finer tuning at 10% can improve performance,

while prolonging cooling time is not significant here.

Service level of ROP is better, but it holds an average inventory many times higher than

that of DBM:

(Approx.: all products) DBM (10%) ROP Retailer




Central Warehouse





76

The same motivations presented in Scenario 1 influences ordering and transportation costs in

these cases. TOC reorder policies should apply a unitary tariff or use small vehicles. In general,

a change to a different transportation system is required. Values in the following table are valid

only if firms do not integrate the new system with their organization, in that case DBM and

TOC are really damaging. As expected, delivered quantity are similar being both pull policies:

(Approx: all products) DBM (10%) ROP

Vehicles delivered ~1200 trucks ~174 trucks

Quantity delivered ~54709 units ~55153 units

Mean Saturation 7,6% (Ret) – 13,0% (CW) 55,4% (Ret) – 79,8% (CW)

Travels Cost (trucks) € 194.981 € 28.566

Travels Cost (quantity) € 18.073 € 18.224

DBM can achieve further improvements working on its responsiveness to demand change

and on its level of detection. This is an even more delicate parameter because it does not

determine “HOW” and “HOW MUCH” its reaction should be, but “WHEN” it has to act. As

explained before, cumulated penetration in Red Zone during replenishment time is chosen as

trigger to activate TMR in these DBM models. By theory, its threshold is set equal to size of

the entire Red Zone. This level of penetration brings some more risk of stockout in presence of

variability. As seen from the precedent results, a little part of demand is lost because of a

delayed correction to Target level.

Two settings of penetration are simulated. 0,9 and 1,2 times the size of Red Zone are tested.

Base case has already had a refinement this time, with 10% of increment/decrement of target

as reaction to the trigger:

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

10% and 90% penetration 10% and 100% penetration 10% and 120% penetration

Profit € 1.003.027 +/- € 4.875 € 1.001.201 +/- € 4.874 € 999.365 +/- € 4.890

Revenue € 2.740.593 +/- € 12.418 € 2.735.202 +/- € 12.361 € 2.729.886 +/- € 12.425

Total Cost € 1.737.566 +/- € 7.843 € 1.734.001 +/- € 7.788 € 1.730.521 +/- € 7.835

Value of sold € 1.689.319 +/- € 7.696 € 1.685.975 +/- € 7.653 € 1.682.690 +/- € 7.698

Carrying € 9.044 +/- € 60,17 € 8.856 +/- € 51,71 € 8.687 +/- € 54,01

Pipeline € 3.942 +/- € 18,29 € 3.934 +/- € 18,15 € 3.926 +/- € 18,19

Ordering € 17.150 +/- € 17,80 € 17.163 +/- € 18,04 € 17.179 +/- € 17,44

Transport € 18.110 +/- € 83,39 € 18.073 +/- € 82,93 € 18.038 +/- € 83,18

Service [Ord] 97,80% +/- 0,067% 97,26% +/- 0,079% 96,75% +/- 0,078%

Service [Q] 99,21% +/- 0,034% 99,02% +/- 0,037% 98,83% +/- 0,041%

Table 18: DBM Variations - Enhancement to Trigger of TMR


77

Reduced threshold seems to be effective. It provided little improvements on the base case at

0.9. It enhances detection of shift in demand rate and applies the finer correction seen before.

On the other hand, a negative correction of 1,2 degrades performances of base case. Average

level of demand is too low and effects are restrained in these simulations, but it is reported in

literature that this parameter acquires weight with larger quantities. It can amplify the effect of

correction or reduce their efficacy.

As before, ANOVA is performed in order to confirm this hypothesis:

PROFIT:

P-value is 0,5676 and F-value near 1. ANOVA does not signal significant differences in profit.

Likely, this is due to the improvement already achieved with a finer regulation. Positive effect

is present, but it is minimal compared to the precedent. Another possibility is that excessive

regulations diminish their effects if cumulated. Controller should limit its interventions on

DBM.

Compared to ROP, results are similar to those of the first scenario. A small reduction of

service levels brings an increment in profit, principally due to lower inventory:

Graph 7: Scenario 2 - DBM Variations: enhancement to Trigger of TMR


78

NETWORK (n=50)

10% and 90%

penetration ROP

∆ ROP

Profit € 1.003.027 € 994.747

+0,83%

Revenue € 2.740.593 € 2.760.294 -0,71%

Total Cost € 1.737.566 € 1.765.547 -1,58%

Value of sold € 1.689.319 € 1.701.464 -0,71%

Carrying € 9.044 € 41.046 -78,0%

Pipeline € 3.942 € 3.964 -0,6%

Ordering € 17.150 € 849 +1921,1%

Transport € 18.110 € 18.224 -0,63%

Service [Ord] 97,80% 99,87% -2,1%

Service [Q] 99,21% 99,93% -0,7%

Table 19: DBM vs ROP - Target Resize 10% and Trigger TMR 90%

ANOVA confirms the improvements:

TOTAL COST:

PROFIT:

Both ANOVA are statistically significant. However, ANOVA on profit highlights how

difference on this performance is less evident. DBM has better results on cost performances

than ROP, but they are very similar on overall profit.

Graph 8: Scenario 2 - DBM vs ROP: Target resize 10% and Trigger TMR 90%


79

Order batching is another typical solution to cope with variability. Ordered quantities

become more regular reducing order frequency. Doing so, replenishments are normalized when

demand is really unstable. This is not the favourite solution for TOC; nonetheless, it is

mandatory in presence of a constraint on minimum order quantity from supplier. It is also

rational in case of unsaturated vehicles. Changing batch size gives the following results in this

simulation:

NETWORK (n=50)

(33% and

Cooling=RLT)

Mean

(�̅�)

Mean

(�̅�)

Mean

(�̅�)

Mean

(�̅�)

Mean

(�̅�)

Batch=None Batch=5 Batch=10 Batch=15 Batch=20

Profit € 992.171 € 994.142 € 996.100 € 990.765 € 988.542

Revenue € 2.710.374 € 2.712.686 € 2.712.130 € 2.690.901 € 2.681.228

Total Cost € 1.718.203 € 1.718.544 € 1.716.030 € 1.700.136 € 1.692.686

Value of sold € 1.670.663 € 1.672.007 € 1.671.776 € 1.658.662 € 1.652.744

Carrying € 9.455 € 9.486 € 9.582 € 9.802 € 10.124

Pipeline € 3.900 € 3.903 € 3.902 € 3.872 € 3.857

Ordering € 16.269 € 15.219 € 12.842 € 10.014 € 8.241

Transport € 17.915 € 17.930 € 17.927 € 17.786 € 17.721

Service [Ord] 95,57% 95,75% 96,29% 95,72% 95,31%

Service [Q] 98,12% 98,20% 98,18% 97,41% 97,06%

Table 20: DBM - Order Batching

Order batching improves ordering costs. A batch size approximately equal to daily demand

increases revenue and profit, with marginal effects on service levels. Larger batches are

Graph 9: Scenario 2 - DBM with batch


80

simulated, but increment in performances disappear because of growing lost sales. Increment

of inventory at point of sales counterbalances part of the gains.

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

33%, Cooling=RLT, Batch =10

Profit € 996.100 +/- € 4.970

+0,14%

Revenue € 2.712.130 +/- € 12.698 -1,74%

Total Cost € 1.716.030 +/- € 8.037 -2,80%

Value of sold € 1.671.776 +/- € 7.865 -1,74%

Carrying € 9.582 +/- € 59,10 -76,7%

Pipeline € 3.902 +/- € 18,75 -1,56%

Ordering € 12.842 +/- € 38,68 +1413,5%

Transport € 17.927 +/- € 85,21 -1,63%

Service [Ord] 96,29% +/- 0,080% -3,6%

Service [Q] 98,18% +/- 0,066% -1,7%

Table 21: DBM with batch

Ideal batch size should be similar to average daily consumption. This quantity regularizes

fluctuations over a certain period, trying to compensate both effects of stockout and

overstocking. As said, this is a constraint more than a solution. It only covers variability pushing

a moderate quantity of stock towards retailers. On the contrary, TOC suggests to expedite orders

and pay an additional transportation cost rather than use a large batch. Replenishment Lead

Time and demand during this interval are the most important parameters for DBM. They are

both compromised using batches. DBM mechanism does not act correctly with orders so sudden

and large. These peaks can be intense at central warehouse, with dangerous effects: batching

induces peaks in upstream demand and DBM activates regulations of targets more easily if

orders are so big. Variability is amplified and transmitted upstream in supply chain.

Graph 10: Scenario 2 - DBM with batch vs ROP


81

5.3.3 - Scenario 3: Demand with seasonality

Case 1: ROP

Demand has seasonal peaks in this scenario. It grows gradually until it reaches two times the

regular level. Pattern is known, so demand rate is set at appropriate value for calculation of the

parameters of ROP:

NETWORK (n=50)

Mean

(�̅�)

ST. Dev. (𝝈)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

Profit € 1.469.421 3218 +/- € 914

Revenue € 4.050.288 8132 +/- € 2.311

Total Cost € 2.580.867 5104 +/- € 1.450

Value of sold € 2.497.636 5083 +/- € 1.445

Carrying € 49.684 110,0 +/- € 31,27

Pipeline € 5.812 17,4 +/- € 4,95

Ordering € 1.033 4,8 +/- € 1,38

Transport € 26.703 121,8 +/- € 34,62

Service [Ord] 99,93% 0,043% +/- 0,012%

Service [Q] 99,96% 0,034% +/- 0,010%

Table 22: ROP, seasonality

Performances of ROP do not deteriorate. Peaks are gradual so it is able to cope with the change

in demand. Correct level of demand is monitored during warm-up period of the model. This is

possible in reality if historical series are available. Parameters of ROP are set in order to make

it performs the best availability. Seasonality increases variability of annual demand and risks

of shortage, so safety stock level is higher.

Graph 11: Scenario 3 - ROP, seasonality


82

Case 2: DBM

DBM is simulated applying the findings of the precedent scenarios. Simulations regards

increment/decrement of Target equal to 33% and 10% combined with triggers of TMR equal to

size of Red Zone or 90% of it:

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

33% and Cooling=RLT 10% and Cooling=RLT

Profit € 1.491.180 +/- € 867 +1,48%

€ 1.491.142 +/- € 871 +1,48%

Revenue € 4.051.773 +/- € 2.267 +0,04% € 4.051.782 +/- € 2.265 +0,04%

Total Cost € 2.560.593 +/- € 1.450 -0,79% € 2.560.640 +/- € 1.444 -0,78%

Value of sold € 2.498.442 +/- € 1.424 +0,03% € 2.498.447 +/- € 1.423 +0,03%

Carrying € 11.682 +/- € 51,14 -76,5% € 11.619 +/- € 28,07 -76,6%

Pipeline € 5.834 +/- € 3,27 +0,38% € 5.828 +/- € 3,32 +0,28%

Ordering € 17.850 +/- € 1,76 +1628,2% € 17.983 +/- € 0,77 1641,1%

Transport € 26.786 +/- € 14,87 +0,31% € 26.764 +/- € 14,97 +0,23%

Service [Ord] 99,99% +/- 0,003% +0,1% 99,99% +/- 0,003% +0,1%

Service [Q] 100,00% +/- 0,000% +0,04% 100,00% +/- 0,000% +0,04%

NETWORK (n=50)

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

Mean

(�̅�)

Confidence

Interval (95%)

(±𝝈

√𝒏𝒕𝒏−𝟏,𝜶 𝟐⁄ )

∆ ROP

33% and 90% penetration 10% and 90% penetration

Profit € 1.491.000 +/- € 863 +1,47%

€ 1.491.048 +/- € 875 +1,47%

Revenue € 4.051.789 +/- € 2.267 +0,04% € 4.051.791 +/- € 2.265 +0,04%

Total Cost € 2.560.789 +/- € 1.454 -0,78% € 2.560.743 +/- € 1.441 -0,78%

Value of sold € 2.498.452 +/- € 1.424 +0,03% € 2.498.453 +/- € 1.423 +0,03%

Carrying € 11.869 +/- € 58,10 -76,1% € 11.713 +/- € 30,47 -76,4%

Pipeline € 5.834 +/- € 3,22 +0,38% € 5.828 +/- € 3,36 +0,28%

Ordering € 17.848 +/- € 2,35 +1628,0% € 17.983 +/- € 0,76 +1641,1%

Transport € 26.787 +/- € 14,66 +0,31% € 26.766 +/- € 15,09 +0,24%

Service [Ord] 100,00% +/- 0,002% +0,1% 100,00% +/- 0,002% +0,1%

Service [Q] 100,00% +/- 0,000% +0,04% 100,00% +/- 0,000% +0,04%

Table 23: DBM Variations: Target Resize and Trigger TMR with seasonality


83

Outputs of simulations are very similar and all of them reach full satisfaction of demand.

ANOVA gives the following results:

PROFIT:

ANOVA is not significant. DBM obtains about the same performances despite corrections, even

with those which were effective in precedent simulations. It is almost insensitive to actions of

controller and its results are quite stable.

These results give evidence that DBM reacts in difference manner to different type of

variability. One of the main assumption of TOC-SCRS is continuity on the short term. In other

words, it assumes that variability is limited within two consequent periods and demand rates

are considered similar. The first scenario simulated stationary demand with low variability that

definitely can be considered as continue between periods. The second pattern of demand had

higher variability and this assumption cannot be applied to it. Indeed, this is the reasons way

finer correction gave better results. Demand has a seasonal component in this third pattern, but

it is based on a demand with low variability. ROP considers variability of a whole year, while

DBM does not require such an estimation. This pattern is similar to the first one under DBM,

Graph 12: Scenario 3 - DBM Variations: Target resize and Cooling time with seasonality


84

so those corrections introduced with high variability are useless and their effect is not significant

in this context.

Even standard parameters proposed in literature are effective. Further corrections have no

effect. ANOVA confirms the improvement with standard parameters comparing DBM to ROP:

TOTAL COST

PROFIT

Both total cost and profit are statistically significant. Controllers can rely on autoregulation of

DBM in such a situation, it is almost completely autonomous.

Graph 13: Scenario 3 - DBM vs ROP, seasonality

85

6. Conclusions

6.1 - Findings

Originality of this work is in findings on the sensitiveness of DBM parameters to variability

that they could face in real applications. Main parameters were tested. Simulations proved that

their intensity vary on level of variability. Their effects can even be neutralized by

autoregulation of DBM.

1) How does TOC perform in a distribution network compared to a Reorder Point

policy?

All simulations aimed to full availability in contexts with regular demand, characterized by a

certain variability or a seasonal pattern. Confrontation aimed to verify if DBM policy is inferior

to (R,nQ), seen low number of real cases and low diffusion in Italy.

Inventory was drastically reduced compared to Reorder Point models. Reduction of stock

level was on average -85% at retailers and -72% at central warehouse. This benefit was

completely offset by ordering and transportation costs. However, it is reasonable to assume that

conditions to these costs cannot be identical to those in an application of ROP. For example,

given a truck with a certain capacity it is unthinkable to use the same vehicle for deliveries with

DBM. Orders sizes was completely different and saturation was less than 10% in many cases,

while it was 55% in ROP models. Assuming the same cost per unit, DBM profit slightly

outperforms ROP, on average about +2%. These results do not consider further gains for

reducing ordering costs. They were evaluated in an additional profit for DBM between 15000-

17000 € in these models.

Service levels were comparable, but for ROP they were so only if parameters were correctly

estimated. DBM did not required the same fine setting, but differences in performances was

minimum. Raw setting of DBM produced almost the same service level achieved by ROP using

precise data. It is believable that such a high level of accuracy is not always possible considering

the complexity of forecast models needed to acquire this data in real cases. ROP is highly

sensitive by its input parameters and this can affect its performances. Also DBM were sensitive

6. Conclusions

86

to parameters setting, but their damages concerned more costs for additional stocks at point of

sales.

Both models replenished downstream with total quantities roughly equal to annual demand,

as expected from pull policies. Indeed, pipelines presented on average the same quantities and

costs. However, DBM had small orders increasing gradually this values, while ROP proceeds

with discrete increment of EOQ size. Consequently, average inventory of DBM at retailer is

lower.

2) DBM has numerous settings that guide its functioning. Which parameters have

greater influence on performances?

It is necessary to highlight that DBM assumes continuity between demand rates of consequent

periods, so these corrections are useless or ineffective if applied with low variability. Findings

presented in this work showed how too many corrections to DBM are unnecessary. Parameters

suggested by theory can give better results in low variability context, while moderate

adjustments can bring advantages with a more variable demand. This is not influenced by

seasonality itself, but from continuity of demand rate between periods. In this work were tested:

Increment/decrement of target: “HOW” and “HOW MUCH” the reaction of DBM should

be. Benchmark values are corrections of ±33% target size. It was observed that lower value,

like ±10%, gives better results in a context with variability. They provide only marginal

gains with a quite stable demand.

Trigger of TMR: it considers cumulated penetration in Red Zone an indicator for a change

in demand rate. It determines “WHEN” to activate TMR. Standard value is 100% size of

Red Zone. Lower values make activation of TMR more frequent. It changes of targets

increasing buffer sizes. Low thresholds can be employed in a context with a variable

demand., but their effects do not add large improvements if other corrections have already

been applied. The opposite correction is used in stable context, in order to further reduce

false alarms.

Cooling-off after TMR: time to wait until a new cycle of DBM can start. Its benchmark

value is one replenishment time, in order to wait for next delivery to refill buffer to the new

target level. It was tested prolonging its value of one day, but it degraded performances.

This parameter can cover delayed replenishment and stockout of suppliers, preventing

another correction of DBM. In these simulations all lead time were deterministic and only

6. Conclusions

87

a limited number of stockout happened. Likely, it is less useful in a context with reliable

suppliers and this certainty in transportation lead time.

Order Batching: TOC-SCRS controls replenishment frequency. Delaying orders and

batching quantities can improve performances, reducing transportation and ordering costs.

Batch dimension is influenced by variability of demand, but best results were obtained with

a size about equal to average daily demand. These improvements were observed with high

variability, while they are lower with stable demand. Gains are limited by lost sales and

negative effects that DBM can cause upstream if not managed. Batches create peaks and

DBM activates corrections of target. This means that small batches can provide benefits

when variability manifests, but setting of DBM parameters is needed in order to avoid

excessive reactions.

The most effective parameter to regulate is increment/decrement of target. Its effect had less

negative impact in case of wrong correction, while it provides a moderate improvement in

performances with high variability. Another findings regards capacity of autoregulation of

DBM. Numerous corrections of controllers are rather ineffective. DBM can operate in

autonomy using standard parameters proposed in literature with stable demand.

3) Which constraints\variables\context provides more limitations to DBM

performance?

Order frequency and transportation lead time are the most limiting factors. Lead time and

frequency of reorder are the two key parameters in setting DBM. Maximum inventory level is

determined by replenishment time and by demand during this period, so TOC-SCRS suggest to

keep a daily frequency of reorder. Batching orders and delaying replenishments increase

exposition at potential stockout, while receiving order made of quantities delayed increases

carrying costs. For the same reasons long lead time of transportation are a risk or a cost.

Although results highlight similar service levels or slightly better profit, they are all direct

consequence of a correct estimation of parameters. Under this point of view DBM is preferable,

especially in presence of demand variability. DBM has more parameters to regulate, but they

do not need a fine setting and model can correct itself. The same parameters have high

importance in setting order quantities, reorder point and safety stock for ROP. TOC has variable

order quantities, reorder points are determined by target and safety stock are already included

in calculation.

6. Conclusions

88

Small vehicles or different tariffs are necessary to reduce transportation costs. TOC accepts

additional costs of transportation if they can provide better availability and profit. However,

they can be very relevant in a first stage of implementation and likely vehicles are sized for

order quantities many times larger than those of a daily replenishment.

Studying the model, it seems that implementations of DBM on products with high mark-

ups provides more chances of success. More the value of a product, more the weight of carrying

cost over transportation and ordering cost. Their high profitability covers completely additional

costs of transportation, while low level of inventory kept at point of sales minimizes carrying

costs. Considering the good performance of DBM with seasonal demand pattern and variability,

it seems particularly indicated for product like clothing. Also perishable products can have

advantages: low inventory level can prevent from great loss due to aging.

4) What are limits and drawbacks in TOC Pull Replenishment?

TOC SCRS aim completely to availability. Its parameters are set under this hypothesis. Demand

and lead time are the main data needed. There is not a direct link to economic value of products;

they are monitored by local performance measures, but they have no direct influence on

regulation of DBM. The concept behind TOC-SCRS is Make-To-Availability, so it has limits

if real goal is profitability. It can be implemented with excellent results even in that case, but

the aim is different. This difference seems to be underestimated in real implementation.

The numerous parameters of DBM have various effects. It is necessary a deep knowledge

of the functioning of DBM. The same reasons that makes it preferable to ROP are the same that

can compromise its success. Controllers and a constant monitoring are required; it is not

automated like ROP. Complete automation of DBM is not a good solution.

Small vehicles and strengthening collaboration are two key elements. Reduction of

transportation time and administration/ordering costs have priority. They can be really relevant

if managed at the same manner of Reorder Point models.

6. Conclusions

89

6.2 - Limits of the model

Deterministic lead times are the principal limitation. Uncertainty in deliveries and unreliability

of suppliers have more relevance in a standard implementation of DBM. The little number of

backorders and stockouts was not sufficient to test adequately cooling-off time. Likely,

fluctuations in transportation time would have been able to highlight its effect.

As said, complete automation of DBM is not possible. Many more actions should have been

taken, but in a simulation this is not possible. One of the main problem during testing was a

stagnation in yellow zone. This is a violation of one of the main principle of DBM (see ”3.5.2

- Make-To-Availability“). It cannot be excluded that performances of DBM could be even

better, but difficulties in its modelization are relevant. A manual action is required when it is

prolonged for many periods, but automating this evaluation would have complicated

excessively the simulations. Simulation of stable demand was particular sensitive to this

problem.

6.3 - Further Developments

Further development should consider the behaviour of the model with not-deterministic lead

time. Parameters of DBM should be furtherly investigated with different pattern of demand. In

general, researches on demand change detection of DBM are needed. It seems to be the most

promising area and literature is not completely developed.

90

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