A System Dynamics Modeling Framework for the Strategic 2004

www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 70 (2005) 351–364

A system dynamics modeling framework for the strategicsupply chain management of food chains

Patroklos Georgiadis *, Dimitrios Vlachos, Eleftherios Iakovou

Department of Mechanical Engineering, Aristotle University of Thessaloniki, Division of Industrial Management,

P.O. Box 461, Thessaloniki 541 24, Greece

Received 3 October 2003; received in revised form 22 December 2003; accepted 23 June 2004

Available online 25 November 2004

Abstract

The need for holistic modeling efforts that capture the extended supply chain enterprise at a strategic level has been clearly rec-

ognized first by industry and recently by academia. Strategic decision-makers need comprehensive models to guide them in efficient

decision-making that increases the profitability of the entire chain. The determination of optimal network configuration, inventory

management policies, supply contracts, distribution strategies, supply chain integration, outsourcing and procurement strategies,

product design, and information technology are prime examples of strategic decision-making that affect the long-term profitability

of the entire supply chain. In this work, we adopt the system dynamics methodology as a modeling and analysis tool to tackle stra-

tegic issues for food supply chains. We present guidelines for the methodology and present its development for the strategic mod-

eling of single and multi-echelon supply chains. Consequently, we analyze in depth a key issue of strategic supply chain

management, that of long-term capacity planning. Specifically, we examine capacity planning policies for a food supply chain with

transient flows due to market parameters/constraints. Finally, we demonstrate the applicability of the developed methodology on a

multi-echelon network of a major Greek fast food chain.

� 2004 Elsevier Ltd. All rights reserved.

Keywords: System dynamics; Supply chain management; Food logistics; Capacity planning

1. Introduction

Supply chain management (SCM) has been met with

increased recognition during the last decade both by

academicians as well as practitioners. However, despite

its significant advances and dramatic improvements in

information technology (IT), the discipline of SCM re-

mains incapable of addressing satisfactorily many prac-

tical real-world challenges. One key reason for thisinadequacy is the interdependencies among various

operations and the autonomous partners across the

chain, which renders all traditional myopic models inva-

0260-8774/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2004.06.030

* Corresponding author. Tel.: +30 2310 996046; fax: +30 2310

996018.

E-mail address: [email protected] (P. Georgiadis).

lid (Iakovou, 2001; Tayur, Ganeshan, & Magazine,1999). Rather, strategic decision-makers need compre-

hensive models to guide them in the decision-making

process so as to increase the total profitability of the

chain.

A critical shortcoming of most of the existing strate-

gic models is their inability to take into account the im-

pact of regulatory legislation within today�s already

volatile environment. This is particularly important forfood supply chains because of their unique characteris-

tics, stemming among others from product storage and

transportation specifications (Hobbs & Young, 2000;

Van der Vorst, Beulens, De Wit, & Van Beek, 1998).

For example, product perishability creates uncertainty

for the buyer with respect to product quality, safety

and reliability (i.e. quantity) of supply. It creates

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352 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364

uncertainty for the seller in locating a buyer, as perish-

able products must be moved promptly to the market-

place to avoid deterioration, leaving sellers unable to

store the products awaiting favorable market condi-

tions. This further leads to the need for frequent deliver-

ies, through dedicated modes of transportation (e.g.refrigerators). Moreover, food products usually exhibit

high seasonality in raw materials availability and in

end-products demand, and therefore they need effi-

ciently designed storage facilities to further ensure their

quality. In addition, food safety issues have profound

ramifications on the design of the supply chain. For in-

stance, proper monitoring and response to food safety

problems requires the ability to trace back small lots,from retailer to processor or even back to the supplying

farm. Another feature of food chains is that few prod-

ucts are transformed from commodity to differentiated

branded foods, while others undergo packaging but re-

main essentially intact in character. All these character-

istics along with the dynamically evolving legislative

framework further hinder the task of managing effi-

ciently food supply chains.The motivation behind this research is (i) to facilitate

the decision-making process for capacity planning of

multi-echelon supply chains in such uncertain environ-

ments by studying the long-term behavior of supply

chains and (ii) to further offer a generic methodological

framework that could address a wider spectrum of stra-

tegic SCM related problems.

Most of the standard methodologies for the analysisof supply chains study the steady state of the system,

i.e. they assume that all transient phenomena have been

diminished. This assumption may be valid in several

supply chains, where product demand exhibits a smooth

pattern, i.e. demand has a low coefficient of variation

(functional items, in (Fisher, 1997)). However, there is

an increasingly important family of products with short-

er life cycles and larger demand variability, for which theutilization of the traditional methodologies may lead to

considerable errors (innovative items, in (Fisher, 1997)).

While focusing on the latter, we employ the system

dynamics (SD) methodology, well known and proven

in strategic decision-making, as the major modeling

and analysis tool in this research.

Forrester (1961) introduced SD in the early 60s as a

modeling and simulation methodology for the analysisand long-term decision-making of dynamic industrial

management problems. Since then, SD has been applied

to various business policy and strategy problems (Ster-

man, 2000). The version of the well-known Beer Distri-

bution Game, an experiential educational game

presented in (Sterman, 1989), is a role playing SD model

of a supply chain originally developed by Forrester. To-

will (1995) uses SD in supply chain redesign to gainadded insights into SD behavior and particularly into

its underlying casual relationships. The outputs of the

proposed model are industrial dynamics models of sup-

ply chains. Minegishi and Thiel (2000) use SD to im-

prove the understanding of the complex logistic

behavior of an integrated food industry. They present

a generic model and then provide practical simulation

results applied to the field of poultry production andprocessing. Sterman (2000) presents two case studies

where the SD methodology is used to model reverse

logistics problems. Georgiadis and Vlachos (2004) use

the SD methodology to estimate stocks and flows in a

reverse supply chain providing specific mechanisms with

a fixed remanufacturing capacity change per year.

Sterman (2000) introduced a generic SD model of the

stock management structure which is used to explain thesources of oscillation, amplification and phase lag ob-

served in supply chains. Haffez, Griffiths, Griffiths, and

Nairn (1996) describe the analysis and modeling of a

two-echelon industry supply chain encountered in the

construction industry, using an integrated system

dynamics framework. Simulation results are further

used to compare various re-engineering strategies.

In this work we develop an SD-based holistic model ofthe entire supply chain, which may be used as decision-

making aid tool, mainly for strategic decision-making.

More specifically, we design generic single-echelon

inventory systems that incorporate all state variables

(stocks on-hand and on order) and policies for both

inventory control and capacity planning. Using this sin-

gle-echelon model as a basic module we demonstrate

how generic multi-echelon supply chain models can beconstructed. Although such an analysis may differ from

one product (or stock keeping unit, SKU) to another,

we keep the proposed model as generic as possible to

facilitate its implementation on a wide spectrum of

real-world cases.

The next section presents the problem under study

and the modeling approach along with the major under-

lying assumptions. In Section 3 we demonstrate theapplicability of the developed model on a multi-echelon

network of a major Greek fast food chain. Finally, we

wrap-up with summary and conclusions in Section 4.

2. Problem and model description

Strategic supply chain management deals with a widespectrum of issues and includes several types of decision-

making problems that affect the long-term development

and operations of a firm, namely the determination of

number, location and capacity of warehouses and man-

ufacturing plants and the flow of material through the

logistics network, inventory management policies, sup-

ply contracts, distribution strategies, supply chain inte-

gration, outsourcing and procurement strategies,product design, decision support systems and informa-

tion technology.

P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 353

The methodological approach developed in this

paper, could potentially be used for capturing most of

the above strategic SCM problems. However, since each

of the problems has its unique characteristics, we present

guidelines for the methodology and further analyze in

depth a specific strategic management problem, that oflong-term capacity planning; this is the problem of iden-

tifying dynamically (at strategic time instances), optimal

levels of vendor sourcing, production, warehousing, dis-

tribution and transportation capacity. Our approach

utilizes a well-proven methodological tool for strategic

decision-making, that of SD.

2.1. System dynamics methodology

A supply chain being the ‘‘extended enterprise’’ that

encompasses vendors, manufacturers/producers, distrib-

utors and retailers is characterized by a stock and flow

structure for the acquisition, storage, and conversion

of inputs into outputs and the decision rules governing

these flows (Forrester, 1961; Sterman, 2000). The flows

often create important feedbacks among the partnersof the extended chain, thus making SD a well-suited

modeling and analysis tool for strategic supply chain

management.

The structure of a system in SD methodology is

exhibited by causal loop (influence) diagrams; a causal

loop diagram captures the major feedback mechanisms.

These mechanisms are either negative (balancing) or po-

sitive feedback (reinforcing) loops. A negative feedbackloop exhibits a goal-seeking behavior: after a distur-

bance, the system seeks to return to an equilibrium situ-

ation. In a positive feedback loop an initial disturbance

leads to further change, suggesting the presence of an

unstable equilibrium. Causal loop diagrams play two

important roles in SD. First, during model development,

they serve as preliminary sketches of causal hypotheses

and secondly, they can simplify the representation of amodel. The structure of a dynamic system model

contains stock (state) and flow (rate) variables. Stock

variables are the accumulations (i.e. inventories), within

the system, while flow variables represent the flows

in the system (i.e. order rate), which are the byproduct

of the decision-making process. The model structure

Fig. 1. Causal loop diagram of an open-lo

and the interrelationships among the variables are

represented by stock-flow diagrams. The mathematical

mapping of a SD stock-flow diagram occurs via a system

of differential equations, which is numerically solved via

simulation. Nowadays, high-level graphical simulation

programs (such as i-think�, Stella�, Vensim�, andPowersim�) support the analysis and study of these

systems.

2.2. Single-echelon model

In Fig. 1 we present the stock and flow structure for a

single-echelon inventory system in its corresponding

causal loop diagram. The verbal descriptions coincidewith the variables of the model. The arrows represent

the relations among variables. The direction of the influ-

ence lines displays the direction of the effect. Signs ‘‘+’’

or ‘‘�’’ at the upper end of the influence lines exhibit the

sign of the effect. When the sign is ‘‘+’’, the variables

change in the same direction; otherwise they change in

the opposite one. The structure of the system�s internalenvironment consists of the stock variables Supply Lineand Inventory. Supply Line monitors the accumulation

of unfilled orders, i.e. orders that have been placed but

not received yet, while Inventory monitors the accumula-

tion of products on hand. Orders increase the Supply

Line. The rate of Order Fulfillment is determined by

the Orders after a time delay equal to Lead time. Order

Fulfillment reduces the stock of products in Supply Line

and increases Inventory. The variable Inventory isdepleted by Sales. This process takes time equal to the

Response Time to Customers� Demand.The clear definition of the boundaries between the

system under study and its external environment is an

essential step of SD; thus, the model and its analysis

are kept as simple as possible while capturing all neces-

sary elements for the analysis of the system under study.

In the simplistic model exhibited in Fig. 1, producers(a term used for vendors, suppliers or manufacturers)

and customers represent the external environment of

the system (source and sink in SD nomenclature, respec-

tively); thus, the SD underlying assumption is that pro-

ducers and customers do not affect the behavior of the

system under study. However, in a different model

op single-echelon inventory system.


producers and/or customers could potentially be in-

cluded in the system boundaries and thus, the effect of

their particular attributes in stock and flows determina-

tion would be captured.

The mathematical equations that describe the stock

and flow structure of the single-echelon inventory sys-tem are the following:

Supply LineðtÞ

¼ Supply Lineðt ¼ 0Þ þZ t

0

½OrdersðtÞ

�Order FullfilmentðtÞ�dt;

InventoryðtÞ

¼ Inventoryðt ¼ 0Þ þZ t

0

½Order FullfilmentðtÞ

� SalesðtÞ�dt;

SalesðtÞ¼ min½InventoryðtÞ=Response Time;

Customers’ DemandðtÞ�;

Order FullfilmentðtÞ ¼ Ordersðt � Lead TimeÞ:

Orders are governed by a decision rule to adjust the

stocks both in Supply Line and the Inventory to the de-

sired values. This decision process converts the open-

loop structure of Fig. 1 into the closed-loop structure

of Fig. 2. Specifically, Orders is defined as the sum oftwo terms, namely:

OrdersðtÞ ¼ Expected DemandðtÞþ Inventory Position AdjustmentðtÞ:

Fig. 2. Causal loop diagram of a closed-lo

The first term is a forecasted value for demand, calcu-

lated from a first order exponential smoothing of the

past values of Customer’s Demand with a smoothing fac-

tor equal to 1/aDL. Hence:

Expected DemandðtÞ

¼ Expected Demandðt � dtÞ þ 1

aDL

½DemandðtÞ

� Expected DemandðtÞ�dt:

The second term is a periodical adjustment, which is

proportional to the difference between Desired Inventory

Position (which is a decision variable) and actual Inven-

tory Position (Inventory Position expresses the sum of

Supply Line and Inventory over time):

Inventory Position AdjustmentðtÞ

¼Desired Inventory PositionðtÞ� Inventory PositionðtÞInventory Position Adjustment Time

;

where Inventory Position Adjustment Time represents

how quickly the firm tries to correct the discrepancy

above and bring the inventory position in line with its

goal. Such a policy for Orders determination is an an-

chor and adjustment policy that is standard in modelingspecifically inventory systems in the SD literature (Ster-

man, 2000). Naturally, Orders are limited by the inven-

tory level of the producers, which is considered adequate

as in this model it is an external variable.

The closed-loop structure of Fig. 2 restricts the end-

less accumulation of inventory (that occurs in the model

of Fig. 1) whatever the demand level may be. This oc-

curs due to two negative feedback loops displayed inFig. 2. Loop #1 is defined by the sequence of the vari-

ables Orders—Order Fulfillment—Inventory—Inventory

op single-echelon inventory system.

TimeP

Demandforecast

Capacityleading

matching

trailing

2P

Fig. 4. Alternative capacity expansion strategies.


Position—Inventory Position Adjustment, while Loop #2

is defined by the variables Orders—Supply line—Inven-

tory Position—Inventory Position Adjustment. To ex-

plain the negative feedback mechanism, we follow the

route around Loop #1. An increase in Orders will in-

crease the Order Fulfillment and thus, Inventory andInventory Position will also increase. This causes Inven-

tory Position Adjustment to decrease, since the Desired

Inventory Position changes slowly and it can be assumed

to be constant for the next time step. Finally, the de-

crease in Inventory Position Adjustment restricts Orders.

Therefore, Orders will stabilize at a finite level and even-

tually the system will reach an equilibrium (steady) state.

2.3. Multi-echelon supply chain model

A supply chain being the total ‘‘extended enterprise’’

that captures all partners including vendors, manufac-

turers, producers, distributors and retailers, extends

over multiple echelons. Each partner of the chain typi-

cally manages his/her own inventory (operating as an

autonomous linkage of the chain), which is replenishedfrom the upstream echelon, while using a control policy

to determine the frequency and magnitude of the orders.

We can design generic multi-echelon food supply chains

that fit real-world cases by linking the appropriate num-

ber of single-echelon inventory models. For example,

Fig. 3 depicts a supply chain with three echelons, where

the causal loop diagram of each actor at each echelon is

equivalent to the causal loop diagrams shown in Fig. 2.Using the SD approach we can expand these generic

multi-echelon supply chains adding strategic supply

chain management issues. Capacity planning and man-

power planning are examples of such issues with the for-

mer being the focus of the rest of the paper.

Capacity may refer to all operations of a supply

chain, e.g. stock space, manpower, production facilities,

transportation means, etc. In the remainder of thispaper we concentrate on transportation capacity and

we examine efficient ways to dynamically determine their

levels. Generally, capacity determination is quite simple

Fig. 3. Generic causal loop diagram o

in a steady-state situation; however, in a evolving envi-

ronment, as in the case under study, it is important to

consider a dynamic capacity planning policy. To develop

a decision-making system for capacity planning, a firm

needs to carefully balance the tradeoff between customer

service maximization and maximization of capacity uti-lization. This is done by either leading capacity strate-

gies, where excess capacity is used so that the firm can

absorb sudden demand surges, or trailing capacity strat-

egies, where capacity lags the demand and therefore

capacity is fully utilized (Martinich, 1997). A third form

of capacity planning is the matching capacity strategy,

which attempts to match demand capacity and demand

closely over time. The three strategies are depicted inFig. 4. In all three cases the firm is making decisions

to acquire new capacity or not, at equally spaced time

intervals with length equal to the review period.

It appears that a decision-maker could determine

capacities for all these operations once in the beginning

of the planning horizon, and that this could be done

using a standard management technique that incorpo-

rates steady-state conditions. However, this is not thecase in the environment under study since product flows

can change dramatically for several reasons; for example

f a three-echelon supply chain.


promotion activities or price variation strategies of the

competitors. Although, such demand shifts take time

to materialize, they have to be considered for the devel-

opment of efficient capacity planning policies. Thus, it is

evident that an appropriate modeling methodology

needs to be able to capture the transient effects of flowsin a food supply chain. SD has this capacity and more-

over, it easily describes the diffusion effects related to

market behavior.

In addition, an operation may be performed using

either owned capacity or additional leased capacity.

The problem of determining the optimal ratio of owned

to leased capacity units (‘‘buy or lease’’ problem) is also

typical for supply chain operations. The causal loop dia-gram of Fig. 5 illustrates the generic single-echelon sys-

tem embellished with a dynamic loop that expresses a

capacity planning decision-making mechanism. Specifi-

cally, we assume that an operation may be performed

using owned and leased (if needed) capacity units. This

control mechanism is modeled as a negative feedback

loop.

More specifically, Capacity Needed is determined by avariable of the supply chain model. For example, if we

study the capacity of the transportation system, this var-

iable may be the Orders, while if we study the necessary

warehouse space this variable may be the on hand Inven-

tory. Capacity Needed is compared with the Actual

Capacity. In case there is a Capacity Shortage, capacity

is then leased to achieve the Desired Service Level.

Capacity Expansion Rate determines the rate ofchange of capacity towards the desired value. We as-

Fig. 5. Capacity planning dec

sume that capacity is reviewed periodically (every P

time units) and then a decision is made whether or

not to invest on capacity expansion and to what extent.

We have found this policy typical for most of the food

supply chains we have encountered, including the one

we discuss in the next Section. Capacity Expansion Rateis modeled by pulse functions, which may be positive

for times that are integer multiples of P. The pulse mag-

nitude is proportional to the Smoothed Capacity Short-

age (obtained from Capacity Shortage using first order

exponential smoothing to avoid unnecessary oscilla-

tions) multiplied by a control variable K. The variable

K represents alternative capacity expansion strategies.

Values of K < 1 represent trailing capacity expansionstrategies, values of K > 1 represent leading strategies,

and values close to 1 represent matching strategies. Nat-

urally, a serious lead time elapses between a decision

epoch of increasing capacity and the actual operation

of the corresponding capacity units. The Capacity

Acquisition Rate captures this time and is determined

by delaying the values of the Capacity Expansion Rate.

Moreover, Actual Capacity has a useful life time(Capacity Life-Time), which regulates the Capacity Dis-

posal Rate.

A decision-maker and/or regulator could further em-

ploy the developed model to capture the impact of var-

ious policies using various levels of the above

parameters; in other words, the model can be used for

the conduct of various ‘‘what-if’’ analyses. For example,

the impact of different leading strategies on the new orunexpected demand satisfaction and the capacity

ision-making structure.


utilization subject to a given capacity review period P

can be evaluated. On the other side, a decision maker

could investigate the impact of different values of capac-

ity review periods for a given capacity expansion policy.

More advanced ‘‘what-if’’ analyses may be further con-

ducted to develop a long-term capacity planning stra-tegy with the optimal values of P and K. In the

following Section we demonstrate how the above gene-

ric single-echelon supply chain model with capacity

planning can be used to model a real-world food supply

chain.

3. An illustrative real-world case study

3.1. A fast-food supply chain

We applied the research approach and modeling

methodology in the food supply chain of a major fast-

food restaurants chain in Greece. The supply chain of

the form is comprised of a central producer and ware-

house (CW) located in Thessaloniki, which then suppliesdirectly sixty restaurants in northern Greece (NR). The

firm also owns a distribution centre (DC) in Athens,

which supplies sixty nine restaurants located in the

southern and coastal Greece (SR). These organizations

maintain a chain partnership (based on franchising con-

tracts) to improve business performance via responsive

operations combined with better utilization of resources.

The franchising contracts cover various issues such asquality, customer service levels, etc. A major component

of the replenishment contracts is related to food distri-

bution (inventory replenishment policies, lead times, re-

quired storing space and conditions, delivery times,

etc.). The specific characteristics of the system are the

following:

• The desired fill rate of the restaurants is 100%. Tomaintain this goal the safety stocks at CW and the

restaurants are considerable, even though the lead

times are short. For the same reason both the inven-

tory and the production capacity of CW in Thessalo-

niki is practically infinite.

• The demand for each restaurant is generally high and

further fits to a normal distribution, the parameters

of which are estimated applying standard statisticaltechniques on real data (fitting the sample mean

and variance to the unknown parameters l and r2

of the distribution).

• The DC in Athens and each restaurant employ an

(R,S, s) policy for inventory replenishment. Thus,

inventory is inspected every R periods. If it is found

to be at a level less than or equal to s then an order

‘‘up to the desired inventory level, S’’ is placed. Thispolicy is formulated as an anchoring and adjustment

process (described in Section 2.2). The review period

R is set to 1 day. The optimal parameters S and s for

each restaurant are determined using classical

inventory management techniques (see Nahmias,

2001).

• The maximum acceptable lead time for an order is

24h. This implies that the central warehouse CW,or the distribution center DC, must adjust their deliv-

ery schedules to satisfy all orders within this time win-

dow. Deliveries may occur any time during day or

night.

• Both the CW and DC maintain two independent

fleets of trucks.

• When the number of the company-owned trucks is

inadequate to satisfy demand, CW and DC currentlylease third party trucks (usually trucks of a 3PL, third

party logistics company) to accommodate increased

demand. There is no additional delay in the acquisi-

tion of leased trucking capacity since the contractual

agreements between the company and the 3PL guar-

antee immediate response for tracks and drivers. Nat-

urally, there are constraints in leased capacity

volume, but based on historical data these limitsnever became active in the past.

In other working environments for which the last

assumption is not valid one would have to tackle the po-

tential delay resulting from leasing capacity and limited

leased-capacity resources and thus, the model would

have to be extended using delays functions to capture

the delayed availability of leased capacity. Such a model,despite its increased complexity, could easily be devel-

oped with the appropriate changes in our Powersim�

code. In our manuscript, we present the simpler in-

stance, since it is actually more reflective of the working

environment that we encountered for the fast food com-

pany that we worked with.

In such a dynamic environment with an absolutely

strict fill rate the company has to simply decide if itshould invest in increasing its fleet size or if should con-

tinue the current practice of using few owned trucks and

leasing 3PL trucks to cover its needs. Thus, the objective

of this case study is the development of efficient deci-

sions regarding the chain�s transportation capacity

(company-owned fleet size), that minimize total trans-

portation cost.

3.2. The simulation model

We first developed the causal loop diagram of the en-

tire chain, taking into consideration the inventory con-

trol policies used by the restaurants and the DC. The

entire diagram, which includes all system variables and

the regulating feedbacks, is exhibited in Fig. 6.

To develop the causal loop diagram, we used the fol-lowing assumptions, the validity of which was thor-

oughly checked with the CW and the restaurants:

Northern Greece Restaurants

Southern Greece RestaurantsDistribution Center

Supply lineNR

Sales

Inventory CW

OrdersNR

Lead TimeNR

Order FulfillmentNR

Demand NR

InventoryNR+- -

+delay

+

+

Inventory position NR

+ +

InventoryPosition

AdjustmentNR

-

Desired Inventory Position

NR

Inventory Position

Adjustment Time NR

-

+

+

+

+

-

SNR

sNR

+

+

Supply Line SR

Sales SROrdersSR

Lead timeSR

Order FulfillmentSR

Demand SRInventory

SR+- -

+

delay

+

+

Inventory Position SR

++

Inventory Position

AdjustmentSR

-

DesiredInventory

Position SR

Inventory Position

Adjustment Time SR

-

+

+

+ +

-

sSR

SSR

+

+Supply

Line DC

OrdersDC

Lead TimeDC

Order FulfillmentDC

InventoryDC

+-

delay

+

Inventory Position

DC

+

+

Inventory Position

AdjustmentDC

-

DesiredInventory

Position DC

+

+

+

-

SDC

sDC

+

+

Transportation Capacity

Needed NRTransportation

Capacity Shortage NR


Leasing NR

DesiredFill Rate

NR

Smoothed Transportation

Capacity Shortage NR


Expansion Rate NR


Acquisition Rate NR

Transportation Capacity NR


Disposal Rate NR

Capacity Life Cycle

NR

+

+

Smoothing +

+

+

+delay+

-

+

-

-


Needed SRTransportation

Capacity Shortage SR


Leasing SR

DesiredFill Rate

SR

SmoothedTransportation

Capacity Shortage SR


ExpansionRate SR


AcquisitionRate SR


Disposal Rate SR

Capacity Life Cycle

SR+

Smoothing +

+

+

+delay+

-

+

-

ResponseTime NR

-

+

-Transportation Capacity SR

Expected Demand NR

+

+

ExpectedDemand SR

+

+

Expected AggregateOrders SR+

+

-

--

OrderHandling Time NR

-

OrderHandling Time SR

-

OrderHandling Time CW

-

ResponseTime SR

-

Fig. 6. Causal loop diagram of the fast-food chain.


• No order is greater than the capacity of a single truck.

• Each truck serves one restaurant at a time. This is

generally true for restaurants that are in the vicinity

of the CW facilities. For the other ones each truck

serves two restaurants at a route. Therefore, this

assumption easily makes sense, assuming that thelead time is half of the loading–transportation–

unloading time.

• There are no emergency deliveries.

• There is no collaboration (no lateral movements)

among restaurants.

The next step of the SD methodology involves the

mapping of the causal loop diagram into a dynamicsimulation model using specialized software. We used

the Powersim� 2.5c software for this purpose. The


embedded mathematical equations are divided into two

main categories: the stock equations and the flow equa-

tions. Stock equations define the accumulations within

the system through the time integrals of the net flow

rates. Another typical form of stock equations is used

to define the smoothed stock variables that are ex-pected values of specific variables usually obtained

from their past values using exponential smoothing

(e.g. the smoothed stock variable Expected Demand

NR in Fig. 6 is obtained from Demand NR using first

order exponential smoothing). Flow equations define

the flows among the stocks as functions of time. Con-

verters and Constants form the fine structure of flow

variables. The holistic model includes 260 state vari-ables and a considerable number of converters and

constants. The mathematical equations for the specific

model, as they are provided by Powersim�, are in-

cluded in Appendix A. It should be noted that the out-

put of Powersim� 2.5c uses the qualifiers ‘‘init’’ for

initial stock (level) equations, ‘‘flow’’ for stock (level)

equations, ‘‘aux’’ for smoothed stock equations and

for flow (rate) equations and converters, ‘‘const’’ forconstants and ‘‘dim’’ for the dimension of vector vari-

ables (single-dimension arrays in Powersim�). The units

of each variable are also included in brackets. Data has

been scaled to respect corporate confidentiality. In the

following subsection we present the results of our sim-

ulation runs.

3.3. Simulation results

The model presented thus far includes a periodically

reviewed capacity planning policy. Therefore, the model

may be used for long-term capacity planning with dy-

namic adjustments occurring at the review points. In

addition, if the length of review period is set to infinity

then the model prescribes optimal truck capacity once,

without the ability of future adjustment.To proceed with the capacity planning process we

need to obtain an understanding of the transportation

demand characteristics. We first estimate the probability

distribution of the transportation demand (Transporta-

0%

2%

4%

6%

8%

10%

12%

14%

10 20 30 40driver-shifts

f(.)

NR

SR

F(

Fig. 7. pdf f(•) and cdf F(•) of transportation d

tion Capacity Needed NR, Transportation Capacity

Needed SR in Fig. 6) measured in vehicle-hours or in

driver shifts. Transportation demand can be calculated

from orders since the busy time of a truck is equal to

two times the lead time (one to deliver and one to return

to the DC) minus the loading and the unloading time(the lead time includes loading, transportation and

unloading times).

Thus, we conducted the simulation experiment using

the model of the previous subsection and then logged

the transportation demand for NR and SR. The proce-

dure was repeated for 1000 times to obtain accurate esti-

mates of the transportation demand distribution. Fig. 7

depicts the probability density function (p.d.f.), f(•), andcumulative distribution function (c.d.f.), F(•), of the

transportation demand in driver shifts per day for both

NR and SR.

The transportation demand pattern fits a normal dis-

tribution. The current numbers of driver shifts per day is

16 for the CW in Thessaloniki and 22 for the DC in Ath-

ens. To determine the optimal fleet size which minimizes

the total system cost, we needed to identify the costsof the alternative strategic decisions (‘‘own’’ or ‘‘lease’’).

The cost of using a company-owned truck for one driver

shift is used as a reference cost and it is set to 100 units.

This cost includes variable costs (cp = 60 monetary

units) which are charged per shift a truck is employed,

and fixed costs (cf = 40 monetary units) which are in-

curred whether the truck is used or not. The cost of leas-

ing a truck is c1 = 180 monetary units per driver shift. Ifx is the demand then the total cost per day, TC, as a

function of capacity A (number of driver shifts per

day) is given by:

TCðAÞ ¼ Acf þ cp

Z A

0

xf ðxÞdxþ cpAZ 1

Af ðxÞdx

þ c1

Z 1

Aðx� AÞf ðxÞdx:

The problem of determining the optimal number ofdriver shifts A* has the form of the well-known news-

vendor problem (Nahmias, 2001) and thus its solution

is given by

0%

20%

40%

60%

80%

100%

10 15 20 25 30 35 40driver shifts

.)

NR

SR

emand for northern and southern Greece.


A ¼ F �1 c1 � cp � cfc1 � cp

� �:

Hence, the optimal policy, prescribes 21 driver shifts

for the CW in Thessaloniki and 26 for the DC in Athens.

This indicates that the transportation capacity of both

the CW warehouse in Thessaloniki and the DC in Ath-

ens has to be increased by five and four driver shifts

units respectively.Moreover, the model may be used to perform ‘‘what-

if’’ analyses regarding the results and the policy param-

eters. For example, we can use the model to answer the

following questions:

• How should we fine-tune the inventory control policy

parameters ‘‘S’’ and ‘‘s’’ in order for the currently

existing transportation capacity to be optimal?• What is the impact of increasing or decreasing the

inventory control policy parameters ‘‘S’’ and ‘‘s’’ on

the optimum fleet sizes?

Using the model we may address the first question; in

this case the firm decides to fine tune operational param-

eters, so that the current fleet size is optimal. Specifi-

cally, the current transportation capacity turns out tobe optimal if we decrease all the reorder point (s) values

by 25% or the base stocks (S) by 10% for the restaurants

in northern Greece and if we decrease the order point

values by 15% or the base stocks by 6% for the restau-

rants in southern Greece. Naturally, such decisions must

be checked with other problem constraints (e.g. the per-

ishability and the life time of the food products, storage

space, etc.).To address the second question we may vary all reor-

der points parameters (s) of the NR restaurants; for

example, by a specific percentage and then repeat run-

ning the simulator. The results are exhibited in Fig. 8.

We note that the optimal number of driver shifts per

day changes from 21 to 26 when s is increased by 20%

(17 when is decreased by 20%). Moreover, if we repeat

the experimentation with the base stock quantities (S)

13

18

23

28

33

38

-30% -20% -10% 0% 10% 20% 30%% change in parameter value

driv

er s

hift

s pe

r da

y

s

S

Fig. 8. Sensitivity of the optimal capacity while varying operational

parameters.

we notice that the optimal number of driver shifts per

day changes from 21 to 14 when S is increased by 20%

(37 when S is decreased by 20%). Therefore, it is evident

that the optimal capacity is more sensitive to base stock

quantity adjustments.

The above procedure that calculates the optimalcapacity appears to be static since the problem seems

to be reduced to the newsvendor problem based on the

empirically derived distributions of necessary driver-

shifts. First, we should note that simulation is needed

to obtain the distribution of transportation demand to

be used in the closed form solution of the newsvendor

problem. On a second hand, the following question

needs to be answered: why should we employ SD to ob-tain F(•), instead of using the classical discrete event

simulation method? The answer is quite straightforward.

If the customers� demand is stationary, then the trans-

portation demand would also be stationary and the opti-

mal capacity may be obtained using either discrete event

or SD simulation. However, if any input variable or

parameter (e.g. demand, inventory policy parameters,

etc.) evolves with time, then the only appropriate meth-odology is that of the SD, since this dynamic behavior

cannot be captured by discrete event simulation.

To this end we conducted another experimentation

assuming that the mean demand exhibits a 10% increase

per year. In that case we assume that the initial transpor-

tation capacity would be equal to the optimal found in

the previous paragraphs, specifically 21 driver shifts

for the CW in Thessaloniki and 26 for the DC in Athens.The capacity review period is set to half a year. Fig. 9

depicts the optimal expansion of owned capacity mea-

sured in driver shifts for a five year period.

Other possible ‘‘what-if’’ scenarios that could be fur-

ther investigated include among others:

• The impact of sudden demand spikes/valleys on the

system�s transportation capacity. In such a case itwould be interesting to measure the length of the

transient phase of the flows or to measure what is

the impact on total system cost. Moreover, if such a

2628

2930

3233

3435

3738 39

2122

2324

2627

2829

3032

33

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9 10half-years

Ow

ned

driv

er s

hift

s SR

NR

Fig. 9. Transportation capacity planning of owned-trucks if demand

exhibits an annual increase of 10%.


disturbance occurs frequently, it would be interesting

to investigate a modified capacity planning policy

which allows for emergency capacity reviews (on time

instances different for the multiples of review period)

when the percentage demand variation in a short per-

iod exceeds a specific level (decision variable).• The impact of potential state regulatory interventions

for food storage and distribution on various opera-

tional parameters (inventory control parameters,

transportation capacity). SD is a methodology that

allows for capturing the diffusion effect of regulatory

interventions, since SD can map efficiently the time

necessary for the manifestation of these interventions

in the system.• The merit of alternative inventory management and

control policies. For example, we can employ similar

methodologies to investigate the impact of a continu-

ous review inventory management policy following

the appropriate information technology investments

(such as Electronic Data Interface, EDI or XML)

that allow for real time communication between

CW and all its restaurants.

4. Summary/Conclusions

We presented a system dynamics-based methodolog-

ical approach for mapping and analyzing multi-echelon

food supply chains. The methodology constructs supply

chain models by linking single-echelon models as mod-ules. The holistic model can be used to identify effective

policies and optimal parameters for various strategic

decision-making problems. The methodology has been

implemented for the transportation capacity planning

process of a major Greek fast-food restaurant supply

chain.

The developed model can be further used to analyze

various scenarios (i.e. to conduct various ‘‘what-if’’analyses) and answer questions about the long-term

operation of supply chains using total supply chain

profit as the measure of performance. The model can

further be tailored and used in a wide range of food sup-

ply chains. Thus, it may prove useful to policy-makers/

regulators and decision-makers dealing with a wide

spectrum of strategic food supply chain management

issues.

Appendix A

Stock equations:

init INVENTORY_CW = INFINITY

flow INVENTORY_CW = �dt * Orders_DC � dt * ARRSUM(Orders_NR) [items]

init INVENTORY_DC = 40000

flow INVENTORY_DC = +dt * Order_Fulfillment_DC � dt * ARRSUM(Orders_SR) [items]

dim INVENTORY_NR = (D = 1 .. 60)init INVENTORY_NR = [. . .]flow INVENTORY_NR = �dt * Sales + dt * Order_Fulfillment_NR [items]

dim INVENTORY_SR = (D = 1 .. 69)

init INVENTORY_SR = [. . .]flow INVENTORY_SR = �dt * Sales_SR + dt * Order_Fulfillment_SR [items]

init SUPPLY_LINE_DC = 0

flow SUPPLY_LINE_DC = �dt * Order_Fulfillment_DC + dt * Orders_DC [items]

dim SUPPLY_LINE_NR = (D = 1 .. 60)init SUPPLY_LINE_NR = 0

flow SUPPLY_LINE_NR = + dt * Orders_NR � dt * Order_Fulfillment_NR [items]

dim SUPPLY_LINE_SR = (D = 1 .. 69)

init SUPPLY_LINE_SR = 0

flow SUPPLY_LINE_SR = �dt * Order_Fulfillment_SR + dt * Orders_SR [items]

init Transportation_Capacity_NR = 0

flow Transportation_Capacity_NR = �dt * Trans_Cap_Disposal_NR + dt * Trans_Cap_Acquisition_NR [trucks]

init Transportation_Capacity_SR = 0flow Transportation_Capacity_SR = + dt * Trans_Cap_Acquisition_SR � dt * Trans_Cap_Disposal_SR [trucks]

Flow equations:

aux Order_Fulfillment_DC = DELAYPPL(Orders_DC,Lead_Time_DC,0) [items/hour]

dim Order_Fulfillment_NR = (D = 1 .. 60)

aux Order_Fulfillment_NR = DELAYPPL(Orders_NR(D),Lead_time_NR,0) [items/hour]


dim Order_Fulfillment_SR = (D = 1 .. 69)

aux Order_Fulfillment_SR = DELAYPPL(Orders_SR(D),Lead_time_SR,0) [items/hour]

aux Orders_DC = IF(Inventory_Position_DC < s_DC,MIN(INVENTORY_CW/Order_Handling_Time_CW,

Expected_Aggregate_Orders_SR + Inventory_Position_Adjustment_DC),0) [items/hour]

dim Orders_NR = (D = 1 .. 60)

aux Orders_NR = IF(Inventory_Position_NR < s_NR,MIN(INVENTORY_CW/Order_Handling_Time_NR,Expected_Demand_NR + Inventory_Position_Adjustment_NR),0) [items/hour]

dim Orders_SR = (D = 1 .. 69)

aux Orders_SR = IF(Inventory_Position_SR < s_SR,MIN(INVENTORY_DC/Order_Handling_Time_SR,

Expected_Demand_SR + Inventory_Position_Adjustment_SR),0) [items/hour]

dim Sales = (D = 1 .. 60)

aux Sales = MIN(INVENTORY_NR/Response_Time_DC, Demand_NR) [items/hour]

dim Sales_SR = (D = 1 .. 69)

aux Sales_SR = MIN(INVENTORY_SR(D)/Response_Time_SR, Demand_SR) [items/hour]aux Trans_Cap_Acquisition_NR = DELAYPPL(Trans_Cap_Expansion_NR,Acquisition_Time_TC_NR,0)

[trucks/hour]

aux Trans_Cap_Acquisition_SR = DELAYPPL(Trans_Cap_Expansion_SR,Acquisition_Time_TC_SR,0)

[trucks/hour]

aux Trans_Cap_Disposal_NR = Transportation_Capacity_ NR/Capacity_Life_Cycle_NR [trucks/hour]

aux Trans_Cap_Disposal_SR=Transportation_Capacity_ SR/Capacity_Life_Cycle_SR [trucks/hour]

Converters:

aux Aggregate_Orders_SR = ARRSUM(Orders_SR)[items/hour]

dim Demand_NR = (D = 1 .. 60)

aux Demand_NR = NORMAL(m_NR,sd_NR)[items/hour]

dim Demand_SR = (D = 1 .. 69)

aux Demand_SR = NORMAL(m_SR,sd_SR)[items/hour]

aux Expected_Aggregate_Orders_SR = DELAYINF(Aggregate_Orders_SR,a_AO_SR,1,Aggregate_Orders_SR)

[items/hour]dim Expected_Demand_NR = (D = 1 .. 60)

aux Expected_Demand_NR = DELAYINF(Demand_NR(D),a_D,1,Demand_NR)[items/hour]

dim Expected_Demand_SR = (D = 1 .. 69)

aux Expected_Demand_SR = DELAYINF(Demand_SR(D),a_D_SR,1,Demand_SR)[items/hour]

aux Inventory_Position_Adjustment_DC = MAX(S_DC-Inventory_Position_DC,0)/Inventory_Position_

Adjustment_Time_DC[items/hour]

dim Inventory_Position_Adjustment_NR = (D = l .. 60)

aux Inventory_Position_Adjustment_NR = MAX(S_NR-Inventory_Position_NR,0)/Inventory_Position_Adjustment_Time_NR[items/hour]

dim Inventory_Position_Adjustment_SR = (D = 1 .. 60)

aux Inventory_Position_Adjustment_SR = MAX(S_SR-Inventory_Position_SR,0)/Inventory_Position_

Adjustment_Time_SR[items/hour]

aux Inventory_Position_DC = INVENTORY_DC + SUPPLY_LINE_DC[items]

dim Inventory_Position_NR = (D = l .. 60)

aux Inventory_Position_NR = INVENTORY_NR + SUPPLY_LINE_NR[items]

dim Inventory_Position_SR = (D = 1 .. 69)aux Inventory_Position_SR = INVENTORY_SR + SUPPLY_LINE_SR[items]

dim Trans_demand_NR = (D = l .. 60)

aux Trans_demand_NR = IF((Orders_NR * TIMESTEP) > 0,(2 * Lead_time_NR * 24-1),0)[hour]

dim Trans_demand_SR = (D = 1 .. 69)

aux Trans_demand_SR = IF((Orders_SR * TIMESTEP) > 0,(2 * Lead_time_SR * 24-1),0)[hour]

aux Smoothed_Tran_Cap_Shortage_NR = DELAYINF(Transportation_Capacity_Shortage_NR,a_TC_NR,1,

Transportation_ Capacity_Shortage_NR)[trucks]

aux Smoothed_Tran_Cap_Shortage_SR = DELAYINF(Transportation_Capacity_Shortage_SR,a_TC_SR,1,Transportation_Capacity_Shortage_SR)[trucks]

aux Total_trans_demand_NR = ARRSUM(Trans_demand_NR)/Hours_per_Shift_NR[driver-shifts]


aux Total_trans_demand_SR = ARRSUM(Trans_demand_SR)/Hours_per_Shift_SR[driver-shifts]

aux Trans_Cap_Expansion_NR = INT(K_NR * (PULSE(Smoothed_Tran_Cap_Shortage_NR,4000,Pr_NR)))

[trucks/hour]

aux Trans_Cap_Expansion_SR = INT(K_SR * (PULSE(Smoothed_Tran_Cap_Shortage_SR,4000,Pr_SR)))

[trucks/hour]

aux Transportation_Capacity_Leasing_NR = Transportation_Capacity_Shortage_NR * Desired_Fill_Rate_NR[trucks]

aux Transportation_Capacity_Leasing_SR = Transportation_Capacity_Shortage_SR * Desired_Fill_Rate_SR

[trucks]

aux Transportation_Capacity_Needed_NR = Total_trans_demand_NR/Driver_Shifts_per_Truck_NR[trucks]

aux Transportation_Capacity_Needed_SR = Total_trans_demand_SR/Driver_Shifts_per_Truck_SR[trucks]

aux Transportation_Capacity_Shortage_NR = MAX(Transportation_Capacity_Needed_NR-

Transportation_Capacity_NR,0)[trucks]

aux Transportation_Capacity_Shortage_SR = MAX(Transportation_Capacity_Needed_SR-Transportation_Capacity_SR,0)[trucks]

Constants:

const a_AO_SR = 12 [hour]

dim a_D = (D = 1 .. 60)

const a_D = 12 [hour]

dim a_D_SR = (D = 1 .. 69)const a_D_SR = 12 [hour]

const a_TC_NR = 12 [hour]

const a_TC_SR = 12 [hour]

const Acquisition_Time_TC_SR = 720 [hour]

const Acquisition_Time_TC_NR = 720 [hour]

const Capacity_Life_Cycle_NR = 40,000 [hour]

const Capacity_Life_Cycle_SR = 40,000 [hour]

const Desired_Fill_Rate_NR = 1 [ ]const Desired_Fill_Rate_SR = 1 [ ]

const Driver_Shifts_per_Truck_NR = 3 [driver-shifts/truck]

const Driver_Shifts_per_Truck_SR = 3 [driver-shifts/truck]

const Hours_per_Shift_NR = 8 [hour/driver-shifts]

const Hours_per_Shift_SR = 8 [hour/driver-shifts]

const Inventory_Position_Adjustment_Time_DC = 1 [hour]

dim Inventory_Position_Adjustment_Time_NR = (D = 1 .. 60)

const Inventory_Position_Adjustment_Time_NR = 1 [hour]dim Inventory_Position_Adjustment_Time_SR = (D = 1 .. 69)

const Inventory_Position_Adjustment_Time_SR = 1 [hour]

const K_NR = 1 [1/hour]

const K_SR = 1 [1/hour]

const Lead_Time_DC = 9 [hour]

dim Lead_time_NR = (D = l .. 60)

const Lead_time_NR = [. . .] [hour]dim Lead_time_SR = (D = 1 .. 69)const Lead_time_SR = [. . .] [hour]dim m_NR = (D = 1 .. 60)

const m_NR = [. . .] [items/hour]

dim m_SR = (D = 1 .. 69)

const m_SR = [. . .] [items/hour]

const Order_Handling_Time_CW = 1 [hour]

const Order_Handling_Time_NR = 1 [hour]

const Order_Handling_Time_SR = 1 [hour]const Pr_NR = 4320 [hour]: NR transportation capacity review period

const Pr_SR = 4320 [hour] : SR transportation capacity review period


dim Response_Time_NR = (D = l .. 60)

const Response_Time_NR = 0.1 [hour]

dim Response_Time_SR = (D = 1 .. 69)

const Response_Time_SR = 0.1 [hour]

const S_DC = . . .[items]

dim S_NR = (D = 1 .. 60)const S_NR = [. . .] [items]

dim S_SR = (D = 1 .. 69)

const S_SR = [. . .] [items]

const s_DC = . . .[items]

dim s_NR = (D = 1 .. 60)

const s_NR = [. . .] [items]

dim s_SR = (D = 1 .. 69)

const s_SR = [. . .] [items]dim sd_NR = (D = 1 .. 60)

const sd_NR = [. . .] [items/hour]

dim sd_SR = (D = 1 .. 69)

const sd_SR = [. . .] [items/hour]

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Documents

A System Dynamics Modeling Framework for the Strategic 2004