Disaggregation and Master Production Scheduling (MPS)

Detailed Production Planning&

Shop-Floor Control

Dealing with the Problem Complexity through Decomposition

Aggregate Planning

Master Production Scheduling

Materials Requirement Planning

Aggregate UnitDemand

End Item (SKU)Demand

Corporate Strategy

Capacity and Aggregate Production Plans

SKU-level Production Plans

Manufacturingand Procurementlead times

Component Production lots and due dates

Part processplans

(Plan. Hor.: 1 year, Time Unit: 1 month)

(Plan. Hor.: a few months, Time Unit: 1 week)

(Plan. Hor.: a few months, Time Unit: 1 week)

Shop floor-level Production Control(Plan. Hor.: a day or a shift, Time Unit: real-time)

Disaggregation and Master Production Scheduling

(MPS)

The (Master) Production Scheduling Problem

MPS

Placed Orders

Forecasted DemandCurrent and PlannedAvailability, eg.,•Initial Inventory,•Initiated Production,•Subcontracted quantities

Master ProductionSchedule:When & How Muchto produce for eachproduct

CapacityConsts.

CompanyPolicies

EconomicConsiderations

ProductCharact.

PlanningHorizon

Timeunit

CapacityPlanning

MPS Example: Company Operations

Mashing(1 mashing tun)

Boiling(1 brew kettle)

Fermentation(3 40-barrelferm. tanks)

Filtering(1 filter tank)

Bottling(1 bottling

station)

Grain cracking(1 millingmachine)

Fermentation Times:Brew Ferm. TimePale Ale 2 weeksStout 3 weeksWinter Ale 2 weeksSummer Brew 2 weeksOctoberfest 8-10 weeks

Example: Implementing the Empirical Approach in Excel

# Fermentors: 1 Unit Cap: 200 Shelf Life: 20

Microbrewery PerformanceWeek 0 1 2 3 4 5 6 7 8 9 10# Fermentors Req'd 0 0 0 0 0 0 0 0 0 0Feasible Loading?Min # Fermentors Req'd 2 2 2 2 2 2 2 2 2 2Fermentor Utilization 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%Total Spoilage 0 0 0 0 0 0 0 0 0 0

Pale Ale Fermentation Time: 2Week 0 1 2 3 4 5 6 7 8 9 10Demand 45 50 40 40 40 40 40 40 40 40Scheduled Receipts 200Fermentors Released 1Inventory SpoilageInventory Position 100 255 205 165 125 85 45 5 -35 -40 -40Net Requirements 35 40 40Batched Net ReceiptsScheduled ReleasesFermentors SeizedTotal Fermentors Occupied

Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10Demand 35 40 30 30 40 40 40 40 50 50Scheduled ReceiptsFermentors ReleasedInventory SpoilageInventory Position 150 115 75 45 15 -25 -40 -40 -40 -50 -50Net Requirements 25 40 40 40 50 50Batched Net ReceiptsScheduled ReleasesFermentors SeizedTotal Fermentors Occupied

Computing Inventory Positions and Net Requirements

Net Requirement:

NRi = abs(min{0, IPi})

Inventory Position:

IPi = max{IPi-1,0}+ SRi+BNRi -Di

(Material Balance Equation)

iDi

IPi

(IPi-1)+

SRi+BNRi

Problem Decision Variables: Scheduled Releases



Pale Ale Fermentation Time: 2Week 0 1 2 3 4 5 6 7 8 9 10Demand 45 50 40 40 40 40 40 40 40 40Scheduled Receipts 200Fermentors Released 1Inventory SpoilageInventory Position 100 255 205 165 125 85 45 5 165 125 85Net RequirementsBatched Net Receipts 200Scheduled Releases 200Fermentors Seized 1Total Fermentors Occupied 1 1

Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10Demand 35 40 30 30 40 40 40 40 50 50Scheduled ReceiptsFermentors ReleasedInventory SpoilageInventory Position 150 115 75 45 15 -25 -40 -40 -40 -50 -50Net Requirements 25 40 40 40 50 50Batched Net ReceiptsScheduled ReleasesFermentors SeizedTotal Fermentors Occupied

Testing the Schedule Feasibility


Microbrewery PerformanceWeek 0 1 2 3 4 5 6 7 8 9 10# Fermentors Req'd 0 1 1 1 0 1 2 1 1 0Feasible Loading? NOMin # Fermentors Req'd 2 2 2 2 2 2 2 2 2 2Fermentor Utilization 0% 100% 100% 100% 0% 100% 200% 100% 100% 0%Total Spoilage 0 0 0 0 0 0 0 0 0 0


Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10Demand 35 40 30 30 40 40 40 40 50 50Scheduled ReceiptsFermentors ReleasedInventory SpoilageInventory Position 150 115 75 45 15 175 135 95 55 5 155Net RequirementsBatched Net Receipts 200 200Scheduled Releases 200 200Fermentors Seized 1 1Total Fermentors Occupied 1 1 1 1 1 1

Fixing the Original Schedule




Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10Demand 35 40 30 30 40 40 40 40 50 50Scheduled ReceiptsFermentors ReleasedInventory SpoilageInventory Position 150 115 75 45 15 175 135 95 55 5 155Net RequirementsBatched Net Receipts 200 200Scheduled Releases 200 200Fermentors Seized 1 1Total Fermentors Occupied 1 1 1 1 1 1

Infeasible Production Requirements# Fermentors: 1 Unit Cap: 200 Shelf Life: 20


Pale Ale Fermentation Time: 2Week 0 1 2 3 4 5 6 7 8 9 10Demand 45 50 40 40 40 40 40 40 40 40Scheduled Receipts 200Fermentors Released 1Inventory SpoilageInventory Position 100 55 205 165 125 85 45 5 -35 -40 -40Net Requirements 35 40 40Batched Net ReceiptsScheduled ReleasesFermentors SeizedTotal Fermentors Occupied 1

Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10Demand 35 40 40 40 40 40 40 40 50 50Scheduled ReceiptsFermentors ReleasedInventory SpoilageInventory Position 150 115 75 35 -5 160 120 80 40 -10 -50Net Requirements 5 10 50Batched Net Receipts 200Scheduled Releases 200Fermentors Seized 1Total Fermentors Occupied 1 1 1

A feasible schedule with spoilage effects



Pale Ale Fermentation Time: 2Week 0 1 2 3 4 5 6 7 8 9 10Demand 45 50 40 40 40 40 40 40 40 40Scheduled Receipts 200Fermentors Released 1Inventory Spoilage 45Inventory Position 100 255 205 165 125 85 245 160 120 80 40Net RequirementsBatched Net Receipts 200Scheduled Releases 200Fermentors Seized 1Total Fermentors Occupied 1 1

Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10Demand 35 40 30 30 40 40 40 40 50 50Scheduled ReceiptsFermentors ReleasedInventory Spoilage 5Inventory Position 150 115 75 45 215 175 135 95 55 5 150Net RequirementsBatched Net Receipts 200 200Scheduled Releases 200 200Fermentors Seized 1 1Total Fermentors Occupied 1 1 1 1 1 1

Computing Spoilage and Modified Inventory Position

Spoilage:SPi = max{0, IPi-1-SRi-1+SRi-2+…+SRi-sl+1)

-BNRi-1+BNRi-2+…+BNRi-sl+1)}

Inventory Position:

IPi = max{IPi-1,0}+ SRi+BNRi -Di-SPi

(Material Balance Equation)

iDi

IPi

(IPi-1)+

SRi+BNRi

SPi

The Driving Logic behind the Empirical Approach

Demand Availability:•Initial Inventory Position•Scheduled Receipts due to initiated production or subcontracting

Future inventories

NetRequirements

Lot Sizing

ScheduledReleases

Resource (Fermentor)Occupancy Product i

FeasibilityTesting

Master Production Schedule

ScheduleInfeasibilities

ReviseProd. Reqs

Compute FutureInventory Positions

Manufacturing Resource Planning&

Scheduling

MRP II:

The “MRP Explosion” Calculus

BOM

MRPMPS

Current Availabilities

PlannedOrder Releases

PriorityPlanning

LeadTimes

Lot SizingPolicies

Example: The (complete) MRP Explosion Calculus

Item BOM:

Alpha

C(2)D(2)

B(1) C(1)

E(1)

E(1)

F(1)

F(1)

Item Lead Time Current Inv. Pos.Alpha 1 10

B 2 20C 3 0D 1 100E 1 10F 1 50

Gross Reqs for AlphaPeriod 6 7 8 9 10 11 12 13Gross Reqs. 50 50 100

Item Levels:

Level 0: Alpha Level 1: B Level 2: C, D Level 3: E, F

The “MRP Explosion” Calculus

Level 0

Level 1

Level 2

Level N

InitialInventories

ScheduledReceipts

External Demand

CapacityPlanning

Planned Order ReleasesGross Requirements

(borrowed from Heizer and Render)

Computing the item Scheduled Releases

Item CPeriod 1 2 3 4 5 6 7 8 9 10 11 12Gross Requirements 12 10 90 75Scheduled Receipts 20Inventory Position: 20 20 40 40 40 40 28 18 18 -72 0 -75 0Net Requirements 72 75Planned Sched. Receipts 72 75Planned Sched. Releases 72 75

Synthesizingitem demand

series

ProjectingInv. Positions

andNet Reqs.

Lot Sizing Time-Phasing

ParentSched. Rel.

Item ExternalDemand

Gross Reqs

ScheduledReceipts

InitialInventory

Safety StockRequirements

NetReqs

Lot SizingPolicy

Planned OrderReceipts

Lead Time

Planned OrderReleases

Lot Sizing• If affordable, a lot-for-lot (L4L) policy will incur the lowest inventory holding

costs and it will maintain a smoother production flow.• Possible reasons for departure from a L4L policy:

– High set up times and costs => need for serial process batching to control the capacity losses

– Processes that require a large production volume in order to maintain a high utilization (e.g., fermentors, furnaces, etc.) => need for parallel process batching

• Selection of a pertinent process batch size– It must be large enough to maintain feasibility of the production requirements– It must control the incurred

• inventory holding costs, and/or• part delays (this is a measure of disruption to the production flow caused

by batching)• Move or transfer batches: The quantities in which parts are moved between the

successive processing stations.– They should be as small as possible to maintain a smooth process flow

Some Lot Sizing Methods employed in the traditional MRP framework

• Main focus: Balance set-up and holding costs• Wagner-Whitin Algorithm for dynamic Lot Sizing• Economic Order Quantity (EOQ): Compute a lot size using the EOQ formula with the

demand rate D set equal to the average of the net requirements observed over the considered planning horizon.

• Periodic Order Quantity (POQ): Compute T = round(EOQ/D), and every time you schedule a new lot, size it to cover the net requirements for the subsequent T periods.

• Silver-Meal (SM): Every time you start a new lot, keep adding the net requirements of the subsequent periods, as long as the average (setup plus holding) cost per period decreases.

• Least Unit Cost (LUC): Every time you start a new lot, keep adding the net requirements of the subsequent periods, as long as the average (setup plus holding) cost per unit decreases.

• Part Period Balancing (PPB): Every time you start a new lot, add a number of subsequent periods such that the total holding cost matches the lot set up cost as much as possible.

Optimal Parallel Batching: A factory physics approach

Model Parameters:k: (parallel) batch size B: maximum batch sizera: arrival rate (parts/hr) ca: CV of inter-arrival timest: batch processing time (hrs) ce: CV for effective batch processing time

Then CT = WTBT + CTq+t

aaaa rkkk

krrk

rkWTBT

21

2)1(1]1...10[1 −

=−

=−

+++=

trktkru

kc

ktkct

uucc

CT aaa

a

aa

eaq b

b >⇒<===−

+= 1 ;

) ;

12

2

2

22

22 σ

From the above,

tu

uckcku

kttu

uckcr

kCT eaea

a

]112

/2

1[12

/2

1 2222

+−

++

−=+

−+

+−

=Remark: Notice that CT as u1 but also as u0 !

Determining an “optimal” batch sizeLet um rat . Then u = um / k k = um / u . Substituting this expression for k in the expression for CT, we get:

tu

ucuucuuut

uuckc

kukCT ema

m

mea ]112

/2

1/[]112

/2

1[2222

+−

++

−=+

−+

+−

=

Recognizing that 022

⏐⏐ →⏐= ∞→ka

m

ak

cu

uc , we set 02

→≅βm

au

uc and we get

tu

uytu

ucuu

CTm

e

m

]12

12

)([]1122

121[

2

+−=+−

++−≈β

where uuc

uuy e −

++≡1)

1) 2β

To minimize CT, it suffices to minimize y(u). This can be achieved as follows:

22

2*22

22

222

1

11

1012)1(0

)1()()1()(

ee

ee

e

ccc

uuucuu

ucudu

udy

++=

−+++−

=⇒=−+−+⇒=−

++−−=

βββ

ββ

and 1c

1u 0e

*

+≈⇒≈β which further implies that trctrk aea >+≈ )1*

Remark: If ce2 0, the term β in the original expression for u* will significant. In that case,

we can set em

a

cuc

+≈

112

*β and obtain u* and k* as before.

Finite-Capacity Planning & Scheduling in the MRP II / ERP context:

Load Reports (Example)Availableresourcetime

Periods1 2 3 4 5 6 7 8

50

100

150

Finite-Capacity Planning & Scheduling in the MRP II / ERP context: More Systematic Approaches

• Bottleneck-based scheduling in a cellular manufacturing context (Goldratt’s Theory of Constraints approach):– Each part (family) has its own production cell with a well-defined bottleneck resource.– Production is scheduled on the bottleneck resource and the schedule for the other

resources are organized around this schedule by taking consideration the expected cycle times.

– Typically, a “cushion” of extra workload is maintained at the bottleneck in order to prevent its starvation, in case of any disruptions in the upstream processes.

– If the bottleneck supports the production of more than one part types, a “single-machine” scheduling problem arises naturally. This is addressed by selecting an appropriate dispatching rule.

• Earliest Due Date (EDD) => minimizes maximum lateness (tardiness)• Least slack (LS), where slack = difference between job due date and expected

completion time => tend to reduce average tardiness• Shortest Processing Time (SPT) => minimizes average flowtime at the bottleneck,

and (by Little’s law) average WIP• Other heuristics addressing different problem variations including weighted

performance measures, non-zero release times, etc.

Finite-Capacity Planning & Scheduling in the MRP II / ERP context:

More Systematic Approaches (cont.)• Cases where the previous approach is not effective:

– There are more than one capacity-constrained resource– Bottlenecks are shifting depending on the product mix– There are operations involving parallel process batching– Process routes are non-linear (e.g., due to routing flexibility, re-entrance, extensive

need for rework)• Remark: The semiconductor manufacturing operational context is a typical example of

all of the above.• A more global view of the system operations is necessary in order to support effective

and efficient scheduling.• Possible approaches

– Employ a set of pertinently selected dispatching rules at the different (critical) resources, and assess its efficacy through simulation (possibly maintain a bank of such rules for different operational conditions – meta-heuristics)

– Generate efficient (not necessarily optimal) global schedules by employing an approach that searches for such a schedule in the space of feasible schedules

Typical approaches employed in the solution of the job shop scheduling problem

• Branch & Bound (B&B): Constructs all possible schedules incrementally, fathoming options that are clearly suboptimal to some other options. Can generate optimal schedules but it is very time consuming.

• Beam search: Similar to B&B, but it employs additional heuristics to increase fathoming.• Local search techniques: Given an initially constructed schedule, try to identify an

improved schedule that is obtained from the original one through a localized change (e.g., through the change of the order of two jobs on a single machine); repeat. Also, need a mechanism to avoid local optima.– Simulated annealing: Seeks to avoid local optima by maintaining a non-zero

probability for transitioning to an inferior schedule. However, this probability is reduced with the passage of time.

– Tabu search: Seeks to avoid local optima by pronouncing certain schedule changes as taboo (these changes are apparent improvements that might attract the schedule back to a local optimum)

– Genetic algorithms: Maintains an entire set of schedules at each iteration, and it updates this set by replacing schedules of inferior performance with new schedules resulting from the “combination” of the most efficient schedules currently available; the synthesis of such new schedules is known as “crossover”. Also, “mutation” provides additional schedules resulting from the local modification of some single schedules.

(borrowed from Heizer and Render)

Pegging and Bottom-up Replanning

Some Limitations of MRP-based Planning• The employment of fixed nominal lead times

– This problem is mitigated in case of a stable operational environment where past experience and / or approximate formal models can provide insight for setting lead times

– Lead time assessment is also facilitated by a well-structured, cellular shop-floor• Possible system nervousness due to re-planning and the applied lot sizing

policies– Potential remedies

• Firm orders• Time fences• L4L planning whenever possible

• Lack of an inherent mechanism for detecting and managing shop-floor congestion – a purely “Push” approach– However, it is possible to combine the planning visibility offered by the MRP

explosion calculus with more sophisticated production control mechanisms that take advantage of the existing technology of Manufacturing Execution Systems (MES).

The Revolution of Just-In-Time (JIT) andLean Manufacturing

The essence of the JIT revolution and Lean Manufacturing

• Try to reduce the system operational inefficiencies and the resulting waste by identifying the sources of these inefficiencies and working proactively to eliminate them as much as possible.

• In the emerging philosophy, inventories should be carefully controlled and they should not function as the mechanism for accommodating the system inefficiencies => Just-In-Time (JIT)

• The aforementioned effort should be an ongoing process towards continuous improvement rather than one-time/shot effort.

Targeting the sources of inefficiency– input

• unreliable quality of raw material• unreliable delivery times

– operation• unreliable processes in terms of

– required processing times– process outcome

• complex interacting process flows• long set-up times• unreliable (irresponsive and irresponsible) personnel

– output• Highly variable production requirements in terms of

– production volume, and– production scope

JIT enabling factors and practices• Emphasis on quality at both the process and the supply side by promoting

– Statistical Process Control (SPC) theory and practice– Quality certification programs– Deployment of stable automated processes and foolproof practices (like

checklists and machines gauges) to guarantee the desired performance– Employee empowerment and knowledge management (quality circles)

• “Tightening” of the supply chain by promoting– Long-lasting and trustful relationships between the different parties in the supply

chain– Timely and reliable information flow across these parties that takes advantage of

modern IT technologies, like• Electronic Data Interchange (EDI), and e-commerce practices• Real-time communications and global positioning systems

– Promotion of vendor owned and managed inventory practices that• Establish economies of scale and protection to variability through pooling• Enhance the demand visibility across the entire supply chain.

JIT enabling factors and practices (cont.)• Simplification of the process flows by promoting cellular manufacturing practices

– Dedication of separate production cells to product families with similar processing requirements

– U-shaped layouts for facilitating employee sharing– Employee cross-training for more flexible and higher utilization

• Set-up time reduction through– The adoption of cellular manufacturing – Externalization of set-up times– Employment of flexible processes and pertinent auxiliary equipment like pertinent fixtures– Part standardization

• Focus on repetitive manufacturing and promote the establishment of stable production rates through

– Smoothing of the aggregate production requirements by appropriate quota setting – Pertinent sequencing of the final assembly to support a desired product mix– Use of buffer capacity (planned overtime) to protect against slippages from the target

production rates– Component standardization

Institutionalizing the JIT practice through the KANBAN-based

Production Authorization MechanismStation 1 Station 2 Station 3

Remarks:• The KANBANS at each station cap the WIP at that station and they offer a natural mechanism for reacting to various disruptions taking place in the system operation.• In particular, production at each station is “pulled” as a result of the downstream activity rather than “pushed” by an MPS-generated schedule.• The KANBANS at each station should be set at a level that enables production at the target rate• A safe approach to set the KANBAN level at each station is by setting it initially to the “historical” WIP level, and subsequently decrease it incrementally while observing its impact on the production rate• Frequent KANBAN changes are ineffective, since the production rate of the line is rather insensitive to these changes, and they should be avoided

From KANBAN to CONWIPStation 1 Station 2 Station 3 FGI

Why?• It maintains the WIP cap but at the same time it offers more operational flexibility than KANBAN.• The unrestricted flow of WIP within the line enables better utilization of the (shifting) bottleneck, and therefore, higher throughput.• Less stress for the line operators since it enables them to work at the “natural pace” of the line.• It enables more flexible scheduling of the line, since in the CONWIP operational context, WIP is interpreted more generally as some aggregate amount of workload loaded into the line (even measured in time-units, rather than number of parts) – new parts are pulled from an available “work backlog” according to a pertinent set of dispatching rules.• Easier to analyze and parameterize through the theory of closed-queueing networks.• Remark: While the above features of CONWIP mitigate the rigidity of the KANBAN-based shop-floor control, its “pull” nature still implies that it requires stable target production rates in order to function well, and therefore, it is appropriate for repetitive manufacturing contexts.

A CONWIP-based “pull” framework(borrowed from Hopp & Spearman)

Course Outline• 1. Inventory Control Theory

– The basic EOQ model and some of its variants– Replenishment coordinating approaches– Dynamic Lot Sizing– Statistical Inventory Control Models

• The News Vendor Model• The Base Stock Model• The (Q,r) Model

– An introduction to multi-echelon models

2. Factory Physics: A queueing-theoretic analysis of serial production systems– Characterizing a flow line as a queueing system– Some fundamental relationships between the line attributes and its performance indices– The nature, role and impact of the operational variability– An introduction to logical control of production systems

Course Outline• 3. Integrating the Factory Physics insights to the OM practice

– Process Design, Capacity Planning and Line Balancing– Hierarchical Production Planning

• The classical hierarchical planning framework• Forecasting• Aggregate Planning• Master Production Scheduling (MPS) and Material Requirement Planning (MRP), and their

limitations• Shop floor scheduling

– Just-in-Time (JIT) and Lean Manufacturing• The JIT philosophy• JIT practices and the KANBAN production authorization system• Shop-floor control based on the CONWIP production authorization model• Production Planning and Scheduling for CONWIP-controlled production systems• The JIT limitations

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Documents

Disaggregation and Master Production Scheduling (MPS)