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Linear & Nonlinear WIP Clearing in Supply Chain Operations Planning

Barış Selçuk, Jan C. Fransoo and A. (Ton) G. De Kok

5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

PU1I0 PU2I1 PU3I2 I3 Customers

SCOP

L1 L2 L3

OPU1 OPU2 OPU3

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Clearing functions in the literature

• Graves (1986), "Fixed lead time"• Karmarkar (1989), "Saturating"

– Zäpfel and Missbauer (1993), Missbauer (2002)

– Asmundsson et.al. (2005)

• Billington et.al. (1983), Hackman and Leachman (1989), "Combined"

μ

α

Fixed Capacity

Fixed Lead Time

Combined

Saturating

WIP

Thr

ough

put

Clearing Function: The mathematical representation of expected throughput over a time period as a function of the work-in-process (WIP) over that period.

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Three different WIP clearing assumptions

5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

tan ,tan

,

WIP if WIPThroughput

otherwise

Traditional Linear (TL):

212

D

WIPThroughput

dWIP

Long Term Nonlinear (LTN):

1

0 ! !

k kWIP

k k WIP

Throughput k e WIP ek k

Short Term Nonlinear (STN):

SCOP

OPU

PU, Exp(μ)R F Customers2, Dd

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Supply Chain Operations Planning (SCOP)

,W t t

5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

SCOP

OPU

PUR F Customers

Demand forecasts , , ,I t t B t t

1 1

1 1 0 0

. , , , ,T T L T L T

f w r qs s s s

Min h I t t s h W t t s c R t t s c Q t t s

,R t t

, 1 , 1 , , , ,I t t s B t t s I t t s B t t s R t t s L d t t s

, 1 , , ,W t t s W t t s R t t s Q t t s

1

0

, , ,t s L

k

W t t s R t t s Q t t s k

, , ,nQ t t s f W t t s R t t s

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Operations Planning Unit (OPU)

,W t t

SCOP

OPU

PUR F Customers

Demand forecasts , , ,I t t B t t

,R t t

( , ), , , ,w t t i t t b t t( , )r t t

1

1 1 0

, , , , ,f w r qs s s

Min h i t t s M b t t s h w t t s c r t t s c q t t s

, 1 , 1 , , , ,i t t s b t t s i t t s b t t s q t t s R t s L t s L

, 1 , , ,w t t s w t t s r t t s q t t s

, , ,nq t t s f w t t s r t t s

Advanced:

, , ,r t t R t tSimple:

, ,w t t W t t

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Experimental design

STNLTN

TL

L=4

Factors Treatments

Clearing Function: TL, LTN, STN

Operational Planning: Simple, Advanced

Utilization: 80%, 90%

Demand Uncertainty: 10%, 50%, 100%

# of Treatments: 36

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Results: Costs

Utilization: 80%, Operational planning: Simple

Utilization: 90%, Operational planning: Simple

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Results: Costs

Utilization: 80%, Operational planning: Advanced

Utilization: 90%, Operational planning: Advanced

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Results: Costs

Conclusions:

• STN is the best choice for a lower total cost. STN provides lowest WIP while indifferent in echelon inventory for the majority of the cases.

• For modelling the short term behaviour in the shop STN clearing function is favorable to TL and LTN clearing functions. SCOP model has a better anticipation of the operational dynamics of the manufacturer in the near future.

• Advanced operational planning is better off only for STN, but not for TL and LTN.

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Results: Delivery performance

Utilization: 80%, Operational planning: Simple

Utilization: 90%, Operational planning: Simple

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Results: Delivery performance

Utilization: 80%, Operational planning: Advanced

Utilization: 90%, Operational planning: Advanced

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Results: Delivery performance

Conclusions:

• For simple operational planning function, STN provides the best delivery performance while TL provides the worst.

• For advanced operational planning function, TL provides the best delivery performance while STN provides the worst.

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5th Int'l Conference on "Analysis of Manufacturing Systems – Production Management", Zakynthos Island, Greece

Future Research

• Development of models and providing analysis for multi-stage manufacturing.

• Development of a lead time adaptive approach for supply chain operations planning.– Single-stage manufacturer and distributor.

– Multi-stage manufacturing.