Impact of shortages on hybrid push-pull

production systems

Paulo Gonçalves(paulog@mit.edu)

ISCM meeting– Cambridge, MADecember 4, 2002

Sloan School of ManagementMassachusetts Institute of Technology

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Variability in Capacity Utilization

INTRODUCTION

Year 1 Year 3 Year 5 Year 7

Cap

aci

ty U

tiliz

ati

on

(A

ll fa

cilit

ies)

25%

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Relevance…

Just-in-time delivery is important:

“All of our [customers] are trying to operate with essentially zero

inventory. They need just-in-time delivery from us and real-time

feedback from the marketplace.” Alan Baldwin, VP planning and

logistics [1]

But JIT is hard to accomplish:

“Demand was very high for Christmas. We came out of Q4 with

lean inventory, and demand has continued to be high,” despite

the historical pattern of a first-quarter letdown. [2]

[1] CIO Magazine, August 15, 1998; [2] Souza (2000) “...as Intel processor shortage pinches OEM earnings” EBN Online, January 28.

INTRODUCTION

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

… And Implications

Supplier view: supply operations manager: [3]

“If Intel does not have the part, customers will tentatively work with

us, that means that they may have to wait. But if they cannot get it,

they might go to AMD.”

Customer’s response: response to chip shortages: [4]

“Gateway Inc. said it will increase the number of microprocessors it

buys from Advanced Micro Devices Inc. to offset Intel Corp.'s

inability to match rising demand.”

[3] Personal interview; [4] Hachman (2000) “Components shortage squeezing profits out of the supply chain” EBN, May 26

INTRODUCTION

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Related Literature

INTRODUCTION

Instability in supply chains in different contextsForrester (1961)

Morecroft (1980)

Sterman (1989a, 1989b)

Diehl and Sterman (1995)

Baganha and Cohen (1996)

Lee et al. (1997a, 1997b)

Anderson and Fine (1999)

Chen et al. (2000)

Graves (2000)

Hybrid systems outperform push and pull systems Hodgson and Wang (1991a, 1991b)

Spearman and Zazanis (1992)

Simulation software for hybrid systemsWang et al. (1996)

Wang and Xu (1997)

Huang et al. (1998)

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Pure Systems

Push systemProduction based on long-term forecastsFlows determined by volume in each stock

MODEL FORMULATION

Pull systemsShipments based on current demandFlows determined by downstream replenishment signals

Fabrication+

Assembly+ Finished

Goods+

Mfg CycleTime

-

AssemblyTime

ShipmentTime

- -

DesiredProduction Forecast

CustomerDemand

+

+

Fabrication Assembly FinishedGoods

CustomerDemand

+

+

ReplenishFinish Goods

ReplenishAssembly

ReplenishFabrication

+ +

++

+

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Hybrid System: Semiconductor Manufacturer

MODEL FORMULATION

FabricationWIP

FinishedGoods

InventoryWaferStarts

GrossProduction

Rate

Shipments

DesiredWaferStarts

ThroughputTime

+

AssemblyWIP Gross

AssemblyCompletion

CustomerDemand

+ +

ReplacingShipments

+

+

+ ForecastedCustomerDemand

+DELAY

++

Hybrid push-pull systemsUpstream = push (wafer fabrication: TPT~13 weeks)

Downstream = pull (assembly testing and packaging: TPT~1 week)

Outperform pure push and pure pull systems

Wafers Dies Chips

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Semiconductor Manufacturing Process and Products

MODEL FORMULATION

Fabricatedwafers

Finished die Packaged chip

Silicon Wafers

Wafer Starts

Fabrication WIP

Assembly WIP

Finish Goods Inventory

Gross Fab.Rate

Gross Asbly.Rate

ShipRate

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Full Model: Stock and Flow Diagram

Incorporate additional complexityInventory management at each stageNonlinear constraints on AWIP and FGIEndogenous demand - low service level leads to lost sales

MODEL FORMULATION

FabricationWIP

(FabWIP)

FinishedGoods

Inventory(FGI)Wafer

StartsGross

ProductionRate

Shipments

DesiredWaferStarts

+ AssemblyWIP

(AWIP)Gross

AssemblyCompletion

AWIP*

AWIPAdjust

++

-

MarketShare

+

CustomerDemand

+

Fraction ofOrders Filled

+

ReplacingShipments +

+

+

+

+

-

R1

Growth ThroughService

B5

Lostsales

ForecastedCustomerDemand

B2

AdjustAWIP

+DELAY

R2

+

ProductionPush

B4 DemandPull

+

DELAY

FabWIP*

FabWIPAdjust

++

-B1

AdjustFabWIP

FGI*

FGIAdjust

+

-

+

B3

AdjustFGI

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Simulation Analysis: Behavior Over Time

MODEL ANALYSIS

System oscillates in response to pulse inputSize of demand pulse matters in final system behavior

System can recover from a small pulse

Large pulse can lead to permanent decrease in performance

Pulse 20% 1 1 1

Pulse 30% 2 2 2

100

75

50

25

0

2 2 22 2

2

2

2

2 2

2

2

2

2

2

2

2

1 1 1 11 1 1 1 1

11

11

11 1 1 1

0 12 24 36 48 60 72

Mar

ket

Seg

men

t S

har

e (M

SS

) (%

)

Time (Months)

2 2 2

2

2

2

2

2

2

2

22

2

2 2

2

2

1 1 1

1

1

1

1

1

1

1

1

1

11 1

1

1

1

0 12 24 36 48 60 72

100

75

50

25

0

Fra

ctio

n o

f O

rder

s F

illed

(F

oF

) (%

)

Pulse 20% 1 1 1

Pulse 30% 2 2 2

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS 11

Analytical Approach: Eingevalue Analysis

Relies on link and loop eigenvalue elasticity:

Forrester 1982, 1983; Kampmann 1996, Gonçalves et al.

2000

Methodology: borrows from linear systems

theory

Linearize the system at every point in time

Compute eigenvalues

Map the evolution of eigenvalues over time

Analyze how eigenvalues change with each feedback loop

MODEL ANALYSIS

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Eigenvalues Describe System Behavior

MODEL ANALYSIS

Positive real eigenvalues lead to exponential growthNegative real eigenvalues lead to exponential decayComplex eigenvalues lead to oscillations

Re(x)

Im(x)

X X

X

X

X

X

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Eigenvalue Analysis: Shifts in Structure

MODEL ANALYSIS

One pair of eigenvalues can evolve out of stabilityEigenvalues change dramatically when

Nonlinearities are bindingShifts in feedback structure occur

-2

-1.5

-1

-0.5

0

0.5

1

1.5

47 48 49 50 51 52 53 54

RealE1&E2 ImagE1 ImagE2

Phase 1 Phase 2 Phase 3

B2 B5 B4 R2

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Eigenvalue Analysis: Active Supply Chain

MODEL ANALYSIS

Binding constraints shift the dominant feedback structureActive supply chain changes from push-pull to push each cycleFeedback structure of production push (R2) is highly unstable

Dominant Feedback Loop

Active Supply Chain

Active Constraints

Phase 1

Adjust AWIP (B2) PushPullPull---

Phase 2

Lost Sales (B5) PushPullPushFGI

Phase 3

Production Push (R2) PushPushPushFGI

AWIPFabWIP FGI

+

AWIP

++

FabWIP FGI

+

AWIP

+

FabWIP FGI

+

AWIP

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Eigenvalue Analysis: Policy Implementation

Implemented policy: Maintain AWIP to meet desired shareAWIP* > (1+s) AWIPReqMSS*, where s=0.05

Implemented policy is stabilizing

MODEL ANALYSIS

100

75

50

25

0

2 2 2 2 2

2

2

2

2 2

2

2

2

2

2

2

2

1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1

0 12 24 36 48 60 72

Ma

rke

t S

eg

me

nt

Sh

are

(M

SS

) (%

)

Time (Months)

Policy w/ Pulse 20%Policy w/ Pulse 30%Pulse 20%Pulse 30%

1 1 12 2 2

INTRODUCTION MODEL FORMULATION MODEL ANALYSIS CONCLUSIONS

Insights and ImplicationsManagerial insights

Policy heuristic - maintain assembly inventory to meet target

market share - can improve capacity utilization and service level

Shed light on tradeoff between lean inventory strategies and hybrid

push-pull production systems

Theoretical contributionsModeling customer demand endogenously leads to a different

inventory strategy for the company

Stock-outs can change the system mode of operation from the

desired PUSH-PULL to a PUSH system

The shift in operation mode can influence demand variability and

service level

Extends linear systems theory to analyze nonlinear systems

through the evolution of eigenvalues plot

CONCLUSIONS