Sloan School of Management
Massachusetts Institute of Technology
Impact of shortages on
hybrid push-pull
production systems
Paulo Gonçalves
(paulog@mit.edu)
ISCM meeting– Cambridge, MA
December 4, 2002
Capacity Utilization
Variability in Capacity Utilization
(All facilities)
25%
Year 1
INTRODUCTION
INTRODUCTION
Year 3
MODEL FORMULATION
Year 5
MODEL ANALYSIS
Year 7
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
Instability in supply chains in different contexts
Forrester (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 systems
Wang et al. (1996)
Wang and Xu (1997)
Huang et al. (1998)
INTRODUCTION
INTRODUCTION
MODEL FORMULATION
MODEL ANALYSIS
CONCLUSIONS
Pure Systems
+
+
Push system
+
-
-
Desired
Production
Assembly
Time
Mfg Cycle
Time
Replenish
Assembly
Replenish
Fabrication
Fabrication
Replenish
Finish Goods
+
+
+
+
Assembly
Pull systems
Shipments based on current demand
Flows determined by downstream replenishment signals
MODEL FORMULATION
FORMULATION
MODEL
MODEL ANALYSIS
+
+
-
Shipment
Time
Forecast
Customer
Demand
+
Production based on long-term forecasts
Flows determined by volume in each stock
INTRODUCTION
Finished +
Goods
Assembly
Fabrication
Finished
Goods
Customer
Demand
CONCLUSIONS
+
Hybrid System: Semiconductor Manufacturer
Replacing
Shipments
Wafers
Dies
Fabrication
WIP
Assembly
WIP
Chips
+
Wafer
Starts
+
Desired
Wafer
Starts
Gross
Production
+
Rate
Gross
Assembly
+ Completion
Throughput
Time
+
+
Forecasted +
Customer
Demand
Finished
Goods
Inventory
Shipments
++
Customer
Demand
DELAY
Hybrid push-pull systems
Upstream = push (wafer fabrication: TPT~13 weeks)
Downstream = pull (assembly testing and packaging: TPT~1 week)
Outperform pure push and pure pull systems
INTRODUCTION
MODEL FORMULATION
FORMULATION
MODEL
MODEL ANALYSIS
CONCLUSIONS
Semiconductor Manufacturing Process and Products
Fabrication
WIP
Assembly
WIP
Finish Goods
Inventory
Silicon
Wafers
Wafer
Starts
Gross
Fab.
Rate
Fabricated
wafers
INTRODUCTION
MODEL FORMULATION
FORMULATION
MODEL
Gross
Asbly.
Rate
Finished
die
MODEL ANALYSIS
Ship
Rate
Packaged
chip
CONCLUSIONS
Full Model: Stock and Flow Diagram
Replacing
Shipments +
Demand
Pull
B4
Wafer
Starts
+
Fabrication
WIP
(FabWIP)
B1
-
Adjust FabWIP
FabWIP Adjust
+
+
Desired
FabWIP*
Wafer
+
+
Starts
+
+
Gross
Production
Rate
B2
Adjust
AWIP
Finished
Goods
Inventory
(FGI)
+
+
Gross
Assembly
Completion
Assembly
WIP
(AWIP)
R1
B3
-
-
Adjust
FGI
AWIP
Adjust
Growth Through
Service
FGI
Adjust
+
-
+
FGI*
AWIP*
R2
Production
Push
Forecasted
Customer +
Demand
Shipments
+
+
+
Fraction of
Orders Filled
B5
Customer
Demand
+
DELAY
Lost
sales
Market
Share
DELAY
+
Incorporate additional complexity
Inventory management at each stage
Nonlinear constraints on AWIP and FGI
Endogenous demand - low service level leads to lost sales
INTRODUCTION
MODEL FORMULATION
FORMULATION
MODEL
MODEL ANALYSIS
CONCLUSIONS
100
100
1 2 12 1 2 1
75
2 12 1
12 1
1
2 12
1
1
1
1
1
2
1
2
50
1
2
2
2
1
Fraction of Orders Filled (FoF) (%)
Market Segment Share (MSS) (%)
Simulation Analysis: Behavior Over Time
2
2
2
2
25
Pulse 20%
Pulse 30%
1
1
1
2
2
2
0
12 12 12
1
1
1
2
1
1
2
1
12
1
1
2
75
1
1
1
2 1
1
50
2 1
2
2
2
2
2
2
2
25
Pulse 20%
Pulse 30%
1
1
1
2
2
2
2
0
0
12
24
36
48
60
72
0
12
24
36
48
60
Time (Months)
System oscillates in response to pulse input
Size of demand pulse matters in final system behavior
System can recover from a small pulse
Large pulse can lead to permanent decrease in performance
INTRODUCTION
MODEL FORMULATION
MODELANALYSIS
ANALYSIS
MODEL
CONCLUSIONS
72
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
INTRODUCTION
MODEL FORMULATION
MODELANALYSIS
ANALYSIS
MODEL
CONCLUSIONS
11
Eigenvalues Describe System Behavior
Im(x)
X
X
X
X
Re(x)
X
X
Positive real eigenvalues lead to exponential growth
Negative real eigenvalues lead to exponential decay
Complex eigenvalues lead to oscillations
INTRODUCTION
MODEL FORMULATION
MODELANALYSIS
ANALYSIS
MODEL
CONCLUSIONS
Eigenvalue Analysis: Shifts in Structure
1.5
Phase 1
Phase 2
Phase 3
1
0.5
B2
B5
B4
R2
0
47
48
49
50
51
52
53
54
-0.5
-1
-1.5
-2
R eal E1&E2
I mag E1
I mag E2
One pair of eigenvalues can evolve out of stability
Eigenvalues change dramatically when
Nonlinearities are binding
Shifts in feedback structure occur
INTRODUCTION
MODEL FORMULATION
MODELANALYSIS
ANALYSIS
MODEL
CONCLUSIONS
Eigenvalue Analysis: Active Supply Chain
Dominant
Feedback Loop
Active Supply
Chain
Phase
1
Adjust AWIP (B2)
PushPullPull
Phase
2
Lost Sales (B5)
FabW IP
---
FGI
AW IP
+
PushPullPush
FGI
FabW IP
FGI
AW IP
+
Phase
3
Active
Constraints
Production Push (R2)
+
PushPushPush
FabW IP
FGI
AW IP
+
+
+
FGI
AWIP
Binding constraints shift the dominant feedback structure
Active supply chain changes from push-pull to push each cycle
Feedback structure of production push (R2) is highly unstable
INTRODUCTION
MODEL FORMULATION
MODELANALYSIS
ANALYSIS
MODEL
CONCLUSIONS
Market Segment Share (MSS) (%)
Eigenvalue Analysis: Policy Implementation
100
12
75
12
12
12
12
12
1
1
1
2
2
12
1
12
2
1
1
1
1
2
2
50
1
1
2
2
2
Policy w/ Pulse 20%
Policy w/ Pulse 30%
Pulse 20%
Pulse 30%
25
2
1
2
1
2
1
2
0
0
12
24
36
48
60
72
Time (Months)
Implemented policy: Maintain AWIP to meet desired share
AWIP* > (1+s) AWIPReqMSS*, where s=0.05
Implemented policy is stabilizing
INTRODUCTION
MODEL FORMULATION
MODELANALYSIS
ANALYSIS
MODEL
CONCLUSIONS
Insights and Implications
Managerial 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 contributions
Modeling 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
INTRODUCTION
MODEL FORMULATION
MODEL ANALYSIS
CONCLUSIONS
CONCLUSIONS