THE IMPACT OF CUSTOMER RESPONSE ON
INVENTORY AND UTILIZATION POLICIES
Paulo Gonçalves, Ph.D.
Assistant Professor
Management Science Department
School of Business Administration
University of Miami
Coral Gables, FL 33124
Phone: (305) 284-8613
Fax: (305) 284-2321
[email protected]
ACKNOWLEDGEMENT
Work reported here was funded by the Supply Chain Visualization Project at MIT and a Ph.D.
Fellowship from the Intel Foundation. The author thanks Gabriel Bitran, Charles Fine, Jim
Hines, Mary Murphy-Hoye, Jim Rice, and John Sterman for their support and comments on
earlier versions of this work. All errors are mine.
THE IMPACT OF CUSTOMER RESPONSE ON
INVENTORY AND UTILIZATION POLICIES
1
Due to part shortages, Boeing stopped production of its 747 airplane and delayed the final
assembly of the 737, leading to “more late deliveries, higher costs, upset customers and
depressed profits” (Holmes 1997). Faced with high demand for its Pentium III processors and
unable to meet demand, Intel planned to introduc e a new fabrication facility. In the following
year, however, Intel scrapped the project blaming an economic slowdown and order
cancellations (Gaither 2001). “Five months after health officials rationed [flu] vaccine because
of a shortage, now there's a glut with one manufacturer and major distributors facing lost revenue
totaling hundreds of millions of dollars” (Henderson 2005).
commonalities.
These stories share a few
First, they highlight that despite the emphasis on effective supply chain
manage ment during the last decade, companies in diverse industries still struggle with supply
chain glitches. Hendricks and Singhal (2003) suggest that glitches (e.g., part shortages, order
changes by customers, production and ramp-up and roll-out problems ) cause up to a 10%
reduction in shareholder value. Second, the stories involve upstream companies, hinting that
upstream companies may be particularly vulnerable to supply chain glitches due to higher
demand variability upstream (i.e., the bullwhip effect.)
Finally, the industries mentioned
(pharmaceuticals, airplane and semiconductor manufacturing) have manufacturing delays in the
order of several weeks or months, suggesting that long production delays, which affect the
company’s ability to maintain adequate inventory levels, can compound the demand variability
and supply chain glitches problems. This study explores how demand variability, supply chain
instability and long manufacturing delays interact and how this interaction may affect inventory
and utilization policies.
With that purpose, we present a model based on a year- long, in-depth field study of
Intel’s supply chain. The supply chain model captures the material flows associated with a
2
hybrid push-pull production system (composed of fabrication, assembly and finished goods) and
includes the customer respons e to the availability of a low-end product (e.g., Celeron
processors). The model incorporates two separate feedback effects associated with customer
response. First, a sales effect captures the balancing feedback whereby product shortages cause
customers to seek alternate sources of supply, reducing demand and easing the shortage.
Alternatively, it captures how an unexpected decrease in demand improves the manufacturer’s
short-term ability to fill orders, allowing it to satisfy customers, increasing its attractiveness and
also its future demand. Second, the production effect captures the reinforcing feedback by which
changes in demand have a delayed impact on the manufacturer’s production decisions. If
demand falls, manufacturers reduce demand forecasts and capacity utilization to avoid excess
inventory. Lower production leads to lower inventory and poor service level, causing a drop in
customer demand.
We show that customer response to inventory availability, through the balancing and
reinforcing feedbacks from the sales and production effects, affect the dynamic behavior of the
model and the inventory and utilization policies adopted by the manufacturer. Influenced by the
emphasis on lean production systems and just-in-time manufacturing, many firms attempt to
maintain low inventory levels and run lean supply chains, allowing them to reduce inventory
costs. However, the interaction of supply chain glitches and demand variability in companie s
faced with long manufacturing delays increases the likelihood of shortages and poor service
level, reducing the attractiveness of lean inventory policies. Furthermore, adopting a flexible
capacity utilization policy to quickly reduce production when demand decreases, may not be the
best response if customer demand is decreasing due to supply shortages and poor service levels.
This research suggests that when customers respond to inventory availability, the supplier should
3
maintain higher safety stock and reduce the responsiveness of utilization to changes in customer
demand caused by inadequate service levels. The model analyzed in this paper gives insights
into the costs of lean inventory strategies and responsive utilization policies in the context of
production systems with long delays subject to customer response.
RESEARCH SITE
The results reported here draw on a year- long, in-depth analysis of Intel Corporation’s
supply chain performed during 2000 and 2001. Intel’s research in silicon, advanced process
technology and manufacturing has allowed them to achieve and maintain industry leadership in
semiconductor manufacturing. Intel has consistently transitioned to processes that significantly
reduce the line width of the metal circuits (e.g., from 0.18- to 0.15- to 0.13 and to 0.09- microns),
allowing it to pack more chips per wafer. At the current line width of 0.09- microns Intel’s
microprocessors contain some 330 million transistors. In parallel, the company has adopted
larger silicon wafers. The new generation 300- millimeter (12- inch) diameter silicon wafer yields
almost two and a half times as many chips as the earlier generation 200-mm (8- inch) diameter
wafers.
In terms of the scale of its operations, Intel is truly a global company. It has 11
fabrication facilities, or Fabs (e.g., Israel, Ireland, Oregon, etc.) and 6 assembly and test facilities
worldwide (e.g., Shanghai, Philippines, Malaysia, etc.), with multiple products (e.g., Pentium
and Celeron processors), and, often times, processes running in each fabrication facility. Intel
employs about 80,000 people worldwide, of which 1,500 are planners responsible for overall
Divisional, Fab, and Assembly planning. Planners schedule production and assembly among the
multiple Fabs and Assembly plants world wide and manage the variability in product line while
matching supply and demand. Model development incorporated the physics of semiconductor
4
manufacturing and the heuristics associated with planning and decision- making. In total, we
conducted almost one hundred semi-structured interviews both during four site visits and through
weekly conference calls with managers in diverse areas, such as supply chain management,
demand forecasting, sales, marketing, etc. The research also involved reviewing Intel’s logs
detailing guidelines for decision- making, and collecting quantitative (e.g., quarterly capacity,
utilization, wafer starts) and qualitative (e.g., managers’ decision heuristics, company’s
guidelines and incentives) data.
SEMICONDUCTOR MANUFACTURING
Semiconductor manufacturing can be divided into a fabrication phase and an assembly
phase. The first phase takes place in a wafer fabrication facility (or Fab) taking wafers, 200
mm/300 mm polished disk-shaped silicon substrates, as the main input to the process. A reentrant flow process, with the same equipment performing multiple steps at different stages of
fabrication, characterizes fabrication. These steps include photolithography, etching, thin films,
diffusion, and ion implantation. The thin film process deposits layers of material (such as
photoresist, insulation between layers, and metal for electrical interconnections) to the entire
surface of the wafer. The photolithography, or lithography, process projects ultraviolet light
through a patterned mask to impose a pattern on an existing photosensitive layer (called
photoresist.) The wafer can then be chemically washed to dissolve the exposed or unexposed
resist. The etch process removes materials from the wafer’s surface. Ion implantation introduces
impurity, or dopant, ions into specific areas of the wafer to modify its electrical properties.
Diffusion is a high temperature process used to either form layers through a chemical reaction or
to thermally treat an existing layer. The process turns polished wafers into fabricated wafers
with hundreds of - inch square integrated circuits, or dies. A vertical cross-section of an
5
integrated circuit reveals a number of layers. Lower layers, produced at the “front-end” of the
fabrication process, include the critical electrical components (e.g., transistors, capacitors).
Upper layers, produced at the “back-end” of the fabrication process, connect the electrical
components to form circuits.
In the assembly phase, the fabricated wafers are cut into dies and stored in Assembly Die
Inventory (ADI) warehouses, collocated with Assembly/Test plants. The dies are packaged to
protect the integrated circuit from the environment and allow the attachment of metal connectors.
Packaged processors are then tested to ensure operability and those that pass the tests are stored
in finished goods warehouses. While fabrication facilities, assembly plants and distribution
centers are dispersed throughout the world, an aggregated representation of the manufacturing
and distribution process provides both a useful framework for understanding the interplay
between supply chain dynamics and customer response and practical suggestions to mitigate
their combined impact. A three stage supply chain, capturing fabrication work-in-process (WIP),
assembly WIP, and finished goods inventory (FGI), represents Intel’s production and distribution
process (Figure 1).
Semiconductor manufacturing takes place in a hybrid push-pull production system,
combining a push system at upstream stages and a pull system at the downstream stages. On
pure push systems, long-term demand forecasts determine production and distribution. In
contrast, on pure pull systems current demand governs production and shipments. In a push-pull
production system the manufacturer produces component inventory based on long-term
forecasts, while current demand determines assembly and shipments. Due to the long delays
associated with semiconductor fabrication, typically 3 months, and the short life-cycles
associated with microprocessors, typically 24 to 30 months, semiconductor manufacturers cannot
6
run a pure pull system. If that were the case, orders placed today would only be available after
four or more months, well into the life-cycle of the product.
Replacing
Shipments
+
R1
Replenishment
Wafers
Dies
Chips
+
Wafer
Starts
Fabrication
WIP
Net
Fabrication
+ Completion
+
Assembly
WIP
Net
Assembly
Completion
Finished
Goods
Inventory
Shipments
+
+
B1
–
Inventory
Control
–
WIP
Adjustments
Fraction of
– Orders
Filled
+
Desired
Wafer
Starts
+
+
DELAY
DELAY
Customer
Demand
+
+
DELAY
Market
Share
+
Forecasted
Customer
Demand
Industry
Demand
Figure 1 – Semiconductor Manufacturing Supply Chain.
Note: The rectangles represent important accumulations in the supply chain (stocks), in this case the work-in process (WIP) in fabrication and assembly and finished goods inventory. The double arrows connecting the stocks
represent the directed flow of materials, capturing the transformation of wafers into fabricated wafers, cut dies and
packaged chips (final products ). For further details see Sterman (2000).
Analogously, due to the high variability in demand, running production as a pure push
system would result in large volumes of undesired product. The combination of a push system at
the upstream stage and a pull system at the downstream stages (in a hybrid push-pull system)
outperforms either of the pure systems. The superiority of hybrid push-pull systems was first
suggested by Hodgson and Wang (1991) and later confirmed by Spearman and Zazanis (1992).
In this context, wafer fabrication, the upstream stage in semiconductor manufacturing, is
characterized by a push production system. The desired production rate (i.e., desired wafer
starts) depends directly on long-term demand forecasts, albeit adjusted weekly by fabrication and
assembly work- in-process (WIP), that is, the WIP adjustments aim at closing any existing gaps
between the current levels of fabrication and assembly WIP and their desired levels. Fabricated
7
wafers are “pushed” into the assembly inventory (after approximately 3 months), where they are
stored until orders for specific products pull them into assembly. In contrast, downstream stages
such as assembly/testing and distribution operate as a pull system. Incoming orders are logged
on the company’s information system and can be filled immediately if the desired chips are
available in finished goods inventory (FGI). In this case, incoming customer orders “pull” the
available chips directly from FGI. If, however, the chips are not available in FGI, they must be
pulled from assembly, which requires an assembly processing time of approximately one week.
Naturally, filling orders from assembly, instead of FGI, increases the delivery delay experienced
by customers and limits the ability of the company to timely meet customer orders.
Replacing
Shipments
+
R1
Replenishment
Wafers
Dies
Chips
+
Wafer
Starts
Fabrication
WIP
Net
Fabrication
+ Completion
+
Assembly
WIP
Net
Assembly
Completion
Finished
Goods
Inventory
Shipments
+
+
B1
–
Inventory
Control
–
WIP
Adjustments
Fraction of
– Orders
Filled
+
Desired
Wafer
Starts
+
+
DELAY
DELAY
Customer
Demand
+
+
DELAY
Market
Share
+
Forecasted
Customer
Demand
Industry
Demand
Figure 2 –Hybrid push-pull system for semiconductor manufacturing.
Note: The single arrows represent the flow of information and the direction of causality. Signs (‘+’ or ‘–’) at the
arrowheads indicate the polarity of the causal relationships: a ‘+’ means that, all else equal, an increase in the
independent variable causes the dependent variable to increase (a decrease causes a decrease); analogously, a ‘–’
indicates that, all else equal, an increase in the independent variable causes the dependent variable to decrease (a
decrease causes an increase). The loop identifier (B1) indicates a balancing (negative) loop, whereas (R1) denotes a
reinforcing (positive) loop. See Sterman (2000) for further details.
Figure 2 captures the hybrid push-pull system characteristic of semiconductor
manufacturing. Thick lines and patterned background refer to a push system, indicating that the
8
upstream fabrication process operates as a push. Thin lines and clear background refer to a pull
system, indicating that assembly and finished goods inventory operate as a pull. Balancing
feedback loop (B1) captures the inventory adjustment effect, whereby the level of fabrication and
assembly WIP are considered before setting the desired production level. Reinforcing feedback
loop (R1) captures the impact of replenishment on FGI, allowing shipments to be sustained by
pulling goods form assembly WIP. (We direct the reader interested in the model equations for
the push-pull production system to the appendix.)
INTEGRATING CUSTOMER RESPONSE
The simple push-pull production system presented above can be useful to understand how
supply chain instability and customer response interact. While we can only hope to understand if
the interaction is significant by studying both together, due to the mathematical intractability
associated with these models, most supply chain models investigate them separately. The
challenges of modeling supply chain instability are by no means new. While Thomas Mitchell
described the mechanisms through which retailers caught short of supply increased their orders
to suppliers back in 1924 (Mitchell 1924), the first formal analytical study of supply chain
instability appeared much later in the work of Jay Forrester (1958, 1961). Forrester used
simulation to address the full complexity of the problem (i.e., multiple and decentralized
decision- making and multiple and nonlinear feedbacks). Recent models investigating supply
chain instability have tended to adopt simplifying assumptions (e.g., perfect rationality, fixed
production lead times, unlimited capacity availability, single period games, etc.) that promote the
analytical tractability of the derived models (see for example Lee et al. 1997a, 1997b, Baganha
and Cohen 1998, Cachon and Lariviere 1999a, 1999b, Chen 1999, Graves 1999, and Chen et al.
9
2000), but when additional complexity is considered, they often must be dealt with in separated
models.
This research contributes to the growing literature on supply chain management by
capturing the impact of customer response on supply chain instability. The most important
insights are developed by integrating customer response to the push-pull production system
presented and formulated above. By adding customer response, we introduce two separate
feedback effects to Figure 2. First, a sales effect captures the balancing feedback whereby an
unexpected increase in demand limits the short-term ability of the manufacturer to fill orders.
Due to the delays associated with assembly and fabrication, the company can readily meet
demand only with the inventory available in finished goods. However, the sudden increase in
demand limits the company’s ability to maintain its service level (captured in the model by the
fraction of orders filled), reducing its ability to retain customers. If the company cannot
adequately fill customer orders, some customers will turn to competitors for their needs,
reducing total company demand and easing the supply constraint for the remaining customers.
Alternatively, an unexpected decrease in demand improves the short-term ability of the
manufacturer to fill orders. Customers receive their orders promptly, which increases the
attractiveness of the company to them and potentially others, leading to a renewed increase in
demand. That is, the sales effect captures a change in demand that feeds back to balance the
impact of the initial disturbance. Second, the production effect captures the reinforcing feedback
by which changes in demand have a delayed impact on the manufacturer’s production decisions.
If demand falls, manufacturers reduce demand forecasts and capacity utilization to avoid excess
inventory. Lower production leads (after approximately 3 months) to lower inventory in finished
goods and poor service level, causing a drop in customer demand by the sales effect discussed
10
above. The delayed production effect generates a reaction that reinforces the impact of the
original disturbance. (We direct the reader interested in the model equations for customer
response to the appendix.)
Replacing
Shipments
+
R1
Replenishment
Wafers
Dies
Chips
+
Wafer
Starts
Fabrication
WIP
Net
Fabrication
+ Completion
+
Assembly
WIP
Net
Assembly
Completion
Finished
Goods
Inventory
Shipments
+
+
B1
–
Inventory
Control
–
WIP
Adjustments
+
Desired
Wafer
Starts
R2
–
Production
Effect
+
+
DELAY
DELAY
B2
DELAY
Sales Effect
Market
Share
+
Forecasted
Customer
Demand
Customer
Demand
+ +
Fraction of
Orders
Filled
Industry
Demand
Figure 3 – Customer response through the sales and production effects.
MODEL ANALYSIS
The sales and production effects interact with each other influencing the dynamic
behavior of the model through opposing balancing and reinforcing feedbacks. Figure 4 shows
backlog, finished goods inventory, capacity utilization and fraction of orders filled for two
simulation runs. The model is initialized in dynamic equilibrium with constant industry demand,
and a 5% safety margin in FGI and assembly WIP (see the appendix for technical details on the
simulation.) In equilibrium the hybrid push-pull system functions as intended: the company
meets its target delivery delay, fills 100% of incoming orders, and maintains the desired levels of
finished goods and assembly and fabrication WIP. At the end of the first simulated year, we
11
introduce a demand pulse by increasing customer demand for a single month by 5% and then
20%, respectively. While we could subject the model to more complicated demand patterns
(e.g., a random signal), it would be difficult to distinguish in the output behavior the impact of
randomness from the system response. Using a single pulse to disturb the model from
equilibrium allows us to isolate the system response.
Backlog Coverage (months)
Capacity Utilization
0.450
1.2
Pulse 5%
Pulse 20%
0.8
0.325
Pulse 5%
Equilibrium
0.4
Equilibrium
0.200
0
12
24
0
36
48
0
12
Time (Month)
(a)
(b)
36
48
Perceived Fraction of Orders Filled
1.00
Pulse 20%
Equilibrium
Pulse 5%
Pulse 5%
0.275
24
Time (Month)
Finished Inventory Coverage (months)
0.300
Pulse 20%
0.90
Pulse 20%
Equilibrium
0.250
0
12
24
0.80
36
48
0
Time (Month)
(c)
12
24
Time (Month)
36
48
(d)
Figure 4 – (a) Backlog coverage, (b) capacity utilization, (c) finished inventory coverage,
and (d) perceived fraction of orders filled for the two simulated scenarios.
The increase in demand raises the order backlog (Figure 4a). The company increases
shipments to customers, pulling chips from finished goods. In parallel, the increase in demand
and backlogs sends a signal to planners for the need to raise production. In the short run,
managers raise production by increasing capacity utilization (Figure 4b), leading to higher levels
of fabrication WIP, assembly WIP, and FGI coverage (Figure 4c). After the manufacturing and
12
assembly delays, additional chips are available in finished goods. While both the 5% and 20%
demand pulses have a similar immediate system response (a surge in backlog, increased
shipments and depletion of FGI), the long term responses differ. The depletion in FGI resulting
from a 5% demand pulse does not constrain shipments. The demand shock creates some supply
chain instability (Figure 4c), but safety stocks in FGI and assembly WIP allow the company to
meet its target delivery delay and fill 100% of its incoming orders (Figure 4d). Despite the 5%
shock, the system operates as desired, i.e., as a hybrid push-pull system. The depletion in FGI
resulting from a 20% demand pulse, however, constrains shipments, despite the availability of
safety stocks in FGI and assembly WIP. As finished goods inventory run out, the pull system
cannot operate at the FGI level. However, the system can still pull chips from assembly WIP.
As the availability of assembly WIP decreases, it eventually constrains assembly. When the
system can no longer pull from assembly WIP, it reverts to a pure push system. In push mode
and depleted finished goods and assembly the supplier is unable to meet all customer orders,
filling only a fraction of orders (Figure 4d).
After decision- making and IT reporting delays, customers perceive the drop in delivery
level and seek alternative sources of supply. The drop in customer orders eases the increase in
backlog coverage. As orders decrease, they eventually equal the volume of shipments that the
company can sustain, allowing the backlog coverage (Figure 4a) to stop increasing and the
fraction of orders filled to stop declining. Even after additional FGI becomes available, customer
orders continues to decrease for a while because of the delay in customers’ perception. Plant
managers decrease capacity utilization (Figure 4b) in reaction to declining demand. A drop in
capacity utilization lowers the level of fabrication WIP, assembly WIP and FGI. Higher levels
of FGI and assembly WIP allow the company to send more shipments, eventually meeting
13
customer orders. As customers perceive the improvement in company performance, customer
orders increase once again and order backlog also rises. Once again shipments are not sufficient
to meet customer demand and the fraction of orders filled decreases. The 20% pulse in demand
generates an oscillatory response that decays as some of the excess demand is lost and the
supplier closes any remaining gap in demand running capacity utilization above normal.
WHY IS CUSTOMER RESPONSE SO IMPORTANT?
The interplay between customer response and supply availability offers further insight
into the causes of oscillation and its importance. Figure 5 compares the behavior of two systems:
one that takes customer response into consideration (equivalent to the system shown in figure 3)
and another that does not (equivalent to the system in figure 2). Customer response to service
quality is not significant if customers do not care about the company’s ability to deliver. In such
context, despite the inability of the company to meet orders (e.g., due to a temporary surge in
demand) customer perception of the fraction of orders filled remains unchanged (Figure 5a).
However, if customers do care about the company’s ability to deliver, then the perceived fraction
of orders filled decreases, also leading to a reduction in future orders. While the impact of poor
delivery on customer response is by itself significant, it has further implications to the company.
Figure 5 suggests that customer response adds some variability to the demand forecast,
production and inventory in the supply chain. Company forecasts (figure 5b) first increase to
meet the surge in demand, but then decrease below the initial order rate due to the lost orders
from unsatisfied customers. The dip in orders sends waves throughout the supply chain, first
increasing production (figure 5c) and inventory (figure 5d) and then depressing them. The
company increases production in response to the demand surge. Due to fabrication delays,
however, the finished goods will not be available for a while. After waiting for orders previously
14
placed but not yet received, customers begin to search for alternative sources. When finished
goods that would allow the company to meet a greater fraction of demand finally become
available, reduced orders from unsatisfied customers prevent the company from selling the
goods. As the manufacturer finds itself with more finished goods inventory and reduced
demand, forecasts are adjusted accordingly and Fab managers reduce capacity utilization,
limiting the company’s ability to meet future demand. Hence, customer response and the long
production delays interact to amplify supply chain instability.
Perceived Fraction of Orders Filled
Normalized Demand Forecast
1.0
115
No Customer Response
0.9
110
No Customer Response
105
Customer Response
Customer Response
100
0.8
95
0
12
24
Time (Month)
36
48
0
12
(a)
24
Time (Month)
36
48
(b)
Normalized Wafer Starts
150
Finished Inventory Coverage (Months)
0.30
No Customer Response
125
No Customer Response
100
0.25
75
Customer Response
Customer Response
50
0
12
24
Time (Month)
36
0.20
48
0
(c)
12
24
Time (Month)
36
48
(d)
Figure 5 – The role of customer response on (a) perceived fraction of orders filled, (b)
demand forecast, (c) wafer starts, and (d) finished inventory coverage.
IMPACT OF INVENTORY AND UTILIZATION POLICIES
More important, the interaction between long production delays and customer response
carries important practical implications to capacity utilization and inventory policies. Consider
15
first the implications to inventory policy. In a world with unpredictable demand changes, costly
finished goods inventory, and rapid technological obsolescence, such as in high-tech industries,
keeping inventories lean minimizes the risk that the firm will be caught with excess stock if
demand unexpectedly declines. The mental model supporting the adoption of lean inventory
policies assumes that demand albeit variable is not significantly affected by supply availability.
If managers’ mental models do not include customers’ response to supply availability, they will
be more prone to adopt a tight inventory policy, with reduced levels of safety stock, believing
that it will still provide a sufficiently high service level. If, however, customers react to delivery
delays (determined by inventory availability), then customer response amplifies supply chain
instability, requiring managers to maintain larger inventory buffers to provide the same service
level. Therefore, when manufacturing delays are long, keeping additional inventory buffers
mitigates the amplification in supply and demand caused by customer response.
Consider now the implications to the company’s capacity utilization policy. If customers
respond to supply availability, a supply shortage will constrain shipments, decreasing delivery
levels and driving some customers away. The resulting decrease in customer demand send s a
spurious signal to production, via demand forecasts, that additional output is not necessary.
However, since the decrease in demand was caused by a supply shortage, additional output is
highly desirable. If the company adopts a flexible capacity utilization policy, managers will
respond to the reduced forecasts and adjust utilization accordingly to prevent the possible
accumulation of excess inventory during periods of low demand. However, by decreasing
utilization managers limit the company’s ability to adequately adjust supply. If production
managers, or forecasters, do not have visibility on the causes influencing demand, a less
16
responsive capacity utilization policy will prevent the company from lowering production levels
precisely when more supply is required.
We can assess the impact of the two types of customer responses on utilization and
inventory policies by taking into consideration inventory holding costs in assembly WIP and
finished goods and a cost for lost sales. The criterion to evaluate the best policies is the
comparison of net present value of cumulative discounted costs. Details of the cost structure are
shown in the appendix. Figure 6 provides the net present value of costs associated with two
inventory policies (lean inventory and safety stock) and two capacity utilization policies
(responsive and unresponsive utilization) for two types of customer response.
NPV Costs ($) – No Customer Response
80 M
NPV Costs ($) – Customer Response
80 M
Safety Stock
40 M
Lean Inventory
40 M
Lean Inventory
Safety Stock
0M
0M
0
12
24
Time (Month)
36
48
0
12
(a)
36
48
(b)
NPV Costs ($) – No Customer Response
80 M
24
Time (Month)
NPV Costs ($) – Customer Response
80 M
Unresponsive
Utilization
40 M
Responsive
Utilization
40 M
Unresponsive
Utilization
Responsive
Utilization
0M
0M
0
12
24
Time (Month)
36
48
0
(c)
12
24
Time (Month)
36
48
(d)
Figure 6 – Impact of customer response on inventory and utilization policies.
Figures 6a and 6b compare the net present cost associated with the two inventory
policies. The lean inventory policy assumes the company carries no safety stock in assembly
17
WIP and finished goods, whereas the safety stock policy adopts a 5% safety margin in each. The
graphs suggest that a lean inventory policy is less costly when customers do not respond to
supply availability. However, when that is not the case, adopting a lean inventory policy leads to
higher costs because the additional instability caused by customer response increases lost sales
and its associated costs. Figures 6c and 6d compare the net present costs associated with the two
capacity utilization policies. In both utilization policies, plant manage rs respond to high desired
production in the same way, by increasing capacity utilization. However, managers respond
differently to low desired production volume. The unresponsive utilization policy captures
managers’ preference to keep the plant running and build up inventory levels rather than slowing
the line or shutting it down. In contrast, a responsive utilization policy aggressively adjusts
utilization by reducing it in proportion to the decline in desired production, avoiding the buildup
of inventory and making the unneeded capacity available for process improvement or preventive
maintenance. While the differences are less pronounced than the inventory policies, the
responsive utilization policy is less costly when customers do not significantly respond to supply
availability (i.e., supply shortages do not affect demand.) However, when shortages affect
demand, adopting a responsive utilization policy leads to higher costs (from lost sales) because
the plant stops producing precisely when more supply is needed to satisfy customers.
The conclusions above reflect only the behavior of the system for one set of costs;
therefore, we explore how a range of cost parameters affects our conclusions. We run the model
2,500 times with independently randomly selected parameter values from uniform distributions
with ranges specified in the appendix, and compute the net present value of cumulative
discounted costs. Table 1 presents mean, median, standard deviation and confidence intervals
(50%, 90%, and 95%) statistics for the net present value of cumulative discounted costs for
18
utilization and inventory policies when customers do and do not respond to inventory
availability. Statistics are evaluated at the end of the simulation (at time t=48 months.)
TABLE 1
UTILIZATION AND INVENTORY POLICY OUTPUTS
NPV Costs (Million $) – No Customer Response
Policy
Mean
Median
Std Dev
90%
C.I.
29, 1241
95%
C.I.
21, 1381
100%
C.I.
14.2, 1548
Median
Savings
374
50%
C.I.
224, 783
Safety Stock (SS)
533
477
Lean Inventory (LI)
511
457
358
215, 750
28, 1189
20, 1323
13.6, 1483
4.2%
Responsive Utilization (RU)
511
457
358
214, 750
28, 1187
20, 1321
13.7, 1481
0.2%
Unresponsive Utilization (UU)
512
458
359
215, 752
28, 1192
20, 1326
13.7, 1487
NPV Costs (Million $) – Customer Response
Policy
Mean
Median
Std Dev
374
50%
C.I.
294,851
90%
C.I.
97,1317
95%
C.I.
68,1429
100%
C.I.
27, 1670
Safety Stock (SS)
602
549
Lean Inventory (LI)
790
745
383
499,1043
234,1499
170,1617
65, 1987
Responsive Utilization (RU)
769
722
378
480,1019
224,1469
161,1589
61, 1947
Unresponsive Utilization (UU)
731
683
374
437, 979
200,1431
143,1549
54,1884
Median
Savings
26.3%
5.4%
Note: Responsive and Unresponsive Utilization policies are tested without any safety stock.
The conclusions above still hold for the range of holding and lost sales costs simulated.
When customers do not respond to supply availability, adopting lean inventory and responsive
utilization policies lead to lower costs. When customers respond to supply availability, a safety
inventory and an unresponsive capacity utilization policies result in lower costs. The largest
savings take place when customers respond to inventory availability. The adoption of a safety
stock policy yields 26% savings ; an unresponsive utilization policy yields about 5% in savings.
These savings reflect independent savings from each policy. However, because the difference
between the utilization policies comes from building up inventory during low demand periods,
the combination of a safety stock policy may reduce the benefit associated with unresponsive
19
utilization. We tested this result combining the inventory and utilization policies. When the
company already maintains safety stock, the responsive and unresponsive policies tested lead to
similar results. Our main result suggests that if customers respond significantly to supply
availability, an inventory policy adopting safety stock is highly recommended.
DISCUSSION
This paper explored the effect of customer response on capacity utilization and inventory
policies in industries with long production delays. The modeling effort drew on extensive field
work at a semiconductor manufacturer. The paper contributes to our understanding of how
customer response and long production delays can lead to increased demand amplification and
supply chain instability. Although a push-pull production system provides a more stable
production environment, it can only operate effectively when sufficient inventory is available.
Inventory shortages can prevent the system from operating as designed (as a hybrid push-pull
mode) and in combination with customer response can amplify demand and supply variability,
shifting the system into a pure push operation mode. That is, when customers respond to
inventory availability, the system operates more effectively when sufficient inventory is
available, suggesting that the manufacturer would benefit by maintaining safety stocks at
assembly and finished goods. While the heuristics of maintaining safety inventory to cope with
supply and demand variability is not new, this research underscores their importance in the
operation of hybrid push-pull systems. These insights may also play an important role in other
industries (e.g. electronics, automotive, airplane and ship building) with long production delays
and hybrid production systems.
Since the benefits associated with a safety inventory policy depend on whether customers
respond to inventory availability, it is important explore if that is the case. Empirical research in
20
Marketing suggests that customers do in fact respond to inventory availability; most of those
studies, however, focus on the retail industry. For instance, Whitin (1957) suggests that
inventory control for retail stores is “complicated by the fact that inventory and sales are not
independent of one another.” Wolfe (1968) and Silver and Peterson (1985) find that sales at the
retail level tend to be proportional to inventory displayed. Dubelaar, Chow and Larson (2001)
report positive and significant links between inventory levels and service level and sales. Since
customers do seem to respond to inventory availability, the manufacturer benefits from the
adoption of a safety stock policy because the savings obtained by avoiding lost sales outweighs
the costs with holding additional inventory. Interestingly, a recent study suggests that companies
that carry too little inventory do not perform as well as companies with some safety stock (Chen,
Frank, and Wu 2005).
Our research also shows that capturing the feedback of product availability on customer
response has implications for the capacity utilization policy. In particular, our analysis suggests
that if the company adopts a lean inventory an unresponsive utilization policy is less costly than
a responsive utilization policy. Because customers respond to supply availability, by cutting
production when demand is perceived to be low, the firm ensures that inventory will be even less
available when it is required, driving customers away and decreasing demand. When the
company adopts a lean inventory policy, the supplier’s effort to meet customer demand in the
short-run may actually hurt customer service in the long-run. However, if the company already
maintains some safety stock, our responsive and unresponsive policies lead to similar results.
These insights are obtained with a constant demand function. Demand growth may
exacerbate some of the responses associated with short supplies. Nevertheless, it may be
challenging to maintain safety stock levels when demand is growing. In addition, the research
21
currently does not address the introduction of new products over time and the characteristic
demand patterns over the product lifecycle, where there are often initial shortages during
production ramp up, followed by a demand decline at the end of the product life. Safety stock
and production heuristics may change over the course of the lifecycle. During production ramp
up it is often difficult to build up safety stocks even though companies often produce at full
capacity. Customers may be more prone to tolerate delays, however, during ramp-ups.
Furthermore, our model incorporates only customer response to current service level. This is
consistent with a finding by Schary and Becker (1979), in which stockouts (generated by a
regional beer strike) had more pronounced short-run than long-run effects on brand share.
Nevertheless, consistent inability to meet customer needs may lead to permanent decrease in
market share for the current product as well as reducing sales for other products. Including this
feature would likely amplify the demand and supply instability and strengthen the importance of
safety stocks. Finally, our model does not include order cancellations. However, if order
cancellations would occur as a result of a decrease in service level, they would amplify the
instability caused by lost sales and strengthen our results.
MANAGERIAL IMPLICATIONS
Managers in different industries often feel pressured to keep inventory levels low, run
lean supply chains, and operate their systems just-in-time, with the promise to reduce inventory
costs. Especially in high-tech industries, where products have short life cycles, unpredictable
demand, costly finished goods inventory, and rapid technological obsolescence, keeping
inventories lean minimizes the risk that the firm will be caught with expensive excess stock if
demand unexpectedly declines. However, the assumption behind the adoption of lean
inventories is that demand will not change significantly because of supply availability, that is,
22
lost sales resulting from poor delivery are insignificant. However, customers do respond to
available supply. Low finished inventories and assembly work- in-process inherent in lean
inventory policies increase the chance of stockouts in different stages in the supply chain,
boosting the likelihood that the system will operate in an undesirable mode (e.g., as a push
system) which amplifies demand variability. In turn, higher demand variability increases the
instability in the supply chain and leads to more severe stockouts. Considering the potential
increase in demand variability caused by customer responses, we note that companies may
underestimate the true costs associated with stockouts and the value of carrying safety stocks.
NOTES
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Chains.” Operations Research. 46: S72-S83.
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Turn-and-Earn.” Management Science. 45(5): pp. 685-703.
Cachon, G., and M. Lariviere. 1999b. “Capacity Choice and Allocation: Strategic
Behavior and Supply Chain Performance.” Management Science. 45(8): pp. 1091-1108.
Chen, F. 1999. “Decentralized Supply Chains Subject to Information Delays.”
Management Science. 45(8): 1076-1090.
Chen, F., Z. Drezner, J. Ryan, and D. Simchi-Levi. 2000. “Quantifying the Bullwhip
Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information.”
Management Science, 46(3): 436-443.
Chen, H., M. Frank, and O. Wu. 2005. “What Actually Happened to the Inventories of
American Companies Between 1981 and 2000?” Working Paper, University of British
Columbia. Canada.
23
Dubelaar, C., G. Chow, and P. D. Larson. 2001. “Relationships between inventory, sales
and service in a retail chain store operation” International Journal of Physical Distribution &
Logistics Management, 31(2): 96-108(13).
Forrester, J.W. 1958. “Industrial Dynamics – A Major Breakthrough for Decision
Makers.” Harvard Business Review. 36(4): 37-66.
Forrester, J.W. 1961. Industrial Dynamics. Cambridge, MA: Productivity Press.
Gonçalves, P. 2003. “Demand Bubbles and Phantom Orders in Supply Chains.”
Unpublished Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA.
Gonçalves, P., J. Hines and J. Sterman. (2005). “Demand Bubbles and Phantom Orders in
Supply Chains.” Working Paper, MIT Sloan School of Management, Cambridge, MA.
Graves, S. 1999. “A Single-Item Inventory Model for a Non-Stationary Demand
Process.” Manufacturing & Service Operations Management. 1: 50-61.
Holmes, S. 1997. “Parts Shortages Delay Boeing Production,” Pittsburgh Post-Gazette
(Pennsylvania), October 4, C-12.
Hachman, M. 1999. “MPU Supply Tightening.” Electronics Supply and Manufacturing.
Jan. 15. http://www.my-esm.com/showArticle.jhtml?articleID=2902238
Hachman, M. 2000. “Gateway doubles quarterly processor purchases from AMD.”
Electronics Supply and Manufacturing. May. 25. http://www.myesm.com/showArticle.jhtml?articleID=2907881
Henderson, D. 2005. “US Flu Vaccine’s Shortage Ends in an Oversupply,” The Boston
Globe, February 9, A1.
Hendricks, K.and V. Singhal. 2003. “The Effect of Supply Chain Glitches on Shareholder
Wealth.” Journal of Operations Management. 21:501-522.
Hodgson, T. J. and D. W. Wang. 1991. "Optimal Hybrid Push-Pull Control Strategies for
a Parallel Multistage System .1." International Journal of Production Research 29(6): 12791287.
Lee, H., Padmanabhan, V, and Seungjin Whang. 1997a. “Information Distortion in a
Supply Chain: The Bullwhip Effect.” Management Science. 43(4): 546-558.
24
Lee, H., Padmanabhan, V, and Seungjin Whang. 1997b. “The Bullwhip Effect in Supply
Chains.” Sloan Management review, Spring: 93-102.
Mitchell, T.W. 1924. “Competitive Illusion as a Cause of Business Cycles.” Quarterly
Journal of Economics, 38(4):p. 631-652.
Schary, P. and B. Becker. 1979. "The Impact of Stock-Out on Market Share: Temporal
Effects." Journal of Business Logistics, 1(1):31-43.
Silver, E. and R. Peterson. 1985. Decision Systems for Inventory Management and
Production Planning, Second edition. New York: Wiley.
Spearman, M. L. and M. A. Zazanis. 1992. “Push and Pull Production Systems - Issues
and Comparisons.” Operations Research 40(3): 521-532.
Sterman, J.D. 2000. “Business Dynamics: Systems Thinking and Modeling for a Complex
World.” Chicago, IL, Irwin-McGraw Hill.
Singhal, V. and K. Hendricks. 2002. “How Supply Chain Glitches Torpedo Shareholder
Value.” Supply Chain Management Review. January/February. 18-33.
Whitin, T. 1957. The Theory of Inventory Management. Princeton, NJ: Princeton
University Press.
Wolfe, H. 1968. “A Model fo r Control of Style Merchandise,” Industrial Management
Review, 9(2): 69-82.
25
APPENDIX
MODEL EQUATIONS FOR THE PUSH-PULL SYSTEM
The model equations associated with the hybrid push-pull system follow directly from the
description of its operations and variables presented in figure 2. Consider first the wafer
fabrication push system. Fabrication work- in-process (FWIP) increases with wafer starts (WS )
and decreases with gross fabricated wafers (WG), composed by the net good wafers completed
(WN) and rejected wafers (WR). Therefore we can write the equation for the rate of change in
FWIP as:
FW& IP (t ) = WS (t ) − WG (t )
(A1)
where the dot over FWIP indicates a first derivative with respect to time.
In push mode, the gross fabrication rate is simply the ratio of the amount of fabrication
WIP (FWIP) and the fabrication time (τF). The fabrication rate, i.e. wafer starts (WS ), is given by
the product of available capacity (K) and capacity utilization (CU). The latter is assumed to be
fixed, reflecting the company’s inability to increase it in the short-term, and is formulated in
terms of other model parameters to assure dynamic equilibrium, which avoids transient dynamics
at the beginning of the simulation (see the appendix for details.) The former is a concave
function of the ratio of desired wafer starts (WS* ) and available capacity (K) operating at the
normal capacity utilization level (CUN), a level of 90% of the total available capacity.
 WS * (t ) 

WS (t ) = K ⋅ fU 
 K ⋅ CU N 
(A2)
Fab planners determine the desired wafer starts considering the desired die inflow (DI* )
requested by Assembly/Test plants and an adjustment for fabrication work- in-process (FWIP),
26
designed to maintain fabrication WIP at a desired level (FWIP * ). A non-negativity constraint
prevents negative production targets.

D*I (t )
FWIP ∗ (t ) − FWIP (t ) 
∗

WS (t ) = MAX  0,
+
τ FWIP
 DPW ⋅ YD ⋅ YL

(A3)
Substituting equations (A2) and (A3), and the gross fabrication rate, we obtain equation
(A4) providing the rate of change in fabrication WIP.


D*I (t )
FWIP ∗ (t ) − FWIP (t )  
 MAX  0,
+

 DPW ⋅ Y ⋅ Y

τ
D
L
FWIP

  − FWIP (t ) τ
FW& IP (t ) = K ⋅ f U 
F

K ⋅ CU N






(A4)
Consider now the pull part of the system. Incoming orders are first backlogged on Intel’s
ordering system. The backlog (B) accumulates the discrepancy between orders received by the
company (D) and its shipments (S). Order cancellations, not included, could be captured as an
additional outflow from the backlog.
B& (t ) = D(t ) − S (t )
(A5)
Shipments (S) are given by the minimum of the desired (S* ) and feasible (SMAX) shipment
rates. By design, shipments flow at the desired rate – meeting orders in backlog (B) with a
desired delivery delay (DD* ) – however, if not enough FGI is available the company ships only
what it is available (FGI) within the minimum order processing time (τOP).
(
S (t ) = MIN B(t ) DD * , FGI (t ) τ OP
)
(A6)
Intel’s demand (D) in a given segment is determined by a share of total customer demand
(TD). The share of demand is determined by the ratio of the company attractiveness (AI) and that
of the total market, given by the sum of the company attractiveness (AI) and its competitors (AC ).
Total demand is constant, with exception to a single month pulse increase introduced at the end
27
of the first simulated year. While demand for semiconductors has steadily increased for decades,
we use a de-trended demand signal because we are interested only in the interplay between
customer response and supply chain instability. Interactions between demand growth and supply
chain stability are left for future research.


AI (t )
 ⋅ TD(t ) − MIN B(t ) DD* , FGI(t ) τ OP
B& (t ) = 
 AI (t ) + AC (t ) 
(
)
(A7)
Incoming customer orders “pull” the available chips from FGI through shipments and as
FGI depletes, it is replenished by “pulling” chips from assembly. Therefore, finished inventory
(FGI) decreases with shipments (S) and replenishes with net assembly completions (AN).
FG& I (t ) = AN (t ) − S (t )
(A8)
Net assembly completions (AN ) are determined by the product of gross assembly
completions (AG) and the unit yield (YU), i.e. the fraction of good chips per assembled die. In
turn, the minimum of desired assembly completions (a pull signal) or the feasible (a push signal)
determine gross assembly completions (AG). By design, assembly operates in pull mode, with
assembly completions determined by the desired net assembly rate (A* N) adjusted by the unit
yield (YU). However, if not enough Assembly WIP is available the system can complete only
what it is feasible by the availability of assembly WIP (AWIP) within the assembly time (τA).
(
AG (t ) = MIN A*N YU , AWIP (t ) τ A
)
(A9)
Substituting equations (A6) and (A9) into (A8), we obtain the equation describing the
rate of change in finished goods inventory:
[
]
[
FG& I (t ) = MIN A*N , AWIP (t )YU τ A − MIN B(t ) DD * , FGI (t ) τ OP
28
]
(A10)
Consider now the stock of Assembly WIP (AWIP). AWIP decreases with gross assembly
completions (AG), composed of net completions (AN) and rejects (AR), and increases with dies
pushed from manufacturing (DI).
AW& IP (t ) = D I (t ) − AG (t )
(A11)
The dies flowing into assembly (DI) result from cutting the good fabricated wafers (WN).
Different chip designs determine how many dies-per-wafer (DPW) are available. Due to the disklike shape of the wafer and variability of the fabrication process, only a fraction of the die
produced, the die-per-wafer yield (YD), proceed into final assembly. In push mode, the number of
wafers manufactured will be given by the ratio of the fabrication WIP (FWIP ) and the
manufacturing time (τF). Moreover, the line yield (YL) determines how many of those wafers are
good. Therefore, the number of dies going to assembly is given by:
DI (t ) = DPW ⋅ YD ⋅ YL ⋅ FWIP(t ) τ F
(A12)
Substituting equations (A9) and (A12) into (A11), we get the rate of change in assemb ly
WIP.
(
AW& IP (t ) = DPW ⋅ YD ⋅ YL ⋅ FWIP (t ) τ F − MIN AN* YU , AWIP (t ) τ A
)
(A13)
Equations (A4), (A7), (A10), and (A13) form a system of non- linear first order
differential equations describing the hybrid push-pull system for semiconductor manufacturing.
MODEL EQUATIONS INTEGRATING CUSTOMER RESPONSE
The production effect incorporates the demand forecast through division planners’
decisions, who are responsible for setting the desired die inflow rate (DI* ). Division planners use
a heuristic that incorporates information on long-term demand forecast (ED) and an adjustment
from assembly WIP, to maintain assembly WIP at a desired level (AWIP * ).
29

AWIP ∗ (t ) − AWIP (t ) 

D*I (t ) = MAX  0, ED(t ) / YU +
τ AWIP


(A14)
At Intel, the demand forecast incorporates a trend component to account for the
exponential growth in semiconductors sales. Since we use a de-trended demand signal due to our
interest in the interplay between customer response and supply chain instability, the demand
forecast, or expected demand (ED), is modeled as an exponential smooth of actual demand (D)
updated over the demand adjustment time (τDAdj).
ED& ( t ) =
D( t ) − ED( t )
τ DAdj
(A15)
The sales effect captures customers’ response to supply availability, or the fraction of
orders filled (FoF), which depends on the ratio between actual (S) and desired shipments (S* ).
When shipments equal the desired rate, the company is capable of shipping the full fraction of
orders demanded by customers; when shipments are lower than desired, the company fills only a
fraction of its orders.
FoF (t ) =
(
S (t ) MIN B(t ) DD* , FGI (t ) τ OP
=
S* (t )
B(t ) DD*
)
(A16)
Customers perceive the fraction of order filled (PFoF) and react to it with a third-order
Erlang lag (λ) with time constant (τP). The third-order Erlang is equivalent in continuous time to
three sequential exponential delays each with time constant (τP /3). For more information on
Erlang lags see Sterman (2000). The high-order smooth captures the plausible distribution of
responses by OEMs, taking into consideration the time customers become aware of the current
state of service, shape their opinions, and make purchasing decisions about current and
alternative products. Below, we show the equation for the first exponential delay.
30
PF&oF1 (t ) =
FoF (t ) - PFoF1( t )
τP 3
(A17)
Substituting equation (A16) into (A17) provides the first term of the customer perception
of the fraction of orders filled (PFoF1 ).
PF&oF1 (t ) =
(
)
MIN B(t ) DD* , FGI (t ) τ OP PFoF1 (t )
−
(τ P / 3) B(t) DD*
τP / 3
(
)
(A18)
Intel’s attractiveness to suppliers (AI), measured in a scale from zero to one, is determined
by a logistic function (f A) of customers’ perception of fraction of orders filled (PFoF). Supply
availability appropriately captures customers’ responses to low-end products. When Intel
struggled with shortages of its low-end Celeron® microprocessors in December 1998, it allowed
Advanced Micro Devices Inc. (AMD), Intel’ s main competitor in the U.S market, to increase its
market segment share by more than two percentage points, even after Intel cut prices on its
Celeron® chips (Hachman 1999). Inability to supply customers the following year, forced
Gateway, one of Intel’s customers, to double the amount of microprocessors it purchased from
AMD (Hachman 2000). The logistic curve captures customers’ mild response to small changes
in supply availability, and more significant responses to large changes in supply availability. The
modeling choice for customer response is conservative, since it captures only the short-term
response to service level. Nevertheless, consistent inability to meet customer needs may lead to a
permanent decrease in the company market share.
AI = f A (PFoF3 (t ) )
(A19)
The system of equations (A4), (A7), (A10), (A13), (A15), (A18), and two additional
equations for the other two terms of the Erlang lag compose our model, a high-order system of
first order nonlinear differential equations that generates the dynamic behavior observed in the
company and replicated in the model. Since the model is highly nonlinear, we cannot obtain
31
closed- form solutions. Therefore, we need to simulate it to gain insight into model behavior.
TECHNICAL DETAILS FOR THE SIMULATIONS
We simulated the model using the Euler integration method and chose a small enough
time step to avoid integration error. The model is initialized in dynamic equilibrium. For a given
demand (TD), the equilibrium capacity (K) required to obtain such equilibrium can be computed
from the normal capacity utilization and yields. The formula for equilibrium capacity (K) is
given by:
K=
TD ⋅ MS 0
CU N ⋅ DPW ⋅ YD ⋅ YL ⋅ YU
(A20)
The model is run for four simulated years. The simulation period is sufficient for all
transient dynamics to play out. At the end of the simulation all parameters return to their initial
values. A demand pulse is introduced at the end of the first simulated year. Parameters chosen
for the base case runs (Table A1) reflect Intel’s manufacturing system (the values are disguised
to maintain company confidentiality.)
TABLE A1
BASE CASE PARAMETERS
Parameter
TD
MS0
DPW
CUN
YL
YD
YU
K
Definition
Customer demand
Initial market segment share
Number of die per wafer
Normal capacity utilization
Line yield: Fraction of good wafers per total
Die yield: Fraction of good die per wafer
Unit yield: Fraction of good chips per good die
Available capacity
32
Value
5.0
80
200
90
90
90
95
28.9
Units
Million units /month
%
Die/wafer
%
%
%
%
‘000 wafers/month
MULTIVARIATE SENSITIVITY ANALYSIS
The model analysis section shows the average trajectory of the model under two different
inputs (i.e., a 5% and 20% demand pulses). While actual parameters may contain uncertainty,
the average trajectory is useful to distinguish the long-run model behavior under different
conditions. Nevertheless, it is possible to explore the stochastic behavior of the model by
incorporating the variability inherent in different parameters. Table A2 provides a sample list of
parameters either under the control of company managers (e.g., forecasting and inventory
adjustment frequency, capacity utilization) or reflecting the characteristics of different customers
(e.g., customer reaction) for which we incorporate a specific range (typically half and double the
base case value) and a distribution (assumed uniform to capture high variability) that serves as
input for the Monte-Carlo (multivariate) simulation. The parameter choice emphasizes the
variability imposed by managerial policies utilized instead of those imposed by process
uncertainty (e.g., production yield, manufacturing time, etc.) It would be straightforward to
explore the variability in model behavior due to variability in process parameters.
TABLE A2
RANGE AND UNIFORM DISTRIBUTIONS FOR PARAMETERS
Parameter
Symbol
Units
Min
Base
Max
Time to Adjust FGI
τAF
Time to Adjust Assembly WIP
τAW
Time to Adjust Fabrication WIP
τFW
Time to Adjust Backlog
τAB
Time to Update Orders
τO
Time to Update Shipments
τS
Weight unresponsive
ωU
Weight customer reaction
ωA
months
months
months
months
months
months
dmnl
dmnl
0.5
0.5
0.5
0.5
0.5
0.125
0
0
1
1
1
1
1
0.25
0. 5
0.5
2
2
2
2
2
0.5
1
1
33
The model is simulated 2,500 times with independent randomly selected parameter
values from its distributions. The variability in parameter inputs leads to substantial variability in
other key model variables, such as wafer starts (WS ), finished inventory coverage (FGIC) and
perceived fraction of orders filled (PFoF). Figure A1 shows the confidence bounds (50%, 75%,
95%, and 100%) for the variables above. While parameter variability associated with managerial
policies may amplify or smooth model behavior, the fabrication process behavior, i.e., the
behavior for wafer starts (normalized by the equilibrium fabrication rate), fabrication and
assembly WIP (not shown), FGI (normalized by the equilibrium demand rate and shown in terms
of coverage), and backlog (also not shown), always follow a pattern of damped oscillations. The
oscillatory behavior originates due to the negative feedbacks with long delays associated with the
supply chain inventory management. Managerial choices associated with the frequency of
forecast and inventory adjustment and capacity utilization policies can influence the dampening
process. All model variables return to the initial equilibrium at the end of the simulation.
Moreover, the stochastic behavior of the model confirms that the company is capable of
absorbing a 5% demand pulse without impacting the fraction of orders filled, whereas a 20%
demand pulse deteriorates service delivery, leading to a customer response that amplifies the
oscillatory behavior of the fabrication process.
Normalized Wafer Starts
Normalized Wafer Starts
Pulse 5% (Results with 2500 Simulations)
Pulse 20% (Results with 2500 Simulations)
150
150
Base
100
100
75%
50%
Base
95%
50
50%
50
100%
100%
0
75%
95%
0
0
12
24
Time (Month)
36
48
0
34
12
24
Time (Month)
36
48
Finished Inventory Coverage (Months)
Finished Inventory Coverage (Months)
Pulse 5% (Results with 2500 Simulations)
Pulse 20% (Results with 2500 Simulations)
0.32
0.32
75%
95%
Base
100%
95%
50%
0.26
0.26
50%
Base
100%
0.20
0.20
0
12
24
Time (Month)
36
48
0
Perceived Fraction of Orders Filled
12
24
Time (Month)
36
48
Perceived Fraction of Orders Filled
Pulse 5% (Results with 2500 Simulations)
Pulse 20% (Results with 2500 Simulations)
1.0
1.0
100%
50%
0.9
0.9
75%
Base
95%
100%
0.8
0.8
0
12
24
Time (Month)
36
48
0
12
24
Time (Month)
36
48
Figure A1. Monte-Carlo simulation for Wafer Starts, FGI Coverage and Perceived
Fraction of Orders Filled for 5% and 20% demand pulses.
Table A3 provides summary statistics from the Monte-Carlo simulations for the three
variables described above for each of the two demand inputs at time 18, six months after the
introduction of the pulse in demand.
TABLE A3
UNCERTAINTY IN OUTPUT VARIABLES
Pulse 5%
Parameter (t=18)
Min
Max
Mean
Median
Std Dev
Deterministic
Norm. Wafer Starts (NWS)
97.4
104.9
99.6
99.2
1.34
100.1
Inventory Coverage (FGIC)
0.2620
0.2646
0.2627
0.2626
4.21x10-4
.2625
Perc. Orders Filled (PFoF)
0.9953
0.9992
0.9975
0.9976
7.36x10-4
.9981
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Pulse 20%
Parameter (t=18)
Min
Max
Mean
Median
Std Dev
Deterministic
Norm. Wafer Starts (NWS)
81.50
120.36
93.64
92.43
5.95
93.91
Inventory Coverage (FGIC)
0.2531
0.2830
0.2668
0.2663
5.6x10-3
.2626
Perc. Orders Filled (PFoF)
0.8531
0.9087
0.8943
0.8963
8.9x10-2
.9016
Note: Values reported for 2,500 simulations at time t =18. The deterministic case reports values from the base run.
MULTIVARIATE SENSITIVITY FOR UTILIZATION AND INVENTORY POLICIES
We can assess the impact of the two types of customer responses on utilization and
inventory policies by taking into consideration inventory holding costs in assembly WIP (CHA)
and finished goods (CHF) and lost sales cost (CL). For simplicity, we do not account for holding
costs in fabrication. Holding costs in each stage are given by the product of the inventory vo lume
in each stage (e.g., AWIP and FGI) and the respective unit inventory holding costs, (βφ and ?δφ,
that is a fraction of the unit finished goods cost φ). Lost sales cost is the product of a factor (α)
of unit finished goods cost (φ) and the amount of lost sales, given by the difference between the
initial market segment share (MS0 ) and the actual (MSt).
CHA = AWIP ⋅ β ⋅ φ
(A21)
CHF = FGI ⋅ δ ⋅ φ
(A22)
CL = (MS 0 − MSt ) ⋅ α ⋅ φ
(A23)
The criterion to evaluate the best policies is the comparison of net present value of
cumulative discounted costs (CDC), with a discount rate (r).
CDC = ∫ e− rt {[( MS0 − MSt ) ⋅ α + AWIP ⋅ β + FGI ⋅ δ ] ⋅ φ }dt
∞
0
36
(A24)
To assess the impact of different cost values in the net present value of cumulative
discounted costs the model is simulated 2,500 times with independently randomly selected
parameter values from its distributions.
TABLE A4
COST PARAMETERS RANGE VALUES
Parameter
Fractional unit FGI holding cost
Ratio fractional unit AWIP to FGI cost
Fractional unit lost sales cost
Symbol
Units
Min
Base
Max
δ
1/month
0.005
0.01
0.2
β/δ
dmnl
0.125
.25
0.75
α
dmnl
0.5
1
5
Note: The simulation is run with a unit finished good cost φ =50 $/unit and a discount rate d = 0.01/month.
37
ABOUT THE AUTHOR
Paulo Gonçalves is an assistant professor in the Management Science Department at the
University of Miami’s School of Business Administration. He holds a M.S. degree in
Technology and Policy from MIT and a Ph.D. in Management Science from the MIT Sloan
School of Management. His research focuses on supply-demand imbalances and the impact of
customer response on supply chain instability, using diverse techniques such as simulation,
nonlinear dynamics, control theory, and game theory. He has received the 2004 Doctoral
Dissertation Award from the Council of Logistics Management and his research has appeared in
California Management Review, IEEE Engineering Management Review and System Dynamics
Review.
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