the impact of customer response on inventory and...

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.

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THE IMPACT OF CUSTOMER RESPONSE ON

INVENTORY AND UTILIZATION POLICIES

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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 introduce 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). These stories share a few

commonalities. First, they highlight that despite the emphasis on effective supply chain

management 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

3

hybrid push-pull production system (composed of fabrication, assembly and finished goods) and

includes the customer response 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 companies

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

4

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 worldwide and manage the variability in product line while

matching supply and demand. Model development incorporated the physics of semiconductor

5

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 re-

entrant 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

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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

7

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.

Forecasted CustomerDemand

Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

+ CustomerDemand

+

+

+ +DELAY

FabricationWIP

FinishedGoods

InventoryWaferStarts

NetFabricationCompletion

Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips

– – Fraction of Orders Filled

Market Share

+

+

DELAY

Industry Demand

+

–

++

InventoryControl

B1

ReplenishmentR1


Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

+ CustomerDemand

+

+

+ +DELAY

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips


Market Share

+

+

DELAY

Industry Demand

+

–

++

InventoryControl

B1

ReplenishmentR1


Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

WIP Adjustments

+ CustomerDemand

+

++

+ +DELAYDELAY

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips


Market Share

++

++

DELAYDELAY

Industry Demand

+

–

++

InventoryControl

InventoryControl

B1B1B1

ReplenishmentR1R1R1

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

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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.


Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

+ CustomerDemand

+

+

+ +DELAY

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips


Market Share

+

+

DELAY

Industry Demand

+

–

++

InventoryControl

B1

ReplenishmentR1


Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

WIP Adjustments

+ CustomerDemand

+

++

+ +DELAYDELAY

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips


Market Share

++

++

DELAYDELAY

Industry Demand

+

–

++

InventoryControl

InventoryControl

B1B1B1

ReplenishmentR1R1R1

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

9

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.

10

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

11

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.)


Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

+ CustomerDemand

+

+

+ +DELAY

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips


Market Share

+

+

DELAY

Industry Demand

+

–

++

InventoryControl

B1

ReplenishmentR1

ProductionEffect

R2

Sales Effect

B2


Desired WaferStarts

+

Demand

+

ReplacingShipments

+

+ +DELAY

WIP Adjustments

WIP Adjustments

+ CustomerDemand

+

++

+ +DELAYDELAY

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips

FabricationWIP

FinishedGoods



Shipments

AssemblyWIP Net

AssemblyCompletion

Wafers Dies Chips


Market Share

++

++

DELAYDELAY

Industry Demand

+

–

++

InventoryControl

InventoryControl

B1B1B1

ReplenishmentR1R1R1

ProductionEffect

R2

ProductionEffect

R2R2R2

Sales Effect

B2

Sales Effect

B2

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

12

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)0.450

0.325

0.2000 12 24 36 48

Time (Month)

Equilibrium

Pulse 20%

Pulse 5%

Backlog Coverage (months)0.450

0.325

0.2000 12 24 36 48

Time (Month)

Equilibrium

Pulse 20%

Pulse 5%

Capacity Utilization1.2

0.8

0.4

0

Equilibrium Pulse 20%

0 12 24 36 48Time (Month)

Pulse 5%

Capacity Utilization1.2

0.8

0.4

0

Equilibrium Pulse 20%

0 12 24 36 48Time (Month)

Pulse 5%

(a) (b)

0.300

0.275

0.2500 12 24 36 48

Time (Month)

Finished Inventory Coverage (months)

Equilibrium

Pulse 20%

Pulse 5%

0.300

0.275

0.2500 12 24 36 48

Time (Month)

Finished Inventory Coverage (months)

Equilibrium

Pulse 20%

Pulse 5%

0 12 24 36 48Time (Month)

Perceived Fraction of Orders Filled

1.00

0.90

0.80

Equilibrium

Pulse 20%

Pulse 5%

0 12 24 36 48Time (Month)


1.00

0.90

0.80

Equilibrium

Pulse 20%

Pulse 5%

(c) (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

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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

14

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

15

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.

1.0

0.9

0.80 12 24 36 48

Time (Month)

Customer Response

No Customer Response

Perceived Fraction of Orders Filled1.0

0.9

0.80 12 24 36 48

Time (Month)

Customer Response



115

110

105

100

950 12 36 48

Normalized Demand Forecast

Customer Response


24Time (Month)

115

110

105

100

950 12 36 48

Normalized Demand Forecast

Customer Response


24Time (Month)

24Time (Month)

(a) (b)

150

125

100

75

500 12 24 36 48

Time (Month)

Customer Response


Normalized Wafer Starts150

125

100

75

500 12 24 36 48

Time (Month)

Customer Response


Normalized Wafer Starts

0.30

0.25

0.200 12 36 48

Finished Inventory Coverage (Months)

Customer Response


24Time (Month)

0.30

0.25

0.200 12 36 48

Finished Inventory Coverage (Months)

Customer Response


24Time (Month)

24Time (Month)

(c) (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

16

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 sends 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

17

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

Safety Stock80 M

40 M

0 M0 12 24 36 48

Time (Month)

Lean Inventory


Safety Stock80 M

40 M

0 M0 12 24 36 48

Time (Month)

Lean Inventory Safety Stock

0 M0 12 24 36 48

Time (Month)

Lean Inventory

NPV Costs ($) – Customer Response80 M

40 M

Safety Stock

0 M0 12 24 36 48

Time (Month)

Lean Inventory


40 M

(a) (b)

80 M

40 M

0 M0 12 24 36 48

Time (Month)

Unresponsive Utilization

Responsive Utilization

NPV Costs ($) – No Customer Response80 M

40 M

0 M0 12 24 36 48

Time (Month)




80 M

40 M

0 M0 12 24 36 48

Time (Month)




40 M

0 M0 12 24 36 48

Time (Month)



NPV Costs ($) – Customer Response

(c) (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

18

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 managers 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

19

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 50% C.I.

90% C.I.

95% C.I.

100% C.I.

Median Savings

Safety Stock (SS) 533 477 374 224, 783 29, 1241 21, 1381 14.2, 1548

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 50% C.I.

90% C.I.

95% C.I.

100% C.I.

Median Savings

Safety Stock (SS) 602 549 374 294,851 97,1317 68,1429 27, 1670 26.3%

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 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

20

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

21

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

22

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,

23

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

Baganha, M. and M. Cohen. 1998. “The Stabilizing Effect of Inventory in Supply

Chains.” Operations Research. 46: S72-S83.

Cachon, G., and M. Lariviere. 1999a. “Capacity Allocation Using Past Sales: When to

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.

24

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.my-

esm.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): 1279-

1287.

Lee, H., Padmanabhan, V, and Seungjin Whang. 1997a. “Information Distortion in a

Supply Chain: The Bullwhip Effect.” Management Science. 43(4): 546-558.

25

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 for Control of Style Merchandise,” Industrial Management

Review, 9(2): 69-82.

26

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:

( ) ( ) ( )tWtWtIPWF GS −=& (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.

( ) ( )

⋅

⋅=N

*

US CUKtWS

fKtW (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),

27

designed to maintain fabrication WIP at a desired level (FWIP*). A non-negativity constraint

prevents negative production targets.

( ) ( ) ( ) ( )

−+

⋅⋅=

∗∗

FWIPLD

*I

StFWIPtFWIP

YYDPWtD

,MAXtWτ

0 (A3)

Substituting equations (A2) and (A3), and the gross fabrication rate, we obtain equation

(A4) providing the rate of change in fabrication WIP.

( )

( ) ( ) ( )

( ) FN

FWIPLD

*I

U tFWIPCUK

tFWIPtFWIPYYDPW

tD,MAXfKtIPWF τ

τ−

⋅

−+⋅⋅

⋅=

∗

0& (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.

( ) ( ) ( )tStDtB −=& (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).

( ) ( ) ( )( )OP* tFGI,DDtBMINtS τ= (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

28

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.

( ) ( ) ( ) ( )( )OP*

CI

I tFGI,DDtBMINtTDtAtA

tAtB τ−⋅

+

=)()(

)(& (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).

( ) ( ) ( )tStAtIGF N −=& (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).

( ) ( )( )AU*NG tAWIP,YAMINtA τ= (A9)

Substituting equations (A6) and (A9) into (A8), we obtain the equation describing the

rate of change in finished goods inventory:

( ) ( )[ ] ( ) ( )[ ]OP*

AU*N tFGI,DDtBMINYtAWIP,AMINtIGF ττ −=& (A10)

29

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).

( ) ( ) ( )tAtDtIPWA GI −=& (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 disk-

like 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:

( ) ( ) FLDI tFWIPYYDPWtD τ⋅⋅⋅= (A12)

Substituting equations (A9) and (A12) into (A11), we get the rate of change in assembly

WIP.

( ) ( ) ( )( )AU*

FLD tAWIP,YANMINtFWIPYYDPWtIPWA ττ −⋅⋅⋅=& (A13)

Equations (A4), (A7), (A10), and (A13) form a system of nonlinear 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*).

30

( ) ( ) ( ) ( )

−+=

∗

AWIPUI

tAWIPtAWIPYtEDMAXtD

τ/,0* (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).

DAdj

)t(ED)t(D)t(DE

τ−

=& (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.

( ) ( )( )

( )*

OP*

* DDtBtFGI,DDtBMIN

tStS

tFoF)(

)()( τ== (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.

31

3)(-)(

)( 11

P

tPFoFtFoFtoFFP

τ=&

(A17)

Substituting equation (A16) into (A17) provides the first term of the customer perception

of the fraction of orders filled (PFoF1).

( )( )( ) 3

)()(3

)()()( 1

1 /tPFoF

DDtB/tFGI,DDtBMIN

toFFPP

*P

OP*

τττ

−=&

(A18)

Intel’s attractiveness to suppliers (AI), measured in a scale from zero to one, is determined

by a logistic function (fA) 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.

( ))(3 tPFoFfA AI =

(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

32

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:

ULDN YYYDPWCUMSTDK

⋅⋅⋅⋅⋅= 0

(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 Definition Value Units TD Customer demand 5.0 Million units /month MS0 Initial market segment share 80 % DPW Number of die per wafer 200 Die/wafer CUN Normal capacity utilization 90 % YL Line yield: Fraction of good wafers per total 90 % YD Die yield: Fraction of good die per wafer 90 % YU Unit yield: Fraction of good chips per good die 95 % K Available capacity 28.9 ‘000 wafers/month

33

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 months 0.5 1 2 Time to Adjust Assembly WIP τAW months 0.5 1 2 Time to Adjust Fabrication WIP τFW months 0.5 1 2 Time to Adjust Backlog τAB months 0.5 1 2 Time to Update Orders τO months 0.5 1 2 Time to Update Shipments τS months 0.125 0.25 0.5 Weight unresponsive ωU dmnl 0 0. 5 1 Weight customer reaction ωA dmnl 0 0.5 1

34

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.

150

100

50

00 12 24 36 48

Time (Month)

Normalized Wafer StartsPulse 5% (Results with 2500 Simulations)

50%

95%

100%

75%

Base150

100

50

00 12 24 36 48

Time (Month)


50%

95%

100%

75%

Base150

100

50

00 12 24 36 48


Time (Month)

50% 75%

95%100%

Base

150

100

50

00 12 24 36 48


Time (Month)

50% 75%

95%100%

Base

35

0.32

0.26

0.200 12 36 48

Finished Inventory Coverage (Months)Pulse 5% (Results with 2500 Simulations)

24Time (Month)

95%100%

50%Base

0.32

0.26

0.200 12 36 48


24Time (Month)

95%100%

50%Base

95%100%

50%Base

0.32

0.26

0.200 12 36 48


24Time (Month)

95%

100%

50%

Base75%

0.32

0.26

0.200 12 36 48


24Time (Month)

95%

100%

50%

Base75%

1.0

0.9

0.80 12 24 36 48

Time (Month)

Perceived Fraction of Orders FilledPulse 5% (Results with 2500 Simulations)

100%1.0

0.9

0.80 12 24 36 48

Time (Month)


1.0

0.9

0.80 12 24 36 48

Time (Month)


100%1.0

0.9

0.80 12 24 36 48

Time (Month)


95%

100%

50%

Base 75%

1.0

0.9

0.80 12 24 36 48

Time (Month)


1.0

0.9

0.80 12 24 36 48

Time (Month)


95%

100%

50%

Base 75%

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

36

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).

φβ ⋅⋅= AWIPCHA (A21)

φδ ⋅⋅= FGICHF (A22)

( ) φα ⋅⋅−= tL MSMSC 0 (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).

( )[ ]{ }∫∞ − ⋅⋅+⋅+⋅−=0 0 dtFGIAWIPMSMSeCDC t

rt φδβα (A24)

37

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 Symbol Units Min Base Max

Fractional unit FGI holding cost δ 1/month 0.005 0.01 0.2

Ratio fractional unit AWIP to FGI cost β/δ dmnl 0.125 .25 0.75

Fractional unit lost sales cost 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.

38

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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