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.
39
Embed
THE IMPACT OF CUSTOMER RESPONSE ON INVENTORY AND ...moya.bus.miami.edu/~pgoncalves/Customer_Response_JBL.pdf · maintain low inventory levels and run lean supply chains, allowing
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
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
8
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.
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
Forecasted CustomerDemand
Desired WaferStarts
+
Demand
+
ReplacingShipments
+
+ +DELAY
WIP Adjustments
WIP Adjustments
+ CustomerDemand
+
++
+ +DELAYDELAY
FabricationWIP
FinishedGoods
InventoryWaferStarts
NetFabricationCompletion
Shipments
AssemblyWIP Net
AssemblyCompletion
Wafers Dies Chips
FabricationWIP
FinishedGoods
InventoryWaferStarts
NetFabricationCompletion
Shipments
AssemblyWIP Net
AssemblyCompletion
Wafers Dies Chips
– – Fraction of Orders Filled
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.)
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
ProductionEffect
R2
Sales Effect
B2
Forecasted CustomerDemand
Desired WaferStarts
+
Demand
+
ReplacingShipments
+
+ +DELAY
WIP Adjustments
WIP Adjustments
+ CustomerDemand
+
++
+ +DELAYDELAY
FabricationWIP
FinishedGoods
InventoryWaferStarts
NetFabricationCompletion
Shipments
AssemblyWIP Net
AssemblyCompletion
Wafers Dies Chips
FabricationWIP
FinishedGoods
InventoryWaferStarts
NetFabricationCompletion
Shipments
AssemblyWIP Net
AssemblyCompletion
Wafers Dies Chips
– – Fraction of Orders Filled
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)
Perceived Fraction of Orders Filled
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
13
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
No Customer Response
Perceived Fraction of Orders Filled
115
110
105
100
950 12 36 48
Normalized Demand Forecast
Customer Response
No Customer Response
24Time (Month)
115
110
105
100
950 12 36 48
Normalized Demand Forecast
Customer Response
No Customer Response
24Time (Month)
24Time (Month)
(a) (b)
150
125
100
75
500 12 24 36 48
Time (Month)
Customer Response
No Customer Response
Normalized Wafer Starts150
125
100
75
500 12 24 36 48
Time (Month)
Customer Response
No Customer Response
Normalized Wafer Starts
0.30
0.25
0.200 12 36 48
Finished Inventory Coverage (Months)
Customer Response
No Customer Response
24Time (Month)
0.30
0.25
0.200 12 36 48
Finished Inventory Coverage (Months)
Customer Response
No 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 ($) – No Customer Response
Safety Stock80 M
40 M
0 M0 12 24 36 48
Time (Month)
Lean Inventory
NPV Costs ($) – No Customer Response
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 ($) – Customer Response80 M
40 M
Safety Stock
0 M0 12 24 36 48
Time (Month)
Lean Inventory
NPV Costs ($) – Customer Response80 M
40 M
(a) (b)
80 M
40 M
0 M0 12 24 36 48
Time (Month)
Unresponsive Utilization
Responsive Utilization
NPV Costs ($) – No Customer Response80 M
40 M
0 M0 12 24 36 48
Time (Month)
Unresponsive Utilization
Responsive Utilization
NPV Costs ($) – No Customer Response
80 M
40 M
0 M0 12 24 36 48
Time (Month)
Responsive Utilization
Unresponsive Utilization
NPV Costs ($) – Customer Response80 M
40 M
0 M0 12 24 36 48
Time (Month)
Responsive Utilization
Unresponsive Utilization
NPV Costs ($) – 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.)
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 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*).
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)
Normalized Wafer StartsPulse 5% (Results with 2500 Simulations)
50%
95%
100%
75%
Base150
100
50
00 12 24 36 48
Normalized Wafer StartsPulse 20% (Results with 2500 Simulations)
Time (Month)
50% 75%
95%100%
Base
150
100
50
00 12 24 36 48
Normalized Wafer StartsPulse 20% (Results with 2500 Simulations)
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
Finished Inventory Coverage (Months)Pulse 5% (Results with 2500 Simulations)
24Time (Month)
95%100%
50%Base
95%100%
50%Base
0.32
0.26
0.200 12 36 48
Finished Inventory Coverage (Months)Pulse 20% (Results with 2500 Simulations)
24Time (Month)
95%
100%
50%
Base75%
0.32
0.26
0.200 12 36 48
Finished Inventory Coverage (Months)Pulse 20% (Results with 2500 Simulations)
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)
Perceived Fraction of Orders FilledPulse 5% (Results with 2500 Simulations)
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)
Perceived Fraction of Orders FilledPulse 20% (Results with 2500 Simulations)
95%
100%
50%
Base 75%
1.0
0.9
0.80 12 24 36 48
Time (Month)
Perceived Fraction of Orders FilledPulse 20% (Results with 2500 Simulations)
1.0
0.9
0.80 12 24 36 48
Time (Month)
Perceived Fraction of Orders FilledPulse 20% (Results with 2500 Simulations)
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