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ble of Contents
When Do Minor Shortages Inflate To Great Bubbles?
Paulo Goncalves
May 15, 2002
Abstract:
When demand exceeds supply, retailers hedge against shortages by placing multiple
orders with multiple suppliers. This artificial growth in orders can severely affect
suppliers, creating excess capacity, excess inventory, low capacity utilization, financial
and reputation losses. This paper contributes to the understanding of order amplification
caused by shortages, by providing a comprehensive causal map of the supplier-retailer
relationships and a formal mathematical model of a subset of relationships. It provides
closed form solutions to the dynamics of supplier backlogs when supplier capacity is
fixed and simulation analysis when it is flexible. Parameter sensitivity provides a deeper
understanding of long-term impacts and suggests emphasis for solution policies. For
instance, the ability to quickly build capacity can effectively reduce the bubble size.
Finally, the time it takes retailers to perceive supplier's delivery delay is an important
leverage in controlling retailers’ inflationary ordering. In particular, longer retailers’
perception delays contribute to system stability.
Keywords:
System dynamics, supply chain, order amplification, supply shortages, simulation.
System Dynamics Group
Sloan School of Management
Massachusetts Institute of Technology
30 Wadsworth St., E53-358A
Cambridge, MA 02142
Phone 617-258-5585
Fax: 617-258-7579
paulog@mit.edu
1. Motivation
Supply shortages constitute a common and recurring supply chain problem, impacting
industries ranging from personal computers to pharmaceuticals. Shortages often take place in
industries characterized by costly capacity and long acquisition delays (Cachon and Lariviere
1999) or during the introduction of new products, when demand is uncertain, and new processes,
when production yield is uncertain (Lee et al. 1997a). Shortages often lead to lower corporate
growth (Savage 1999) and loss of shareholder value (Singhal and Hendricks 2002). In addition,
they can lead to excess production capacity and inventories, as the example from the
semiconductor industry shows (Baljko 1999, Greek 2000).
During a 1995 shortage of microprocessors, suppliers like Intel and AMD had to allocate
production capacity among several retailers such as Dell, Compaq, HP, and several others. To
improve their chances of supply, retailers placed multiple orders with suppliers. Since suppliers
could not differentiate between true demand and retailer-created demand, they easily mistook
retailers’ speculative orders for an increase in demand. Hence, suppliers responded by increasing
safety stock of raw materials and components, speeding up production, adopting overtime
policies, and building additional production capacity. However, as production capacity increased
allowing suppliers to meet demand, the retailers’ need to hedge against supply shortages
disappeared and so did their speculative orders. The artificial bubble in demand quickly burst
leaving manufacturers with huge inventories, reduced prices and unwanted excess capacity.
Sadly, order cancellations (and products returns) are common practice in several
industries. Hence, examples of inflated demand generated by product shortages are abundant.
For instance, orders for DRAM chips in the 1980's went through a similar process (Lode 1992).
Hewlett-Packard lost millions of dollars in unnecessary capacity and excess inventory after a
demand surge for its LaserJet printers (Lee et al. 1997b). Facing shortages of Pentium III
processors in November 1999, Intel planned to introduce a new production plant early 2000
(Foremski 1999). Later that year, blaming order cancellations by large customers and economic
slowdowns, Intel wamed that its revenues would fall short of projections and that sales would be
flat for the quarter (Gaither 2001). More recently, Cisco Systems lost over US$ 2.5 billion in
inventory write-offs due to inflated retailer orders for their products (Adelman 2001).
While the immediate consequences of shortages are clearly identified in the literature,
some of the long-term impacts and the mechanisms leading to them are not well understood. This
research investigates the impact that retailers’ locally rational decisions may have in reinforcing
the initial shortage dynamics, leading to more dramatic and long lasting impacts to supply chain
performance. The research follows a system dynamics methodology to study this problem and to
investigate policies capable of mitigating its impacts. The aim is to inform both academics and
practitioners dealing with demand bubbles generated by shortages
My analysis suggests that a transient shortage in supply can permanently drive the
supplier to a low performance equilibrium, in which backlogs and delivery delays are high, when
she cannot increase capacity to meet retailers’ needs. In addition, supplier’ s ability to bring
capacity online can help reduce the impact of shortage. However, she still goes through a
transient period of low performance, as it takes time to bring new capacity online. When the
additional capacity becomes available and retailers start receiving their orders, the bubble bursts.
The burst is characterized by a period of order cancellations followed by a period of reduced
demand, while retailers are depleting their excess inventories - an inverse bubble when orders
are much lower than they would traditionally be. As the bubble bursts, suppliers are left with
excess inventories and capacity greatly exceeding the amount of product in short supply.
Furthermore, the faster the supplier can add new capacity the lower the impacts of the bubble,
that is, it will require less capacity, it will face a shorter period of low performance with lower
backlogs and shorter delivery delays. Hence, the ability to quickly bring capacity online helps
suppliers prevent the growth in the bubble. However, capacity flexibility alone may not be a
sustainable way to prevent demand bubbles, since it is costly and suppliers are still left with
excess capacity. As it tums out, the perception of shortages will depend both on supply and
demand, hence acting on both aspects can have more effective results. For instance, the size of
the bubble is also greatly influenced by the amount of competition in the industry, hence the
fiercer the competition among retailers the greater the bubble in retailers’ orders. To avoid the
impact of competition, suppliers may choose to give priority to preferred retailers or to limit the
number of retailers that they will work with.
Moreover, my analysis suggests that an important leverage point in the system is the time
delay it takes retailers to perceive the supplier’ delivery delays. When the supplier provides real-
time information about delivery delays to retailers the system is highly unstable. This takes place
because retailers react instantaneously to the readily available information. So, if retailers see an
increasing delivery delay they will respond rapidly and will inflate their orders to hedge against
shortages only making the situation worst. In contrast, when the supplier provides information
about delivery delays with a long time delay to retailers the system is more stable, because it will
take time before retailers over-react, giving the supplier an opportunity to act - speeding up
production, increasing overtime, increasing safety stocks of raw material and components - to
reduce delivery delays. Interestingly, the idea of suppliers providing delayed information about
delivery delays and inventory availability goes in direct opposition to current industry trend to
introduce information systems providing real-time information to all parties in the supply chain.
Unfortunately, these real-time information systems may be introducing a great deal of instability
leading to the creation of larger than ever demand bubbles. While companies claim to have saved
millions of dollars in purchasing and ordering operations, the costs associated with over- ordering
may far exceed the savings generated from the accurate processing of orders.
This paper proceeds as follows. The next section provides an overview of the relevant
academic literature. Section 3 describes the phenomenon and discusses its dynamics. Section 4
presents a formal model followed by results and analyses in section 5. I conclude the paper with
a discussion about insights and areas for further research.
2. Literature Review
There is an extensive system dynamics and operations management literature addressing
inventory instability in supply chains. The first formal system dynamics model on inventory
oscillations date back more than 40 years ago and coincide with the emergence of the field of
system dynamics (Forrester 1958, 1961). Forrester suggested that the oscillatory behavior in
demand was caused by the structure (including the feedback nature) of the system. Around 1958,
Willard Fey converted this early supply chain work into a game, which subsequently evolved
into the famous beer game. Subsequent system dynamics research focused on investigating
oscillations in different supply chain settings. For instance, Mass (1975) considered the
interrelationship of inventory oscillations and its impacts on a company’s labor force. Morecroft
(1980) investigated the implementation of Material Requirements Planning (MRP) systems on a
company’s supply chain and showed that the faster response time could increase the frequency
and amplitude of inventory oscillations.
Departing from the modeling work in supply chains and motivated by research on
bounded rationality and experimental economics, researchers in system dynamics focused their
attention on experimental research. In the context of supply chains, system dynamicists have
focused on characterizing how managers make decisions and investigating whether such actions
can generate pathological dynamics. For instance, Sterman (1989a, 1989b) conducted human-
subject experiments in a four stage supply chain setting to demonstrate that the sources of
oscillation and increase in variability were managers’ misperceptions of feedback and their
inability to account for the supply line of orders. Diehl and Sterman (1995) continued this work
to consider how feedback complexity, in a two-echelon supply chain, affected decision-making.
In sharp contrast to this behavioral explanation of supply chain instability, the operations
management literature offers a number of operational explanations. For instance, Lee et al.
(1997a, 1997b) suggest that rational agents are able to generate demand variability through four
operational causes: demand signal processing, rationing (supply shortages), order processing,
and price variations. Chen et al. (2000) verify that the bullwhip effect takes place because of two
operational causes: a specific demand forecasting technique and order lead times. While the
dispute among researchers defending operational or behavioral causes of supply chain instability
is far from over, a recent article by Croson and Donohue (2000) suggests that the bullwhip effect
still exists in the absence of three (e.g. price fluctuations, order batching and demand estimation)
out of the four normal operational causes offered by Lee et al. (1997a, 1997b). Their study does
not control for product shortages, which is the emphasis of this paper.
Papers addressing supply shortages emphasize two aspects of them: the games that take
place among different agents and the impact that the product allocation mechanism has on
retailers’ demand variability. For instance, Lee et al. (1997a) develop a single period game
theory model with rational agents to show that strategic behavior among retailers, leading to
demand inflation, can take place when the supplier allocates insufficient capacity in proportion to
retailer orders. The supplier in their model has imperfect information since she cannot
distinguish true demand (customers’ orders) from those inflated by retailers. The authors suggest
that capacity allocation in proportion to past sales (tum-and- earn) can mitigate this problem, but
they do not model this case. Cachon and Lariviere (1999a) examine how a turn-and- eam
allocation mechanism impacts retailer behavior and supply chain performance, showing that it
allows suppliers to improve profits at the expense of retailers’ and even the supply chain
performance. Cachon and Lariviere (1999b) explore the impact of other allocation mechanisms
and the supplier’ s decision to build capacity. They build a sequential game theory model where
suppliers choose the allocation scheme, retailers place their orders and then suppliers decide on
how much capacity to build. Their findings suggest that no truth-inducing allocation mechanism
can maximize retailer profits, and attempts to implement such a mechanism may result in lower
profits for all (supplier, retailers, and the supply chain).
While previous research on demand variability provides a rich context for the impact of
shortages, the emphasis on game theory requires equilibrium and supply chain assumptions that
may not be realistic in real supply chains. This papers expands on this research by investigating
out-of-equilibrium dynamics and more realistic production physics, such as: (a) capacity
constraints that may take place due to long capacity acquisition delays; (b) endogenous and
variable delivery delays, due to changing order backlog and supplier capacity; and (c) perception
and adjustment delays, rather than instantaneous access to information and immediate adjustment
to desired levels. Finally, previous research explores policies that are limited in nature to address
different allocation mechanisms. I propose to investigate a broader set of policies, under a
proportional allocation mechanism, and the impact of different parameters in mitigating the
amplification in orders.
3. Dynamic Hypotheses
In a decentralized chain with a single supplier and multiple retailers (Figure 1), I
hypothesize that retailers’ managers inflate orders when insufficient supply is allocated in
proportion to retailers’ orders. This takes place in the following way: Under supply shortage,
suppliers will have long delivery delays and high delivery uncertainty. Consider retailers’
reactions to a long delivery delay. First, they will adjust the increase in the delivery delay by
ordering ahead of their needs. If they keep a supply line of 2 weeks of inventory to meet
expected sales for a product with 2 weeks delivery delay, once the delivery delay increases to 4
weeks retailers will adjust the supply line accordingly. Retailers will order twice as much to
maintain the same supply line. By ordering ahead retailers increase even further the backlog of
orders, resulting in an even higher delivery delay. Another consequence of longer lead times is
retailers’ desire to build up of safety stocks - correcting inventory to lead times -, since a larger
inventory buffer would prevent retailers from running out of stock due to longer lead times.
However, retailers must place more orders to build up safety stocks, which increases the
supplier's order backlogs and makes future lead times even longer. Figure 2 shows the
reinforcing loops (R1) Order Ahead and (R2) Correct Inventory to Lead Time.
Customer
Orders
i <——_
Retailer [<— >
Retailer <>
Shipments
Supplier
Retailer ----»
Customer
Orders
4
Retailer <— >
Figure 1. Supply chain structure
Now, consider the retailers’ reactions to receiving only a fraction of their orders. As
shipments fall short of retailers’ orders, retailers’ perception of suppliers’ delivery reliability
drops. Retailers adjust to this reduction in reliability by ordering more than necessary. Since
they expect to receive just a fraction of their total orders, retailers inflate orders - ordering
defensively - in hopes of getting just what they need. So, if retailers have been receiving half of
their orders when the supplier allocates capacity in proportion to his orders, they double their
orders hoping to get the quantity desired. By ordering defensively retailers increase supplier's
backlog of orders even further, resulting in an even more restrictive allocation policy.
Furthermore, retailers increase their safety stocks in response to reduced delivery reliability -
correcting inventory to delivery reliability. But to increase their safety stocks retailers must place
even higher orders building up supplier’ s backlog of orders even further. This results in an even
tighter allocation policy and a further decrease in delivery reliability. Figure 2 shows the
reinforcing loops (R3) Order Defensively and (R4) Correct Inventory to Delivery Reliability.
The supplier can expand capacity to balance the effect of the reinforcing loops in the
system - Adjust Capacity - loop (B2). Interestingly, as supply becomes available the reinforcing
loops begin to act in a virtuous way. As backlog decreases and delivery delay falls, retailers
have no need to order ahead or to maintain large safety stocks. Hence, they reduce their supply
line and their desired inventory levels accordingly. This leads to a decrease in orders and a
further drop in supplier’s backlog level. Analogously, as backlog drops delivery reliability
improves and retailers stop ordering defensively, leading to further decreases in backlogs. Once
the supply becomes available, orders disappear quickly by virtue of the same reinforcing loops
that caused them to increase in the first place.
i Lead
Capacity Time
a
he
+ R1
®) Order Ahead Inventory to
. jer Aheat invent
Adjust Lead Tine
Capacity
Delivery
iF
* Reliability “> Desired
4n3) Ara) Safet
Channel Order Channel ,, Correct stoc
Order Defensively Desired — Delivery
Backlog 4e1)
+ Adjust
Supply Line - Desired
Channel inventory
Orders
Mac ustomer
Orders
Figure 2. Dynamic hypothesis for demand bubble problem
From the description above, it appears that the characteristic behavior of demand bubbles
would be represented by an overshoot-and-collapse in orders due to retailers’ response to a
supply shortage. During the initial shortage period, retailers’ over-reaction inflates the bubble
through over-ordering. Then as supply normalizes, the bubble bursts due to retailers’ over-
reaction in canceling outstanding orders. Moreover, since shortages occur frequently due to
costly capacity, long capacity acquisition delays, uncertain demand for new products, and
uncertain production yields for new processes we can expect to see repeated cycles of sharp
overshoot-and-collapse in orders typical of demand bubbles. In addition, since demand bubbles
occur during supply shortages, demand bubbles do not take place in a predictable fashion. In that
sense, understanding why and when shortages take place can be very helpful in mitigating their
impacts.
Finally, to gain a deeper understanding of the processes generating the bubbles and to
investigate policies that can effectively mitigate their impact I build a formal mathematical
model of the relationships discussed above.
4. The Model
The model emphasizes the internal causes of system behavior. In particular, the focus of
is on retailers’ endogenous reactions to supply shortages and the positive loops reinforcing such
actions to create bubbles in demand. While exogenous shocks can influence system behavior,
they provide little policy leverage to managers, since their causes lie beyond their control. The
model presented here includes only one of the possible retailers’ reinforcing loops: the Ordering
Ahead (R1) loop. While this provides a limited view of the problem complexity, if by itself it is
capable of generating the demand bubble phenomenon, it can be useful in guiding the derivation
of insights. In addition, if included, other reinforcing loops would only make the problem more
pronounced. For the sake of simplicity, I consider the relationship of a single supplier selling a
single product to multiple retailers.
The supplier's backlog of orders (B(t)) increases by retailer demand (R(t)) and decreases
by shipments (S(t)) and cancellations (C(t)), according to the differential equation 1. Retailer
demand has two terms: a true customer demand (d(t)) and a backlog adjustment term (AdjB). The
first term is the real demand retailers observe. The second term is the adjustment between the
channel desired backlog (B*(t)) and suppliers’ actual backlog. This term allows the supplier to
adjust her backlog over an adjustment time (1s) if she observes an increasing desire for her
products. Equation 2 shows retailer demand. In addition, the desired channel backlog is a
function (f) of delivery delays, which is given by the ratio of backlog to shipments. The function
of delivery delay represents retailers’ response to supplier's ability to fill demand.
B(t) =R(t) —S(t) -C(t) (1)
B*(t) —B(t) (2)
B
R(t) =d(t) +
Consider now the flows of shipments and cancellations. The minimum of desired
shipment rate (S*(t)) and available capacity (K(t)) determine the amount of shipments (S(t)). That
is, shipments will normally be determined by the desired shipment rate unless there is not
sufficient capacity. Also, the desired shipment rate depends on the ratio of backlog and the target
delivery delay (t), as shown in equation 3. Cancellations depend on the difference between total
orders received by retailers (S,) and total customer orders (D.). If there are more retailers’ orders
than customer orders then retailers will cancel the excess in the time to cancel orders (1%). If
there are less retailers’ orders than customer orders there are no cancellations (eq-4).
8 =MIN(BA K) (3)
= D, -S,
C =MAX(0, V4 ) (4)
The supplier’s capacity (K(t)) is a smooth of retailer demand (eq-5), with a time constant
given by the time to build capacity (t, ). Moreover, the amount of total orders received by
retailers (S,) accumulates supplier’s shipments to retailers (eq-6) and total customer orders (D.)
simply accumulates true customer demand (eq-7)
_ R(t) -K(t)
Kt) (5)
q&
§, =K (6)
D, =d (7)
An additional simplifying assumption allows the supplier to maintain a fixed market
share over time. While prolonged poor reliability will, in general, lead to loss of market share,
there are instances when suppliers can retain their market share despite poor performance. This is
often the case when the companies have patented products or their industries have huge barriers
to entry.
To represent retailers, I aggregate them into a single retailer. This assumes homogeneity
among different retailers, that is, that they will influence model behavior in the same way due to
shortages. This assumption does not hold in general since retailers have different size,
negotiating power, inventory policies, etc. however, retailer heterogeneity has little impact on
retailers’ reactions to delivery delays. When delivery delay is larger than desired, retailers inflate
their orders. While each retailer will inflate by different amounts the model provides an estimate
of the average inflation by all retailers. Hence, the assumption of retailer homogeneity does not
impact the model dynamics. Furthermore, I assume that retailers can cancel orders without
incurring any penalties. This holds true in many industries such as semiconductors, networking
equipment, electronics, agribusiness, and several others.
10
A function (f) captures retailers’ locally rational behavior of placing speculative orders
when the delivery delays increase above normal. In particular, when faced with long delivery
delays retailers order ahead, that is, they increase their expected delay above the delivery delay
quoted by the supplier. Increasing their expected delay is intendedly rational to retailers, since
they believe that the supplier will try to avoid loosing sales at all costs, even by giving a delivery
delay quote that is more optimistic that what it really is. The retailer’s bias can be captured in a
number of different ways. In the simplest case, I assume a retailer's bias proportional to the
actual delivery delay quoted by the supplier, that is, that retailers will adjust their expected delay
more for longer delivery delay quotes. ' Hence the retailers’ response to delivery delays can be
captured by a linear function of delivery delay with a slope of a ( f = a B/K, where a>1).” This
function embeds the assumption that supplier shipments will be proportionately distributed
among retailers. The business press provides ample anecdotal evidence for retailer’s speculative
ordering behavior under proportional allocation (Greek 2000). Academic research also supports
this assumption. Using a game theory model, Lee et al. (1997a) show that retailers behave
strategically, inflating orders, when a supplier allocates capacity in proportion to orders. Hence,
in aggregate, retailers’ action to inflate orders is intendedly rational.
It is rational for retailers to place more orders than necessary because the more they
order, under a proportional allocation mechanism, the more product they are likely to receive.
Moreover, by over-ordering retailers avoid the psychologically difficult possibility of being left
without supply. Furthermore, often in industries plagued by such retailer behavior the costs
associated with over-ordering (penalties for cancellations and returns - if they exist) are much
smaller than the costs associated with under- ordering (unsatisfied customers, unrealized sales
and potential loss in market share). All such aspects provide an additional incentive for retailers’
strategic behavior. Finally, retailers will cancel orders once the total amount of products received
from suppliers surpasses the total demand from customers as shown in equation 4.
‘| also assume that when delivery delays are lower than the target, retailers simply adjust their ordering without a
bias.
? The linear function capturing the proportional bias of retailers is useful to obtain a closed form solution to the
problem when the supplier does not invest in new capacity. When the supplier has fixed capacity shipments are
bounded by available capacity and hence delivery delays are determined by the ratio of backlog and capacity. In the
more general case, used throughout the simulations including the case for variable capacity, the function (f) is a non-
linear function that captures a stronger adjustment as delivery delays increase but saturates for delivery delays of 6
months and higher.
11
Initial
Actual Input
Channel —-» pemand <— (beta)
Demand (d)
ra Desired a 4
Retailer's —f Backlog xpectet
Demand perceived * (B*) Delivery Table
Inflow Demand ey, Eff DD
Time to Adjust © (f)
+» Backlog (TB)
- Backlog
‘Cumulative Adjustment Initial
Demand ’ Backl Delivery
(Dc) ‘acklog Delay
+ |-* Wi
g| Backlog
Retailer (B) i
Demand shinee nts
Time to (R)
Cancel \ 4 #
Excess Cancellations || Desired
(Cc) Shipments
(sy
Target it +
Excess Delivery Senge
Orders Delay Orders
(TD) Received
- f* Kg ‘i
me Desired
‘upply Capacit 7
Demand pack ait Orders
+ apaci
impaionce a By Retles
(Sr)
Figure 3. Model diagram for supplier-retailer system
Now consider the supplier’s actions. One possibility is to assume that the supplier does
not respond strategically to retailers’ order inflation, that is, the supplier is oblivious to retailers’
actions despite order cancellations and product retums. This does not seem plausible.
Alternatively, it is possible to assume that over time the supplier learns to discount retailers’
orders when delivery delays are high. Consider the outcome. When the supplier discounts the
orders received she intensifies the product rationing perceived by retailers, resulting in even
more inflated orders. A gain, the supplier knows better than to believe in the retailer so she
discounts part of the orders and sends whatever she believes appropriate. The problem is that the
supplier does not know true customer demand, making it difficult for her to assess how much to
discount. Consequently, retailers will always have an advantage in their ability to order more to
compensate for supplier's actions. So, even when suppliers are compensating for (discounting)
retailers’ orders it is plausible to assume that order inflation will prevail. Instead of explicitly
12
representing the supplier’s discounting of retailers orders, it is possible to interpret the shape of
the linear function’ as the net result of retailers’ and supplier's actions.
In terms of the supplier’s operations, she adjusts her backlog level according to the
desired channel backlog and she attempts to fill orders to maintain a desired target delivery
delay. Capacity constraints, however, can limit the supplier's ability to ship, causing delivery
delays to increase. Finally, the supplier can expand capacity as she perceives demand to increase.
Figure 3 shows the system dynamics model described above. And the set of differential
equations (8-11) below represent a fourth order system of first order differential equations when
the supplier is capacity constrained and there are no order cancellations.
bB, =d (8)
S, =K (9)
Kao gd f(B/K)-B_K (10)
Tr Tp ‘Tr Tr
Bad +2 FIED By (11)
B
5. Model Analysis
This section investigates the behavior of the model in greater detail. First, it provides a
closed form solution to the model when the supplier has fixed capacity. Then, it considers model
behavior when supplier has flexibility to change capacity. Since the model complexity increases
significantly insights in this case is derived from simulation. Finally, the last section provides
sensitivity analysis to explore the impact of important parameters on model behavior.
5.1. Fixed Capacity
First I investigate the model behavior when the supplier does not introduce new capacity.
I implement this by setting the time to build capacity (TK) to an extremely high value. This has
the equivalent effect of breaking the feedback link from supplier demand to available capacity. I
simulate the model for five years with a transient increase and subsequent transient decrease in
true customer demand, using actual (customer) demand as the input to test model behavior. I
start the model in steady state equilibrium. (In the absence of any changes in demand the model
3 And the non-linear table function in the case of flexible capacity.
13
behavior remains the same.) Then, I introduce an input composed of a 10% temporary increase
(a pulse starting at t = 6, lasting for 6 months) followed by a 10% temporary decrease (a pulse
starting at t = 12, lasting for 6 months) in demand (Figure 4). This is equivalent to a period of
supply shortage followed by a period of excess supply.
1+8)-K, if t) st <t,
d Bei if t; <t <t, (12)
A K,ift, st<T
5,000
4,500
4,000
3,500
3,000
0 6 12 18 24 #30 36 42 48 54 60
Time (Month)
Figure 4. A transient increase and decrease in customer demand
Since the increase and decrease in demand have the same magnitude and duration, any
changes in model behavior capture retailers’ response to relative shortages in supply. That is, if
retailers would not over-react to during the supply shortage period, then the period of excess
capacity would be exactly sufficient to bring the system back to equilibrium. During the high
demand period retailers never receive all orders placed. However, during the low demand period
suppliers have a chance to meet the excess demand from the previous period exactly due to the
symmetry of the test. Since suppliers will never ship more products than real customer demand,
when capacity is fixed and limited, retailers never have a reason to cancel orders. Hence, the
fourth order system characterized by equations (8-11) can be reduced to a first order system.
Since cancellations do not take place information about total customer orders (D<) and orders
received by retailers (S;) in equations (8-9) does not impact the state of the supplier’s backlog or
retailer’ s response. Hence we can ignore equations 8-9. And since capacity is fixed equation 10
reduces to a constant. The system is reduced to equation 11, where it is possible to consider a
linear function (f = a B/K, where the slope a>1) for retailers’ response to delivery delays. This
captures a retailers’ bias proportional to the actual delivery delay - the higher the delivery delay
14
the higher retailers’ expected delivery delay.’ Hence, the resulting system is given by equation
13.
jag LOBE WB (13)
Ts
d-a/K +1 Fi vog F hari “i
Now, let y =—————_ and let @ =d - K then substituting 12 into 13 it is possible to
B
write:
BB = (14)
Ha-l)+0p/ j
g Uhr itty sts BK, if t, <t<t,
where: y =H + * if t, st <t, o =d -K ts ‘K, if , <t<t,
H OY ita and H 0, ift, <t<T
Note that the equilibrium for the model is given by B = and that y represents the
eigenvalues of the system. Hence, it is possible to describe the system stability for each region.
Given that a > 1, we note that in the first region (t, <t <t, ) the eigenvalue is real and positive
resulting in an unstable system. Since the supplier’s capacity is smaller than demand retailers
inflate orders and backlog increases exponentially with a growth rate of (a) 7h . Inregion
two (t, <t <t, ), when demand drops below the supplier capacity, the system is still unstable if
B se, that is, when the relative aggressiveness of retailers’ responses (@ “ly ) is larger than
the percentage increase in demand (f). Hence, very aggressive retailers will continue to increase
their orders even when the system has excess capacity to meet customer demand. Moreover,
when retailers are not aggressive, the system is stable and backlogs decrease exponentially to
equilibrium with a rate of (a -1) a4 . Note that for a > 1, the rate of growth in period one
B
strictly higher than the rate of decline in period two. Hence the supplier backlog cannot return to
the initial level after the period of excess supply. The difference between the initial backlog and
the backlog level at the end of period two captures the impact of retailers’ aggressiveness to the
“ Under fixed capacity delivery delay never drops below one; hence, there is no need to worry about order deflation.
15
supplier. In the last period (t, <t <T ), the system is always unstable for a > 1, since the
eigenvalue vis given by ( , . Note that when a = 1, that is, when retailers order the exact
amount to perfectly compensate for the delivery delay they experience (myopic retailers), the
previous results change. First, the rate of growth ( oe ) in the first period equals the rate of
decline ( 4 ) in the first period. Hence, backlogs can return to the initial equilibrium level
when the magnitude and duration of excess demand is the same as the excess supply. Finally,
when a = 1, the eigenvalue in the last period (t, <t <T ) becomes zero (y = 0), revealing that the
system will remain in equilibrium. It is possible to write the equations for backlog over time, by
finding the solution to the first order differential equation given by eq- 14:
B=? 40-0" (15)
Y
And, when ty = 0, e“ =1. So: C =B, “4, where i =1, if ty <t <t,;i =2,if t, <t <t,;i =3,if t, <t <T
B =(B, +91) sgt) _o
i Vi
O, , Bkt OC) pe .
{By + ye a) Yaayep if ty st<t
a —1) +0
B =H, ay ae)? Ae 5 Viesvens T, <t <t, (16)
q (oy)
Bue “* ~, ift, st<T
co
To further describe the behavior of retailers we include a saturation effect for the
maximum delivery delay (M) tolerated by retailers. This captures the idea that after a maximum
delivery delay retailers will not invest their time to adjust their orders further and instead may
look for alternative sources of supply.
pop MS
TT
Atts)/
B=(B,—MK):e 7? +MK
The equation for supplier backlog, when retailers tolerate a maximum delivery delay, is a
goal seeking behavior leading to a final equilibrium value of MK. Now consider the range of
16
possible retailers’ reactions. As illustrated before reactions can range from the myopic to the
very aggressive. A myopic retailer will adjust his orders exactly to compensate for the increase in
delivery delay. In this case, the slope of the retailers’ response to delivery delay function is one
(a = 1). An aggressive retailer will adjust orders by much more than the required compensation.
The slope of the expected delivery delay function is more than one (a@ >> 1) such that the relative
aggressiveness of retailers’ responses (& xy ) is higher than the percentage increase in demand
(B). A “normal” retailer will still adjust orders by more than the required amount but the relative
aggressiveness of retailers’ responses is lower than the percentage increase in demand. As seen
in the earlier derivation, even myopic retailers will order more during shortages to compensate
for the supplier’s inability to meet demand. However, as soon as demand lowers, retailers reduce
their ordering accordingly until suppliers’ backlogs return to equilibrium. Normal retailers,
however, order more than necessary to compensate for the short supply and while backlogs
decrease when there is excess supply, they never return to the equilibrium level. In addition,
since delivery delays are above normal and retailers have a consistent bias to inflate orders, the
system becomes unstable. With the introduction of the saturation, the system reaches a low
performance equilibrium, where the delivery delay equals the saturation delivery delay (M) and
the product of customer demand and the saturation delay (KM) determines the equilibrium level
for the supplier’ s backlog. This situation is similar for aggressive retailers, with the exception
that backlogs do not decline during the period of excess supply. Figure 5 shows the behavior of
supplier backlogs, with the introduction of a saturation effect.
0 12 24 36 48 60
Time (Month)
Aggressive = + + 3 = + + Units
Normal 2— Units
Myopic --3- Units
Figure 5. Supplier’ s backlog with saturation effects’
° Where the following parameter have been used: B =0.1, M. = 10, Mn = 7.5, K = 4,000, a = 1.2, & = 1.05.
17
Naturally, suppliers have a chance to invest in new capacity when they experience
shortages. However, production capacity can only come online after some time delay. The next
section investigates the impact of capacity flexibility on system behavior.
5.2. Variable Capacity
Allowing the supplier to introduce new capacity makes the system much harder to solve.°
Hence, I simulate the model for five years (from equilibrium) with a transient increase in demand
to gain intuition about the model behavior. Then, at the end of the first year I allow a transitory
10% increase in demand that lasts one year.
Shipments and Capacity
6,000
Lp,
4,500
0 12 24 36 48 60
Time (Month)
Units/Month
Units/Month
3- Units/Month
Backlog
24,000
16,000
8,000
0
0 12 24 36 48 60
Time (Month)
Steady State
Backlog -—~
Desired Backlog : Pulse
Figure 6. Supplier’s (a) shipments and (b) backlog for a 10% transient increase in
customer demand
5 It results in the fourth-order system (8-11) of nonlinear differential equations presented in section 4.
18
Figure 6a shows demand, shipments and capacity for the supplier; figure 6b shows
supplier actual and desired backlog compared to the steady state equilibrium. Due to the increase
in customer demand, retailer orders surpass the supplier’ s capacity causing an increase in
backlog. Over time, the supplier builds capacity to meet the increase in demand. At the end of
year two, available capacity finally meets customer demand, but retailers still inflate their orders
due to large backlogs and delivery delays. Since supplier capacity is still insufficient to meet
retailers’ inflated demand, backlogs continue to increase. As a result of the sustained increase in
retailers’ demand, the supplier continues to invest in capacity to satisfy a booming market. The
increase in supplier’ s capacity and backlog represents an important aspect of the system
behavior. While customer demand increases by 10% during a model year, capacity increases by
more than 30% to balance the order inflation by retailers. Comparatively, backlogs increase by
300% relative to its equilibrium level in response to the transient increase in demand. Hence, the
increase in customer demand causes a disproportionately high increase in supplier capacity and
backlogs.
When supplier shipments finally meet retailers’ demand, the backlog reaches its
maximum. At the same time, as more capacity becomes available and shipments increase,
delivery delay decreases. Retailers respond to lower deliver delays by not inflating their orders.
In fact, retailers start canceling orders as supply availability normalizes and the total retailer
orders increase beyond total customer orders. Interestingly, the initial boom of the demand
bubble is in sharp contrast with the steep decrease in orders that takes place when the bubble
bursts. The burst is characterized by a sharp increase in order cancellations followed by a period
of reduced demand, while retailers are depleting their excess inventories. The behavior is not
only characterized by the inflated increase in demand but also by the sharp burst (inverse bubble)
caused by cancellations and reduced order rate. Figure 7 shows the evolution of supplier’ s actual
and retailer’ s expected delivery delays as well as retailers’ order cancellations.
19
Delivery Delay
0 12 24 36 48 60
Time (Month)
Actual —$——4——3- 3-3. 3.3.3.4. Month
Expected =e Qe Qe Qn enn Jonna one Month
Cancellations
6,000
4,500
3,000
1,500
0 a er a
12 24 36 pr 0
Time (Month)
Cancellations 3344.43. __3 Units/Month
Figure 7. (a) Delivery delays and (b) cancellations for a 10% transient increase in
customer demand
The relationship between delivery delays and supply-demand imbalance becomes clear in
the following phase plot (Figure 8). The graph shows that as shortages take place and total
customer orders (D,) exceed the total amount of orders received by retailers (S,), the expected
delivery delay increases. Also, since the supply-demand imbalance is given by the difference
between total orders received by retailers and customer orders (S, - D.), the supply-demand
imbalance becomes negative. As a result of long delays, retailers inflate their orders and over
time the supplier invests in new capacity to meet the perceived growth in demand. Suppliers’
ability to increase shipments prevents the supply-demand gap from decreasing even further.
However, delivery delay continues to increase for a while because the supplier still accounts for
retailers’ inflated orders. Moreover, supplier ’s still high backlogs translate into high delivery
20
delays and further inflated orders. So, even though the retailers are closing the gap on customer
demand, supplier's delivery delay is getting worse.
Phase Plot
6
i
§ 4
3
2
| _
“0
-3000 0 3000 6000
Supply Demand Imbalance
Figure 8. Phase plot supply-demand imbalance for a 10% transient increase in
customer demand
When the supply-demand gap is zero, retailers start canceling orders. However, backlogs
and delivery delays will continue to increase while retailer demand is larger than shipments and
cancellations. As the supply-demand imbalance increases, retailers cancel a greater fraction of
their orders. With more supplier capacity available and more cancellations, suppliers can run
down their backlogs and decrease delivery delays. Retailers adjust by not inflating their orders.
Now as the positive loops act on the virtuous way, retailers do not inflate their orders and
suppliers can quickly run down backlogs. Consequently, at the time of the inverse bubble, when
retailers are canceling existing orders, suppliers experience low retailer demand, excess capacity
and run down backlogs. Over time, the additional capacity and the improved performance of the
supplier allow her to run down the backlog to its initial equilibrium condition. But as figure 6
shows it takes more than one year after the shortage in supply for backlog to retum to
equilibrium. Finally, since capacity acquisition and disposal takes much longer, capacity is still
above the equilibrium level three years after the end of the shortage in supply. To get further
insight into the model the following sections provide sensitivity analysis on several model
parameters.
21
5.3. Sensitivity Analysis
This section investigates the sensitivity of the model behavior with respect to changes in
the time to build capacity, the time it takes retailers’ to perceive the actual delivery delay quote
provided by suppliers and retailers’ reactions to delivery delay and. For the first two tests, I run
the simulation model allowing the parameter to be twice as high and half as low as the base case
run. For the last test, I introduce different (table) functions to capture retailers’ responses.
5.3.1. Time to build capacity (, )
Now let me investigate the impact of the time to build new capacity on system behavior. I
test how the model behaves under different capacity acquisition delays ranging from 6 months to
2 years. Figure 9 shows the results for backlogs.
Backlog
30,000
0 12 24 36 48 60
Time (Month)
Fast Cap
Normal
Slow Cap
2,000
0 12 24 36 48 60
Time (Month)
Fast Cap Units/Month
Normal
Slow Cap
Figure 9. Supplier’s (a) backlog and (b) capacity under different delays to build capacity
22
Shorter capacity acquisition delays (FastCap) leads to lower capacity level and an earlier
peak. Longer delays (SlowCap) result in a higher capacity level as well as a later peak and a
longer period of excess capacity. The results suggest that the supplier's ability to build capacity
quickly can reduce the size of the bubble and the duration of the problem. Since introducing new
capacity typically requires a long delay companies have devised strategies that gives them
flexibility to ramp up production. In particular, the semiconductor industry builds the building
infrastructure (the shell) well in advance such that it does not become an additional constraint in
ramping up production of a new fabrication facility. The equipment then is positioned as it
becomes necessary. While rapidly building capacity prevents the bubble from growing, it is
important to notice that even when capacity can be quickly introduced, backlogs still doubled in
size, for a 10% increase in demand.
Suppliers often have the flexibility of adding capacity to deal with a long trend increase
in capacity. But capacity expansion is always costly and once the investment has been made
suppliers would like to make the most out of it. However, we observe that due to the order
inflation, suppliers tend to introduce much more capacity - the longer the delay in introducing
capacity the higher the capacity commitments - than the actual increase in customer demand.
Unfortunately, the additional capacity brought online is poorly used. As soon as the bubble
collapses, the supplier is left with unused excess capacity. Actually, the situation portrayed in the
model is very conservative since it assumes that it is possible to run down capacity as quickly as
it is to introduce it. This assumption often does not hold. A more realistic assumption, accounting
for longer delays to run down production capacity, would lead to higher excess capacity for
suppliers. Hence, while capacity flexibility mitigates the problem, by itself it may not be an
effective means to deal with the impact of retailer strategic ordering due to shortages.
5.3.2. Time for Retailers’ to Perceive Delivery Delay
I now examine the model's sensitivity to the perception delay retailers experience before
they learn about the supplier's quoted delivery delay. Information systems providing real time
information about quantities available to promise and delivery quotes between a supplier and a
retailer have decreased this delay to virtually zero. However, this push towards system
integration and information sharing often takes place when there is a dominant player in a supply
chain. While many large companies adopt such integrated information systems, with the intent of
23
increasing chain visibility for better planning and forecasting, the majority of small and medium
companies do not yet have such integrated systems in place.
Here, I investigate the impact of the length of the retailers’ perception delay on system
behavior. I test the model under different perception delays ranging from no delay (No
Perception Delay which represents integrated information systems providing real time
information to retailers) to 2 months (Long Perception Delay which represents Mom & Pop
businesses checking their inventory positions sporadically). Figure 10 shows the results.
Backlog
30,000
0 12 24 36 48 60
Time (Month)
No Perception Delay
Capacity
6,000
4,666
3,333
2,000
0 12 24 36 48 60
Time (Month)
Long Perception Delay. —% z + + 7 + + + Units/Month
Nomal 2. 2 2 2 2 2 2 2 2 2-- Units/Month
No Perception Delay a 3 Units/Month
Figure 10. Supplier’s backlog under different perception delays
The system is much more stable when retailers learn about delivery delays with a long
perception delay. By providing all parties real time information, current supply chain
management systems, linked seamlessly through the Internet, may be introducing a great deal of
instability in supply chains. The business press provides some commentary of how real time
supply chain management impacts the economy (Schwartz 2001).
24
“The Internet, with its myriad online connections, speeds the transmission of ideas, good and bad,
and amplifies their reach. It has allowed business managers to peek into every link of the supply
chain that feeds their manufacturing processes, and to change direction with a nimbleness that
would have been unimaginable just a few years ago.”
The Chairman of the Fed, Alan Greenspan, supports a similar point of view:
“The faster adjustment process raises some warming flags. Business managers have access to more
information, but everyone gets similar signals. As a consequence, firms appear to be acting in far
closer alignment with one another than in decades past. The result is not only a faster adjustment,
but one that is potentially more synchronized, compressing changes into an even shorter time
frame.”
While the new supply chain management systems provide more accurate and real time
information capable of reducing purchasing and ordering costs, no one realized how the
information might be used. In particular, these systems have not been designed to account for
feedback complexity and the impact of the use of the information. The results of the analysis
suggest that allowing faster adjustment (No Perception Delay) may cause more aggressive
behavior by retailers and a stronger impact of shortages, which explains the larger magnitude of
more recent impacts (Figure 10). The experience of business managers tends to agree with this
result (Clancy 2001).
“By sharing knowledge of orders or parts shortages or other factors, companies across the high-
tech industry are probably more in sync than they ever have been before. This has been the
promise of the e-business revolution, but no one ever realized how this information might be used.
I'd say we're getting our first taste of how companies might react to up-to-the-minute operational
information. In short, they would move more quickly to protect profits. Even Fed Chairman Alan
Greenspan has theorized publicly that the improved efficiency of forecasting systems has
exacerbated the severity of the economic slowdown, which gripped the country more quickly than
anyone predicted.”
Finally, the results suggest that the costs associated with over-ordering may far exceed
the savings generated from accurate processing of orders. In that sense, it is important to further
investigate the role that supply chain management tools may be playing in the economy.
5.3.3. Retailers’ reactions to delivery delay (f)
I now explore the aggressiveness of retailers’ reactions to quoted delivery delays. A fully
myopic (or naive) strat egy for retailers simply adjusts their orders in proportion to the increase in
the delivery delay. There is no bias under the myopic strategy (am =1). This strategy is myopic
because it does not take into consideration the strategic actions of other retailers competing for
the same scarce supply. And it is naive in its assumption that the supplier provides the true
delivery delay quote. Hence, this strategy represents the mildest possible way in which retailers
25
react to delivery delays. In contrast to the myopic case, retailers in the base case (normal) will
adjust their expected delivery delay to account for strategic behavior from other retailers or the
supplier. The function that describes retailers’ expected delivery delay is a non-linear function
that captures a stronger adjustment as delivery delays increase but saturates (when actual
delivery delays equals 6 months) at a value of 7.5 months. Under the aggressive strategy,
retailers’ inflate their orders more aggressively than under the base case, which translates into a
function with a higher slope and a higher saturation value, at 10 months. In the following set of
tests, I run the model under the three strategies. Figure 11 shows the functions representing
retailers’ reactions under each strategy.
Expected Delivery Delay
Delivery Delay
Figure 11. Sensitivity of retailers’ reactions to delivery delay
Figure 12(a) shows backlogs under each retailer response. First, it is important to notice
that even under retailers’ myopic scenario - no strategic ordering among retailers - backlog and
the expected delivery delay still increases. This result is analogous to the case when capacity is
fixed. However, backlogs returns to the equilibrium level gradually rather than decreasing
sharply as systems with strategic ordering. Second, the aggressiveness of retailers’ competition
matters. In the normal case, a maximum retailer bias increases the expected delivery delay by
25% (from 6 to 7.5 months), causing backlogs to increase by a factor of four (reaching a level
that is higher than 16,000 units). In the aggressive case, a maximum retailer bias causes a 66%
(from 6 to 10 months) increase in the expected delivery delay, leading to an increase in backlogs
by a factor of seven times (reaching a level that is almost 30,000 units).
26
Backlog
0 12 24 36 48 60
Time (Month)
Aggressive + + + =o = + + + = i— Units
Normal
Myopic
Capacity
8,000
0 12 24 36 48 60
Time (Month)
Units/Month
~~ Units/Month
-3 Units/Month
Aggressive
Normal. -
Myopic
Figure 12. Supplier’ s (a) backlog and (b) capacity, different retailers’ reaction functions
Figure 12(b) shows the supplier’s capacity under different retailers’ strategic scenarios. In
the myopic case the supplier increases her capacity by 5%; in the normal case, by 30%; and in
the aggressive scenario by more than 65%. Thus the supplier accumulates much more capacity
than desired when retailers have a very aggressive strategy to obtain their orders. There are a
couple of different interpretations for retailers’ responses. One possibility is that it represents
individual retailers’ responses to shortages. Hence, individuals with more aggressive natures may
respond in a more emphatic way than other individuals, inflating their orders more. In this
context, the supplier may choose to focus on managing the orders of aggressive retailers, to
prevent the reaction of other competitor retailers.
Another possibility is that the responses capture the competitive environment retailers
face. Hence more aggressive responses can be expected in more competitive environments. In
27
that case, we would expect to see more pronounced demand bubbles in industries where the
amount of competition among players is intense. Furthermore, since the number of players can
influence the nature of the competition, limiting the number of retailers that a supplier tends to
may help suppliers to mitigate order inflation. Alternatively, suppliers may choose to give
priority to preferred retailers, preventing them from being impacted by shortages when they
occur.
6. Policy Discussion
In this paper, I considered the phenomenon of bubbles in demand that can take place
when retailers compete for the supply of scarce products. The paper contributes to the
understanding of the phenomenon by providing a comprehensive causal map of the relationships
leading to retailers’ inflation of orders. In addition, I provide a formal mathematical model for
one of the possible retailers’ reinforcing loops: the Ordering Ahead (R1) loop. By assuming that
supplier capacity is fixed, it is possible to obtain closed form solutions to the behavior of supplier
backlogs. Even when myopic retailers order the exact amount to compensate for an increase in
delivery delays system performance decreases, leading to higher backlogs and longer delivery
delays. If retailers are aggressive, the analysis suggests that a transient shortage in supply can
permanently drive the supplier to a low performance equilibrium, in which backlogs and delivery
delays are high, when she cannot increase capacity to meet retailers’ needs. The supplier's ability
to bring capacity online can help reduce the impact of shortage. However, she still goes through
a transient period of low performance, as it takes time to bring new capacity online. When the
additional capacity becomes available and retailers start receiving their orders, the bubble bursts.
The burst is characterized by a period of order cancellations followed by a period of reduced
demand, while retailers are depleting their excess inventories. As the bubble bursts, suppliers are
left with excess inventories and capacity greatly exceeding the amount of product in short
supply. In fact, the supplier’s capacity and backlog represents important aspects of the system
behavior. For instance, a 10% transient (one year) increase in customer demand can induce
capacity increases on the order of 30% to balance retailer’ s order inflations and backlogs can
increase by 300% relative to its equilibrium level.
Furthermore, the faster the supplier can add new capacity the lower the impacts of the
bubble, that is, it will require less capacity, it will face a shorter period of low performance with
28
lower backlogs and shorter delivery delays. Hence, the ability to quickly bring capacity online
helps suppliers prevent the growth in the bubble. However, capacity flexibility alone may not be
a sustainable way to deal with demand bubbles. Even when they limit the impact of the demand
bubble, suppliers are left with excess capacity. This effect is particularly important when
adequate time constants for the depreciation of capacity are taken into consideration. Since a
rapid introduction of new capacity can have a significant reduction in the size of the demand
bubble, it is important to consider flexible strategies for quickly bringing new capacity online.
In addition, the analysis suggests that an important leverage point in the system is the
time delay it takes retailers to perceive the supplier’ delivery delays. When the supplier provides
real-time information about delivery delays to retailers the system is highly unstable. This takes
place because retailers react instantaneously to the readily available information. So, if retailers
see an increasing delivery delay they will respond rapidly and will inflate their orders to hedge
against shortages only making the situation worst. In contrast, when the supplier provides
information about delivery delays with a long time delay to retailers the system is more stable,
because it will take time before retailers over-react, giving the supplier an opportunity to act -
speeding up production, increasing overtime, increasing safety stocks of raw material and
components, and bringing up new capacity online - to reduce delivery delays. Interestingly, the
idea of suppliers providing delayed information about delivery delays and inventory availability
goes in direct opposition to current industry trend to introduce information systems providing
real-time information to all parties in the supply chain. Unfortunately, these real-time
information systems may be introducing a great deal of instability leading to the creation of
larger than ever demand bubbles. While companies claim to have saved millions of dollars in
purchasing and ordering operations, the costs associated with over-ordering may far exceed the
savings generated from the accurate processing of orders.
Interpreting the aggressiveness of retailers’ responses as a measure of market
competitiveness, the results suggest that more pronounced demand bubbles would take place in
industries where competition among retailers is intense. To avoid the impact of competition,
suppliers may choose to give priority to preferred retailers or to limit the number of retailers that
they will work with.
Finally, a number of researchers (to name a few: Kaminsky and Simchi-Levi 1996,
Gupta, Steckel and Banerji 1998) have analyzed policies (e.g., centralizing ordering decisions,
29
reducing order lead-times, and sharing Point-of-Sales (POS) data) for reducing demand
variability. Particularly important to demand bubbles is the availability of POS data. If suppliers
had access to such data it is arguable that they would not be facing such harsh conditions since
they could distinguish true demand from retailer-inflated demand. However, it is unrealistic to
expect that retailers plagued by shortages would be willing to share such information with their
suppliers in the first place, since it would limit their ability to obtain more products when needed.
In addition, those retailers who might be willing to share such information would potentially risk
receiving less than others who would be inflating their orders.
In summary, this paper contributes to the discussion of order amplification in supply
chains due to supply shortages. It offers a comprehensive causal map of the relationships leading
to retailers’ inflation of orders and a formal mathematical model of one reinforcing loops of
retailers’ response. It provides a closed form solution to the behavior of supplier backlogs when
supplier has fixed capacity and an analysis of the simulation when capacity is flexible. Finally,
parameter sensitivity analysis explores how the model behavior changes due to parameter
changes, leading to a deeper understanding of the long-term impacts of demand bubbles and
policies solutions that may mitigate their impacts.
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