Download The Impact of the Secondary Market on the Supply Chain

The Impact of the Secondary Market
on the Supply Chain
Hau Lee • Seungjin Whang
Graduate School of Business, Stanford University, Stanford, California 94305
[email protected] • [email protected]
T
his paper investigates the impacts of a secondary market where resellers can buy and sell
excess inventories. We develop a two-period model with a single manufacturer and many
resellers. At the beginning of the first period resellers order and receive products from the
manufacturer, but at the beginning of the second period, they can trade inventories among
themselves in the secondary market. We endogenously derive the optimal decisions for the
resellers, along with the equilibrium market price of the secondary market. The secondary
market creates two interdependent effects—a quantity effect (sales by the manufacturer)
and an allocation effect (supply chain performance). The former is indeterminate; i.e., the
total sales volume for the manufacturer may increase or decrease, depending on the critical
fractile. The latter is always positive; i.e., the secondary market always improves allocative
efficiency. The sum of the effects is also unclear—the welfare of the supply chain may or
may not increase as a result of the secondary market. Lastly, we study potential strategies
for the manufacturer to increase sales in the presence of the secondary market.
(Supply Chain; Secondary Market; Exchanges; Market Equilibrium)
1.
Introduction
has the function of facilitating transactions of the secondary market. In fact, for many market exchanges,
business transactions in the secondary market are the
only transactions that occur today. Hence, the secondary market is an important element of general
market exchanges.
This paper is motivated by one such market
exchange in the high-tech industry called TradingHubs.com, set up by Hewlett-Packard Company
(HP). We start by describing the trajectory of TradingHubs.com. The high-tech industry is plagued with
highly uncertain demands, as well as with continuously shrinking product life cycles and high risks of
product obsolescence. The inability to accurately forecast demand for short-life-cycle products has resulted
in resellers of computer products either having to
write off excessive obsolete inventory or losing significant profits because of stockouts at the end of a product life cycle. It is also common that one reseller may
have excess inventory while another has a shortage.
0025-1909/02/4806/0719$5.00
1526-5501 electronic ISSN
Management Science © 2002 INFORMS
Vol. 48, No. 6, June 2002 pp. 719–731
The Internet is becoming a dominant technology platform for the conduct of business. The advance of
business-to-business commerce has resulted in the
establishment of many “eMarketplaces.” eMarketplaces bring potential buyers and sellers together in
an Internet-based exchange, whereby business transactions can take place.
There are many types and characteristics of these
market exchanges: They can be private or public, and
one-to-many or many-to-many (i.e., involving multiple buyers and multiple sellers). They can be used
to trade primary materials for production or indirect
materials for business operations. They can serve as
the primary market, as the secondary market (i.e.,
to dispose of or buy excess inventory), or both. This
paper focuses on the impact of a market exchange as
the “secondary market”—that is, for the disposal and
acquisition of excess inventory. Almost every market exchange that we have come across in practice
LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
Because the resellers have to absorb these operational
costs, the existence of the channel results in higher
product costs to the consumers.
Companies that employ a direct channel, such as
Dell and Gateway, therefore have a definite advantage over companies like HP and Compaq that rely on
the reseller channel to move their products. The cost
advantage enjoyed by consumer-direct manufacturers
has translated to increasing loss of market share by
the manufacturers using reseller channels (see Austin
et al. 1997). Moreover, excess inventory in the channel at the end of the product life cycle is also a liability to HP, due to price protection (see Lee et al.
2000) and returns allowances paid by the manufacturer. This motivated HP to develop a strategy to
help the channel reduce its inventory-related costs,
with hopes of closing the cost gap between consumerdirect manufacturers and channel-based manufacturers. This was the genesis of a market exchange created
by HP.
In May 1999, HP launched an Internet-based
exchange—TradingHubs.com. Among other things, it
provided a secondary market for HP’s resellers to
trade their computing and electronics products on
the Internet. Hence, if HP or a reseller had excess
inventory, it could use TradingHubs.com to seek other
resellers to buy the excess inventory. Similarly, a
reseller who needs certain products that cannot be
provided by the manufacturer can seek resellers who
have extra inventory to dispose of. Initially, products in the secondary market of TradingHubs.com
included microprocessors, memory, drives, and storage devices.
From July 1999 to April 2000, over $45 million
of parts and products were traded in the secondary
market of TradingHubs.com. The success of TradingHubs.com has prompted HP to work with other
manufacturers to create a much bigger eMarketplace
that would have an expanded scope of product offerings. On May 1, 2000, AMD, Compaq, Gateway,
Hitachi, HP, Infineon, NEC, Quantum, Samsung,
SCI Systems, Solectron, and Western Digital formed
an independent company, named eHITEX, that will
operate an open Internet-based exchange to serve
the needs of the electronics and high-tech community (eHITEX 2000). The new venture will provide
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online sales services to buyers and sellers involved
in computing- and electronics-related industries, a
market that is estimated to be about $600 billion
over the next few years. A major part of eHITEX
(later renamed Converge) is to provide a secondary
market function allowing trade of excesses and surpluses. In 2001, Converge decided to scale back their
market exchange offerings, and it is interesting to note
that it is the secondary market function that it still
keeps and that constitutes almost all the activities of
this exchange today.
Although the originators of TradingHubs.com
were convinced that the creation of an online secondary market would help the resellers reduce their
inventory-related costs, they were not as sure about
the impact of it on HP itself (Billington 1999). One
school of thought was that a reseller, expecting that
the secondary market could make it effortless to dispose of excess inventory at a later stage of the product
life cycle, would therefore purchase more from HP at
the beginning of the product life cycle. This would
benefit HP, as higher product sales at the beginning
of the product life cycle would give rise to more revenues, as a result of both higher sales volumes and
higher profit margins at the beginning of the product life cycle. On the other hand, a pessimistic view
was that a reseller, knowing that the secondary market enables him to purchase more products, if needed,
at a later stage of the product life cycle, would therefore purchase less from HP at the beginning of the
product life cycle so as to avoid product overage. This
would hurt HP’s bottom line.
The impact of the online secondary market on HP
and resellers is also complicated by the fact that the
collective purchase decisions of the resellers affect
the amount available to be traded in the secondary
market, and ultimately the secondary market price.
If most resellers aggressively purchase products from
HP at the beginning of the product life cycle, then
the potential excess inventory available in the secondary market will be larger, and the price in the
secondary market will be depressed. This expectation will in turn make resellers reconsider buying so
much from HP. The converse holds if most resellers
underpurchase from HP. Thus, the market price has
a dual role in the secondary market: to match supply
Management Science/Vol. 48, No. 6, June 2002
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The Impact of the Secondary Market on the Supply Chain
with demand, and to form an expectation for resellers
to use in deciding the quantity to buy from HP and
in the secondary market.
Hence, although HP launched TradingHubs.com
and later worked with other manufacturers to create eHITEX, the impact of the online secondary market remains a key question faced by HP executives.
Would a reseller indeed purchase more at the beginning of a product life cycle with the existence of the
online secondary market than without the market?
Would the overall sales of HP products to consumers increase or decrease with the secondary market? Would we see more or fewer stockouts at the
resellers as a result of the secondary market? Would
there be less excess inventory at the resellers towards
the end of the product life cycle, so that there would
be fewer product returns for which HP is liable, due
to the secondary market? This paper seeks to provide
partial answers to these questions.
There is a literature of research related to secondary
markets. First, auctions have been used extensively
as the mechanism for conducting trades in secondary
markets, and there has been a tradition of research in
economics on the theory of auctions (see, for example,
Riley and Samuelson 1981 and Milgrom and Weber
1982). More recent research that deals with auctions
in e-marketplaces can be found in Gallien and Wein
(2000) and Vakrat (2000). Our current paper is not
about the mechanics of online secondary markets, but
rather on the impact of such markets on operational
performance of manufacturers and resellers. A more
relevant line of research is the literature on inventory
pooling and component commonality in the operations management area.
The existence of a secondary market has the effect
of allowing the resellers to share inventory after initial purchases have been made. Hence, this is similar
to inventory pooling (see Eppen and Schrage 1981 or
Tagaras and Cohen 1992) or lateral transshipments in
the multiechelon literature (see Lee 1987 or Axsaster
1990, for example). It is also similar to component
commonality in manufacturing (see Baker et al. 1986
and Gerchak et al. 1988, for example). In both cases,
the impacts of inventory pooling and commonality
have been modeled. The differential impacts on the
manufacturers and the resellers, however, were not
Management Science/Vol. 48, No. 6, June 2002
considered. More recently, the work by Anupindi and
Bassok (1999) represents the first attempt to examine
the impacts of inventory sharing at the retail level
on the manufacturer, and shows that a manufacturer
may be worse off with inventory pooling at the retail
level; i.e., the resellers may sometimes purchase less
from the manufacturer compared with the case of no
inventory pooling. A similar result has been obtained
by Dong and Lee (2000) in the case of parts commonality, and therefore special incentive systems have to
be developed so that manufacturers would be willing to participate in designing commonality into their
products.
The past research on inventory pooling and commonality were, however, limited in their direct applicability to online secondary markets. As mentioned
earlier, most of the past research has centered around
the impacts only on the resellers or the system as a
whole, and not the differential impacts on manufacturers, resellers, and the supply chain. Second, the
number of resellers was often limited (generally to
two), which presumably is not the case with online
secondary markets. Third, the market price in the use
of inventory pooling or commonality was assumed to
be exogenously given and constant, which is not the
case with online secondary markets where prices are
dynamically determined endogenously according to
supply and demand.
Given the scarcity of research capturing “markets”
in the inventory literature, our objective is modest.
We develop a simple mathematical model (i.e., the
newsvendor model that is modified to capture the
basic characteristics of the secondary market), and
analyze the properties of the equilibrium and differential performance of the manufacturer, resellers, and
the supply chain as a whole. We also give managerial insights and implications for industry that follow
from our research.
The paper is organized as follows. In §2 we describe
the basic model that will be used throughout the
paper. Section 3 characterizes the equilibrium of the
model, while §4 and §5 investigate the quantity effect
and allocation effect of the secondary market. Section 6 discusses potential strategies for the manufacturer. Additional comments, limitation of the model,
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The Impact of the Secondary Market on the Supply Chain
and future research directions are given in §7, thereby
closing the paper.
2.
The Standard Setting
with No Secondary Market
Consider n resellers who order a single product from
the manufacturer and sell it over a short sales season.
The short sales season setting is typical of the hightech industry. Product life cycles are short, so the
resellers often do not have the opportunities to resupply stocks from the manufacturer after initial purchases at the beginning of the product life cycle. Each
reseller buys each unit at p1 , sells at to end consumers, and the salvage value of the units left unsold
by the end of the sales season is zero. The manufacturer has a constant unit production cost which
is normalized at zero. The sequence of events is as
follows. At the beginning of the season, reseller i
orders Qi from the manufacturer, which is delivered
immediately. Retail sales zi are realized over the sales
season where zi is a random variable independently
drawn from F ·. This means that the resellers’ respective retail markets are segregated from each other. We
assume that F is twice differentiable over 0 , with
a finite mean , and we assume its inverse function
exists. Unfilled orders are lost forever. This is the standard setting for the newsvendor problem which can
be formulated as
Qi
max zf z dz + Qi
f z dz − p1 Qi Qi
0
Qi
The optimal stock level is:
o
−1 − p1
Qi = F
3.
The Model of the
Secondary Market
(2.1)
Now suppose that a secondary market opens at some
point during the sales season; based on this point
the sales season is divided into Periods 1 and 2. The
sequence of events is as follows. At the beginning of
Period 1, reseller i orders Qi from the manufacturer
722
(or equivalently, in the primary market), which is
delivered immediately. First-period retail sales xi are
realized where xi is a random variable independently
drawn from F1 · with a finite mean 1 . At the end
of Period 1 the secondary market is opened, where
resellers trade units at a uniform price. The price
p2 is endogenously determined to clear the market, and resellers buy and sell at the same price
(i.e., there are no transaction fees or transportation
costs). Given the price p2 , each reseller chooses a
stock level qi for the second period. Sales yi are
realized in Period 2—drawn from an independent
distribution function F2 · (with its mean 2 ), and
the game ends. We assume that xi and yi are independent for each i. This independence assumption
implicitly requires that the demand process over
time has statistically independent increments, such
as Brownian or Poisson demands. To be consistent
with the model with no secondary market, F is the
convolution of F1 and F2 (thus, = 1 + 2 ). We
are interested in the case in which n is infinitely
large (which mimics an Internet-based market), so
each reseller is a price-taker in the secondary market:
i.e., dp2 /dQi = 0.
Reseller i’s strategy is captured by the pair
Qi qi —the stock levels for Periods 1 and 2. Thus,
the symmetric (subgame-perfect) equilibrium Q∗ q∗ is defined, 1 such that moving backwards in time,
(1) given any Q x, and p2 , reseller i chooses the
second-period stock level qi∗ to maximize his expected
profit for Period 2;
(2) given any Q and x, the market clears at a
market-clearing price p2 so that demand equals supply; and
(3) taking other resellers’ strategies Q∗−i = Q1∗ ∗
∗
∗
Q2 Qi−1
Qi+1
Qn∗ as given, reseller i
chooses Qi , so that his expected profit over the two
periods is maximized.
We ignore the time cost of money in this paper
mainly for the simplicity of the exposition, although
the analysis will not materially change when a discount factor is used in the revenue and cost of
Period 2.
1
A boldface letter denotes the n-vector of corresponding variables:
e.g., Q = Q1 Q2 Qn .
Management Science/Vol. 48, No. 6, June 2002
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The Impact of the Secondary Market on the Supply Chain
3.1. Second-Period Stock Level
Given arbitrary p2 Q, and x, reseller i determines its
stock level qi∗ , such that
q
i
yf2 y dy + qi
f2 y dy
qi∗ = arg max qi
0
From this we have:
Theorem 1. Given a positive Q,
(a) (Law of Large Numbers)
p̂2 = lim p2 = 1 − F2 1 Q
n→
qi
− p2 qi − Qi − xi + Note that the last term may be either negative or positive depending on whether reseller i buys or sells in
the secondary market.
The optimal solution is
− p2
(3.1)
qi∗ = F2−1
By symmetry, let qi∗ = q ∗ for each i. Note that q ∗ is the
critical fractile solution to the newsvendor problem
applied to the second period only.
3.2. Equilibrium Price in Period 2
Given any Q and x, total demand under p2 is given
by nq = nF2−1 − p2 /, whereas total supply is
n
+
i=1 Qi − xi . The market price p2 is determined
by equating these two entities, so that in market
equilibrium:
n
1
+
p2 = 1 − F 2
(3.2)
Q − xi n i=1 i
By symmetry, Qi = Q for all i. If n is infinitely large,
then the law of large numbers yields:
Q
n
1
Q − xi + = EQ − x+ =
Q − xf1 x dx
n→ n
0
i=1
Q
=
F1 x dx = 1 Q
lim
0
Q
where i Q = 0 Fi x dx for i = 1 2 throughout the
paper.
From this and the Slutsky Theorem (Serfling 1980),
we obtain the limiting price p̂2 as follows.
p̂2 = lim p2 = 1 − F2 1 Q
n→
Note that p2 and p̂2 are functions of a given Q, but
to simplify notation, we suppress the argument Q.
Management Science/Vol. 48, No. 6, June 2002
(b) (Central Limit Theorem) p2 is asymptotically distributed according to N p̂2 2 f22 p̂2 n2 , where
1 Q
n2 =
1 x dx − p̂2 2 2
n
0
Proof. (b) Let zi = Q − xi + . Then, from the cen
tral limit theorem, ni=1 zi /n is asymptotically normal
with mean 1 Q and variance n1 EQ − xi + 2 − p̂22 Q
or n1 2 0 1 x dx − p̂2 2 . From Theorem A of Serfling
(1980, p. 118), if x is AN n2 (meaning asymptotically normal), then a differentiable transformation hx is AN h h 2 n2 assuming h = 0.
Hence follows the result. Note from Theorem 1(a) that due to the assumption
of large n, the market price is independent of specific realizations of first-period demands x. The only
determinant of the price is first-period order quantities Q. Part (b) shows the asymptotic behavior of
the price when the number of resellers grows large.
Clearly, as n approaches infinity, n2 approaches zero,
and Part (b) collapses to Part (a)—the usual relationship between the law of large numbers and the central limit theorem. When the number (n) of resellers
is on the order of hundreds, as is typically the case
in an Internet-based market, the variance of the price
is small enough to justify our analysis of the limiting
case. For the rest of the paper, we will assume that n
is large enough for us to take p̂2 as the market price,
and all resellers are pricetakers.
The following theorem offers sensitivity analysis
showing the behavior of p2∗ and q ∗ for small changes
in Q.
Theorem 2. (a) The secondary market price
decreases in Q.
(b) The optimal stock level for the second period
increases in Q.
Proof.
(a)
d p̂2 /dQ = −f2 1 QF1 Q < 0
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LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
(b) From (3.1) and Theorem 1(a),
∗
−1 − p̂2
q = F2
= 1 Q
so dq ∗ /dQ = F1 Q > 0. Both results are intuitively clear. As each reseller
increases the initial purchase amount from the manufacturer, the secondary market price will go down,
and this will encourage each reseller to carry more
stock for the second period.
3.3. Optimal Order Quantity in Period 1
We now determine resellers’ optimal first-period purchase decisions Q as the symmetric equilibrium
strategy.
Let p2∗ Q and q ∗ Q, respectively, denote the equilibrium market price and the equilibrium secondperiod stock level, when resellers make the decisions
Q in the first period. To derive the symmetric Nash
equilibrium first-period stock levels Q∗ , we take other
resellers’ decisions Q∗−i = Q∗ Q∗ Q∗ as given
and derive reseller i’s optimal decision Qi . Letting for
short p2∗ Qi = p2∗ Q∗−i Qi and q ∗ Qi = q ∗ Q∗−i Qi ,
reseller i’s decision problem is given by
Q
i
max xf1 xdx +Qi
f1 xdx −p1 Qi +V2 Qi Qi
Qi
0
where
V2 Qi = E q ∗ Qi 0
yf2 y dy + q ∗ Qi q ∗ Qi f2 y dy
+ p2∗ Qi Qi − xi + − q ∗ Qi In the above, V2 Qi represents the reseller’s expected
profit for the second period when the first-period
order quantity is Qi .
As n approaches infinity, we have: dp2∗ Qi /dQi =
dq2∗ Qi /dQi = 0, due to the price-taker assumption,
and thus we can use the definition p2∗ = p2∗ Qi and
q ∗ = q ∗ Qi . Therefore, we can show that
d Qi
lim V2 Qi = p2∗
Qi − xi f1 x dx = p2∗ F1 Qi n→
dQi 0
Using this, and by differentiating the objective with
respect to Qi , the first-order condition for an optimal
order quantity for Period 1 satisfies
− p1
F1 Qi =
(3.3)
− p2∗
724
The symmetric equilibrium for the first period is thus
Q∗ = Q∗ Q∗ Q∗ , where Q∗ satisfies (3.3).
From the above discussions, the equilibrium of
the model is fully characterized by the first-period
order level Q∗ , the secondary market price p2∗ , and
the second-period stock level q ∗ as in the following
theorem.
Theorem 3. For n large enough, the first-period order
quantity Q∗ , the second-period equilibrium price p2∗ , and
the second-period stock level q ∗ satisfy the following simultaneous equations:
F1 Q∗ =
−p1
−p2∗
p2∗ = 1 − F2 1 Q∗ and
∗
q =
F2−1
−p2∗
(3.4)
(3.5)
The equilibrium secondary price p2∗ has the following property.
Theorem 4. In equilibrium, p2∗ < p1 .
Proof. The theorem follows from (3.3):
p2∗ = −
− p1
< − − p1 = p1 F1 Q∗ The theorem demonstrates that the price in the secondary market is strictly lower than the original purchase price. The unit made available in the second
market has already lost the chance of being sold in
the first period, so that the expected revenue from the
unit should be smaller than the unit available in the
first period.
4.
The Impact of the Secondary
Market—The Quantity Effect
Will a secondary market increase or decrease the sales
of the manufacturer in the first period? Intuition can
direct us either way: A reseller may increase the purchase quantity because she faces a smaller risk of getting stuck with unsold inventory. By purchasing more
from the manufacturer, she can avoid stockouts in the
first period. At the same time, a reseller may also
have an incentive to buy less from the manufacturer
because she can observe the sales of the first period,
decide later how much more she needs for the next
Management Science/Vol. 48, No. 6, June 2002
LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
period, and buy from the secondary market. This is
exactly the question faced by HP with regard to TradingHubs.com. We term this effect of the secondary
market the quantity effect.
The answer is an outcome of a complex trade-off
among multiple factors like inventory and stockout
costs. In short, the secondary market may increase or
decrease the manufacturer’s sales, depending on the
critical fractile.
Theorem 5. In equilibrium the secondary market
increases the manufacturer’s sales (i.e., Qo ≤ Q∗ ) if and
only if
F1 F −1 # · F2 1 F −1 # ≤ #
A
where # is the critical fractile − p1 /.
Proof. Combining (3.3) and (3.4) yields:
− p1
−
= p2∗ = − F2 1 Q∗ F1 Q∗ Theorem 6. If limx→0+ f x > 0, there exists a strictly
positive # , for which if # ≤ # , the secondary market
increases the manufacturer’s sales.
This in turn gives
F1 Q∗ F2 1 Q∗ =
− p1
(4.1)
In the case of the standard newsvendor setting, we
have from (2.1)
− p1
= #
(4.2)
F Qo =
Let Hx = F1 xF2 1 x. It can be easily shown that
Hx strictly increases in x. Therefore, if Qo ≤ Q∗ , then
F1 Qo F2 1 Qo ≤ F1 Q∗ F2 1 Q∗ = #
o
Since Q = F
−1
#, it holds that
F1 F −1 # · F2 1 F −1 # ≤ #
The reverse can be shown in a similar manner. To better understand Condition A, we investigate
two special cases of the uniform and exponential
distributions of demands.
Example 1. Suppose that F1 and F2 are independent
and identically distributed according to a uniform
distribution over 0 1. We have:

x2 /2
if 0 ≤ x ≤ 1
2
F x = F1 ∗ F2 x =
x
−1 + 2x −
if 1 ≤ x ≤ 2
2
Applying Theorem 5, Qo ≤ Q∗ if and only if # ≤ 1/2.
Management Science/Vol. 48, No. 6, June 2002
Thus, for the uniform distribution case, Condition A translates to the critical fractile being less than
one half. In this case, the reseller facing the secondary
market increases the original purchase quantity if and
only if the profit margin is small enough in percentage terms.
Example 2. Next consider Fi x = 1 − exp−x, for
i = 1 2; i.e., the demand in each period is exponential.
Then, F x = 1−exp−x−x ·exp−x. The application
of Theorem 5 gives: Qo ≤ Q∗ if and only if # ≤ #o ,
where #o = 1 − exp−xo − xo · exp−xo and xo is the
unique positive solution to x − exp1 − exp−x · 1 −
exp−x = 0.
Again for the exponential distribution, Condition A
is equivalent to a small critical fractile.
For general distributions, a weaker form of this
result holds as follows.
Proof. Let R# = F1 F −1 # · F2 1 F −1 # − #.
Then, Condition A can be rewritten as R# ≤ 0. Then,
lim+ R # = lim+
#→0
#→0
f1 F −1 #
F F −1 #
f F −1 # 2 1
+ F1 F −1 #f2 1 F −1 #
F1 F −1 #
−1
f F −1 #
= −1
Hence, R# starts at zero with a negative slope and
crosses first, if at all, the x axis from below. Denote the
first crossing point by # . If it never crosses, choose
any arbitrarily large number for # . Then follows the
result. Note that both of the previous examples, as well as
normal distributions, satisfy the condition of Theorem
6, while beta and gamma distributions do not.
Theorems 5 and 6 show that the secondary market has the effect of “regression towards the mean”
in the following sense. In the traditional newsvendor
problem, the optimal order quantity is small or large
depending on whether the critical fractile is small or
large. On the other hand, however, the existence of
the secondary market dilutes this logic, because the
reseller orders more than the newsvendor solution if
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The Impact of the Secondary Market on the Supply Chain
the critical fractile is small, but less if the critical fractile is large. Figure 1 illustrates this result for normal
demands. The phenomenon is attributed to the price
effect of the secondary market—the opposing force to
neutralize the individual optimization effect (i.e., the
newsvendor logic). Consider a product with a small
critical fractile. Using the single-period newsvendor
solution will mean a smaller order quantity by the
resellers and, stochastically, a lower leftover inventory
at the end of the first period. As a result, the price
in the secondary market will be relatively high, and
this will invite resellers to buy more initially from the
manufacturer than the newsvendor solution. Symmetrically, for a high-fractile product, using the singleperiod newsvendor solution will mean a higher order
quantity and, stochastically, a higher leftover inventory at the end of the first period. Thus, the price in
the secondary market will be low, and this encourages
resellers to purchase less initially from the manufacturer. As a result, the secondary market serves both
as a hedge against excess inventory for a small critical fractile case and a hedge against stockouts for
a large critical fractile case. In other words, the secondary market makes wholesale demands less elastic
to the critical factor.
Now suppose Condition A is not met. Then, each
reseller will buy less than the newsvendor solution, and the manufacturer will be worse off as a
result of the secondary market. Even without the secondary market, the newsvendor solution is already
smaller than the optimal order quantity for the supply
chain due to “double marginalization” (Pasternack
1985). Thus, the secondary market aggravates double
marginalization if Condition A is violated.
5.
The Impact of the Secondary
Market—The Allocation Effect
We have seen in the previous section that the secondary market does not always increase the order
quantity by resellers. By contrast, resellers always
benefit from the secondary market. This is because a
reseller can always achieve the same performance of
the single-period newsvendor model by ignoring the
secondary market. Hence, the secondary market gives
an option that is of nonnegative value.
How about the impact of the secondary market on
the performance of the supply chain as a whole? We
call this impact the allocation effect of the secondary
market. The next theorem investigates three supply
chain measures—consumer sales, stockouts, and leftover stock (at the end of the second period)—as a
result of the secondary market.
Theorem 7. For a given positive Qo , the following
holds:
(a) There exists &<0, such that the expected sales in
the channel with a secondary market is larger than that
without a secondary market if and only if Q∗ − Qo > &.
(b) The expected number of stockouts in the channel
with a secondary market is smaller than that without a
secondary market if and only if Q∗ − Qo > &.
(c) There exists &>0, such that the expected leftover inventory in the channel with a secondary market is
smaller than that without a secondary market if and only
if Q∗ − Qo < &.
Proof. (a) Define
T & = & + Qo − 2 1 Qo + &
First, note that
T 0 = Qo − 2 1 Qo ≥ 0
Figure 1
∗
o
Q Versus Q Under Normal Demands
1
Q*<Qo
F1(Q)F2(Γ (Q))
F(Q)
(5.1)
(5.2)
To show this, we have:
Qo
o
Q =
2 Qo − x dF1 x
0
Qo
o
o
2 1 Q = 2
Q − x dF1 x 0
and 2 · is a convex function, so Jensen’s inequality
holds. Also, we have: T & = 1−F2 1 Qo +&F1 Qo +
& > 0. Thus,
Q*>Qo
Q
726
T & > 0
∀ & > 0
(5.3)
Management Science/Vol. 48, No. 6, June 2002
LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
At & = −Qo (the minimum feasible value of &), we
have:
T −Qo = −Qo + Qo < 0
(5.4)
From (5.3) and (5.4), therefore, T & is a strictly
increasing function whose value is negative at
& = −Qo , and positive at all & ≥ 0. Thus, there exists
a unique & ∈ −Qo 0, such that T & = 0.
Now, without a secondary market, the expected
sales over the two periods (per reseller) are:
S o = Qo − EQo − x+ = Qo − Qo (5.5)
With the secondary market, the total expected sales in
the two periods are:
S ∗ = Q∗ − 1 Q∗ + q ∗ − 2 q ∗ = Q∗ − 2 1 Q∗ (5.6)
where we used q ∗ = 1 Q∗ (by applying (3.4) to (3.5)).
Hence, the difference is:
S ∗ − S o = Q∗ − Qo + Qo − 2 1 Q∗ = T Q∗ − Qo Hence follows the desired result of Part (a).
(b) The expected number N o of stockouts with
out a secondary market is Qo x − Qo dF x dx =
Fx dx = Qo , where Fx = 1 − F x. LikeQo
wise, the expected number N ∗ of stockouts with a
2 q ∗ , where i Q =
market is 1 Q∗ + secondary
x
dx.
Noting
that
Q
=
−Q
+
+
F
i
i
i Q, for
Q i
i = 1 2 and the null case, the difference between the
two cases is N o − N ∗ = Qo − 1 Q∗ − 2 q ∗ = Q∗ −
o
o
∗
∗
o
Q + Q − 2 1 Q = T Q − Q . From this point
on, the proof parallels that of Part (a).
Alternatively, note that under the lost-sales model,
the sum of the expected channel sales and the
expected stockouts are the mean demand, so Part (b)
immediately follows from Part (a).
(c) Without a secondary market, the expected
second-period leftover inventory is EQo − x+ =
Qo , while for the case of the secondary market, it
is 2 1 Q∗ . Consider
o
o
T1 & = Q − 2 1 Q + &
Again as shown in the proof of (a), we have T1 0 =
T 0 ≥ 0. Moreover, T1 & = −F2 1 Qo + &F1 Qo +
& < 0. Also, note that T1 −Qo = Qo > 0 and
Management Science/Vol. 48, No. 6, June 2002
&>0, such that
lim&→ T1 & < 0. Thus, there exists T1 & = 0. Hence, the desired result follows. The theorem reports a varying degree of performance depending on the value of Q∗ relative to Qo .
= Qo + Let Q = Qo + & and Q
&. Because Q < Qo , the
implication of Theorem 7(a) and (b) is that when Qo ≤
Q∗ (i.e., when Condition A holds), we will always
have Q < Q∗ , and the expected sales in the channel with a secondary market will be greater than
that without a secondary market, while the expected
stockouts are lower (see Figure 2). This is a situation in which both the manufacturer and the channel see higher sales. Also, the expected sales in the
channel can be greater with a secondary market when
Q∗ < Qo , as long as Q∗ > Q. Hence, it is possible that a
secondary market will drive greater sales in the channel, even if the channel may actually buy less from
the manufacturer. This would be of great concern to
a manufacturer who is primarily interested in market
share and consumer sales of its product. When Q ≤
we have the scenario in which the expected
Q∗ ≤ Q,
sales in the channel is higher with less expected stockouts, while the expected leftover inventory is lower
with the secondary market. Further, if Qo ≤ Q∗ ≤ Q,
all four measures improve due to the secondary market, creating a win-win situation for the manufacturer,
resellers, and the supply chain as a whole. In particular, this includes the case of Qo = Q∗ . Thus, after controlling the quantity effect of the secondary market,
the secondary market unambiguously improves the
allocative efficiency of the supply chain by increasing
Figure 2
Four Measures Depending on Q∗
1. Higher Manufacturer sales
Q
Qo
Q
Newsvendor
Solution
2. Higher Channel Sales
3. Lower Stockouts
4. Lower Leftover Inventory
727
LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
sales to end consumers, and decreasing stockouts and
leftover stock.
6.
The Manufacturer’s Options
What can the manufacturer do if sales are not guaranteed to be higher with the secondary market? Based
on our results, if the manufacturer can control the
types of products traded in the secondary market,
he would choose only low-margin items to be traded
in the market. Boeing, for example, is a major shareholder in an eMarketplace that includes the operation
of a secondary market. In the secondary market, only
commodity-type parts are exchanged among its airline customers. Specialized items (usually with high
margins) would be purchased only direct from the
manufacturer. If the manufacturer cannot control the
secondary market, then the manufacturer has several
options to offset or mitigate the secondary market
impact using his market power.
The first option is to enforce a minimum order
quantity (MOQ) to each reseller. If the manufacturer
has the market power, he may require the reseller to
buy, for example, Qo at the minimum. Alternatively,
the manufacturer may induce the same purchase
quantity by offering a small quantity discount. Note
that this arrangement of MOQ or quantity discount
is not driven by logistics concerns as discussed by
Lee and Rosenblatt (1986), or Corbett and deGroote
(2000), but by the secondary market impact. In fact,
the present model assumes away delivery costs, so
the frequency of deliveries does not matter so long
as the total purchase equals or exceeds the targeted
quantity. If the required or induced purchase quantity
is Qo , it would represent a weak Pareto-improvement
to all supply chain members over the premarket equilibrium, as discussed in the previous section.
The second option for the manufacturer is to complement the secondary market with a return policy.
As Pasternack (1985) points out, a well-designed
return policy can eliminate the quantity distortion
driven by double marginalization. In other words, by
offering a rebate on reseller’s unsold inventory, the
manufacturer can induce the reseller to choose the
order quantity that is optimal for the welfare of
the supply chain as a whole, or for the maximal profit
of the manufacturer.
728
Likewise, our manufacturer can choose an appropriate rebate to maximize the profit. To derive
the optimal rebate, consider the manufacturer who
offers a rebate of ) for each unit left unsold by
the end of the second period. Then, the effect of
the rebate propagates in the following sequence—first
the inventory level q ) , then the limiting secondary
)
market price p2 , and ultimately the order quantity Q)
in the primary market.
Thus, the counterpart of (3.3)–(3.5) for the rebate
case can be obtained as follows:
F1 Q) =
−p1
)
−p2
(6.1)
)
p2 = − − )F2 1 Q) and
q ) = F2−1
)
− p2
−)
(6.2)
(6.3)
From (6.1) and (6.2):
F1 Q) · F2 1 Q) =
− p1
−)
(6.4)
Because the function H x = F1 x · F2 1 x strictly
increases in the range of 0 1, there is a one-to-one
mapping between Q and ) in the appropriate range of
values. Thus, ) can be set to induce a given quantity
of Q. The manufacturer can then choose an appropriate ) that would optimize his profit.
The third, rather intriguing, option available to the
manufacturer is to intervene in the secondary market by releasing a prepared quantity. This way the
manufacturer can sell more in the secondary market,
but it may have other effects. To see this, suppose
that the manufacturer prepares a quantity *n (i.e., *
per reseller) and releases it in the secondary market.
Omitting the straightforward details similar to those
in §3, the counterpart of Theorem 3 for this case is
F1 Q* =
−p1
*
−p2
*
p2 = 1 − F2 1 Q* + * and
q * = F2−1
*
− p2
(6.5)
(6.6)
(6.7)
Management Science/Vol. 48, No. 6, June 2002
LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
where the superscript * is used to highlight the
dependence of the quantities on *.
Using (6.5) and (6.6), we also derive the counterpart
of (4.1):
F1 Q* F2 1 Q* + * =
− p1
(6.8)
Comparing this with (4.2), we observe that Q*
decreases in *, i.e., the more the manufacturer intervenes, the less resellers buy from the manufacturer.
This is intuitively clear. If the manufacturer intervenes
heavily, the market price will go down in the second period, so resellers will have less incentive to buy
much initially from the manufacturer, and will rely
more on the secondary market to augment their stock
later. The problem of maximizing the total profit to
the manufacturer is given by
*
max +* = n p2 * + p1 Q* *
subject to Constraints (6.5)–(6.7).
The solution is not straightforward due to complex
*
interactions among p2 Q* , and *, but marginal analysis at * = 0 shows that
d+* dQ* ∗
=
np
+
np
(6.9)
1
2
d* *=0
d* *=0
and
dQ* −F1 Q∗ f2 1 Q∗ =
d* *=0 F12 Q∗ f2 1 Q∗ + f1 Q∗ F2 1 Q∗ Equation (6.9) shows the exact trade-off facing the
manufacturer in deciding whether or not to intervene
in the secondary market. With the market intervention, she gains in the secondary market at the rate
of p2∗ per reseller, but loses in the primary market at
the rate of p1 dQ* /d**=0 . The final result depends
on the relative magnitude. An interesting observation is the case of the uniform distribution as shown
in Example 1. In Appendix 1, we can show that
dQ* /d**=0 > 0 if # > 05. This is a useful result, as
we have shown that if # < 05, then Qo < Q∗ so the
manufacturer is already better off with the secondary
market. However, if # > 05, then Qo > Q∗ , and this
Management Science/Vol. 48, No. 6, June 2002
is the case when the manufacturer may see itself as
worse off with the secondary market and be anxious
to find a way to prevent profit reduction. Indeed, the
result of Appendix 1 shows that the manufacturer can
always improve its profitability by intervention in the
“unfavorable” secondary market condition.
7.
Conclusions
This paper investigates the impacts of a secondary
market where resellers can buy and sell excess inventories. We develop a two-period model with a single
manufacturer and many resellers. At the beginning
of the first period, resellers order and receive products from the manufacturer, but at the beginning of
the second period, they can trade inventories among
themselves in the secondary market. We endogenously derive the optimal decisions for the resellers,
along with the equilibrium market price of the secondary market. The secondary market creates two
interdependent effects—a quantity effect (sales by the
manufacturer) and an allocation effect (supply chain
performance). The former is indeterminate; i.e., the
total sales volume for the manufacturer may increase
or decrease, depending on the critical fractile. The
latter is always positive; i.e., the secondary market
always improves allocative efficiency. The sum of the
effects is also unclear—the welfare of the supply chain
may or may not increase as a result of the secondary
market. Lastly, we study potential strategies for the
manufacturer to increase sales in the presence of the
secondary market.
The model is built on several strong assumptions.
One of them is the zero transactions-cost assumption. Although the Internet would clearly lower the
cost of operating a marketplace, there remain nontrivial transactions costs such as logistics costs and
transaction fees to the exchange. Suppose we relax
this and assume that a transactions cost c per unit
traded is paid by the seller. In the second period,
not every reseller would choose the same inventory position. Because sellers pay the transaction fee,
overstocked resellers will take an inventory position
strictly larger than understocked resellers. In particular, the resellers slightly overstocked will not find
it worthwhile to trade paying transaction fees. More
729
LEE AND WHANG
The Impact of the Secondary Market on the Supply Chain
specifically, the resellers are divided into three groups:
sellers, buyers, and no traders, and the analysis gets
very complicated.
Another restrictive assumption of the model is that
demands over the two periods are independent and
that their distributions are known to all parties at
the beginning of the season. In reality, the demand
information is revealed as the sales season progresses
(Ananth and Fisher 1996). Particularly interesting is
the case in which an unexpected demand is experienced in the first period, which alerts resellers of
larger-than-expected demands in the next period. The
secondary market may serve as a rationing device
and mitigate the bullwhip effect (Lee et al. 1997). This
“market intelligence” model requires a significantly
different setup (including the primary market operating in both periods), and thus we leave it for future
research.
We have also assumed that demands of the retailers
are independent. In reality, demands across retailers
are likely to be positively correlated. When that is the
case, we expect that the value of the secondary market to the retailers will be smaller than in the current
model. A more elaborate model incorporating both
demand correlation and market intelligence will be a
viable direction of further research.
The current model assumes one production and
one selling opportunity by the manufacturer. While
this assumption may be reasonable for very-shortlife products like fashion apparel, they are not generally valid. Future research can also involve multiple
production and selling opportunities by the manufacturer, as well as multiple periods in which transactions in the secondary market can take place.
Finally, our model is still a partial equilibrium
model because the retail price is exogenously given.
A true equilibrium model would endogenize the formation of the retail price so that retail demand distributions may be affected by the existence of the secondary market. To do so, one needs a richer model
than our newsvendor model to capture the retail
demand function with uncertainty. Clearly, this is well
beyond the scope of this paper, and we hope more
future research will follow to enrich our understanding of the impacts of the secondary markets and the
Internet on the supply chain.
730
Acknowledgments
The authors thank the associate editor and two referees for numerous constructive comments and encouragement. They also thank
the participants at the Second Thought Leaders Roundtable on
Supply Chain Management sponsored by Eindhoven University
in 1999, and seminars at the University of Washington, University of Dayton, and Purdue University for useful comments. Special thanks go to Thomas Schmitt, Ted Klastorin, Prabudha Dee,
Lee Schwartz and Corey Billington. In addition, the authors thank
Mr. Tunay Tunca for the computation of numerical examples and
refinement of Theorem 5. The authors gratefully acknowledge the
partial financial support from Global Supply Chain Forum at Stanford University.
Appendix 1
We prove that under the uniform distribution of Example 1,
dQ* /d**=0 > 0 if # > 05. Note that under the uniform distribution of Example 1, 1 Q = Q2 /2 Fi x = x, and fi x = 1 for appropriate ranges of x. Hence, (4.1) becomes Q∗ 3 /2 = #, and so 05 <
# < 1 is equivalent to 1 < Q∗ 3 < 2. Now
dQ* −2
=
d* *=0 3Q∗
Thus,
d+* n
n
=
6Q∗ − 4 − Q∗ 3 > ∗ Q∗ − 1 > 0
d* *=0 6Q∗
Q
since Q∗ 3 < 2 and Q∗ > 1.
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