Competition in multi-channel supply chains.
Shao, Bin ; Wu, Chongqi ; Li, Kunpeng 等
INTRODUCTION
Two strategies of market competition have been widely observed in
SC systems. One strategy is price competition which is often defined as
Bertrand competition in economics literature. The other is quantity
competition which is typically defined as Cournot competition in
economics. In price competition, prices are often compelled to marginal
cost while in quantity competition positive price-cost margins are often
achieved.
Distribution channel structure has been another major strategic
concern for SC system. Many distribution channels have been observed
ranging from traditional retail channel to the direct sales model and
the clicks-and-mortar channel (Gap/Gap.com, Staples/Staples.com etc.).
The contracting arrangement between a manufacturer and a retailer also
varies from channel to channel. Some manufacturers use an exclusive
arrangement with a retailer while others use multiple channels. The
direct channel is a vertically integrated channel often controlled by a
manufacturer (Dell, for example).
The efficiency of a decentralized SC system is defined as the ratio
of its total equilibrium profit to the optimal profit of the centralized
system. The objective of this paper is to study the disparity of SC
efficiencies between price competition and quantity competition. To that
end, consider two substitutable products, produced either by a single
manufacturer or by two manufacturers. The products are sold through
utmost two retailers. Within this framework, consider different SC
arrangements ranging from a centralized configuration to several
decentralized multi-channel ones. The decentralized configurations
include the single retailer channel (two manufacturers, each producing
one product; both sell their products through a single retailer), the
single manufacturer channel (one manufacturer, two retailers), and the
exclusive channel (two manufacturers and two retailers; each
manufacturer sells through only one retailer and each retailer carry
only one product). This paper is intended to answer the following
questions. Does price competition result in the same efficiencies for SC
configurations as quantity competition? Is one competition strategy
always superior to the other one? How does product substitutability
affect competition strategies?
Many of the channel arrangements described above are observed in
practice. The factory outlets and the direct distribution channels are
the typical examples of centralized SC between a manufacturer and a
retailer. The exclusive channel is most often observed in
manufacturer-distributor relationships in various industries ranging
from chemicals and paper to appliances and Beer. For example, Hercules
Inc. is the exclusive distributor for GE Specialty Materials' water
treatment solutions to the paper industry (Challener, 2003); Diego
Suarez is the exclusive distributor of Coors brand of beers in Puerto
Rico (Allio & Allio, 2002). The Wall Street Journal (October 28,
2003) reports that Estee Lauder has created a new company division,
called BeautyBank, to develop cosmetic products exclusively for
Kohl's (Merrick & Beatty, 2003). Different auto makers often
sell vehicles through a single dealer in smaller cities, giving rise to
a distribution channel similar to the single retailer channel noted
above. Wu et al. (2009 & 2010) have used similar SC configurations
in their study.
This paper compares and contrasts price and quantity competition
strategies in these decentralized SCs, and studies how the differences
between the two strategies change with the degree of substitutability.
LITERATURE REVIEW
SC structure, conflict and coordination have been extensively
studied in operations literature. The majority of the works assume a
single manufacturer and a single retailer. The typical approach is to
study the source of inefficiency (often related to double
marginalization), and mechanisms for achieving coordination. Cachon
(2001) provides a review of this stream of literature. The channel
conflict literature typically considers the scenario where the
manufacturer is simultaneously a supplier to and competitor of its
retail partners(s). Chiang et al. (2003) consider whether a single
manufacturer should sell exclusively through a retailer, direct over the
Internet, or through a hybrid channel. Their key finding is that the
manufacturer may use a direct channel as a way to combat double
marginalization in the retail channel. Ahn et al. (2002) consider the
competition between independent retailers and manufacturer-owned stores
where parties compete in price. The manufacturer sells an identical
product through two spatially separated markets. Tsay and Agarwal (2002)
provide a review in modeling channel conflict and coordination. This
stream of literature typically considers a single manufacturer selling
identical products, whereas our work considers multiple manufacturers
selling substitutable products.
Existing comparative work of price and quantity competitions is
fruitful in the field of Economics and Supply Chain Management. Singh
and Vives (1984) show that in a duopoly game with linear demand and
constant marginal cost, firms should employ quantity competition
strategy if products are substitutable and take price competition
strategy if products are well differentiated. Cheng (1985) studies the
equilibrium outcomes of price and quantity competitions with
differentiated products and finds that quantity competition is superior
to price competition under certain assumptions. There are other studies
that show preference to price competition. For example, Amir and Jin
(2001) provide support to the result that Bertrand equilibrium is
intrinsically more competitive than Cournot equilibrium in an oligopoly
model with linear demand, and a mixture of substitute and complementary
products under some limitations. On the other hand, Miller and Pazgal
(2001) demonstrate the equivalence result in a two-stage
differentiated-products oligopoly model under certain assumptions.
The third stream of literature related to our work is product
substitutability which has also been studied extensively in both
Operations and Marketing literature. In Operations, for instance, Boyaci
(2003) considers a multi-channel distribution system in presence of both
vertical and horizontal competition. He concludes that there is a
tendency for both manufacturer and retailer to overstock due to
substitutability. In Marketing, Raju et al. (1995) consider the
introduction and performance of store brands vis-a-vis a national brand.
Mahajan and van Ryzin (1999) provide a comprehensive survey of research
on demand substitutability. However, these studies take the SC structure
as given and do not address the issue of SC efficiency. Our work differs
from these studies by quantifying SC efficiency.
MODELS
Consider multi-channel distribution systems for two substitutable
products, denoted by 1 and 2. The products reach the end consumer
through a two-echelon SC involving manufacturer(s) and retailer(s).
Multi-channel systems studied in this paper involve utmost two
manufacturers and utmost two retailers. The manufacturers are denoted by
[M.sup.1] and [M.sup.2] (or by M, if there is only one manufacturer),
while the retailers will be denoted by [R.sup.1] and [R.sup.2] (or by R,
if there is only one retailer) respectively. Vertical competition is
introduced by considering decentralized decisions made within the
channels; while, the horizontal competition is introduced by
substitutable products. Several different multi-channel distribution
systems are considered. Figures 1(a) and 1(b) schematically describe
these configurations. The configurations in Figure 1(a) involve either
one manufacturer or one retailer, while the configurations in Figure
1(b) involve two manufacturers and two retailers.
The centralized system (denoted as C) is a fully integrated system
where a single manufacturer produces both products and sells them
through an integrated channel. It yields the highest system profit and
serves as a benchmark for the decentralized systems. Figure 1(a)
describes three decentralized systems. The decentralized single
manufacturer single retailer system (denoted as DS) involves one
manufacturer producing both products and selling them through a single
retailer. The retailer makes stocking decisions of the two products
independent of the manufacturer. A single manufacturer system (denoted
as SM) involves one manufacturer and two retailers. The sole
manufacturer produces both products and sells each product exclusively
through one independent retailer. Under a single retailer system
(denoted as SR), there are two manufacturers, each producing one
product. The manufacturers sell their products through a single retailer
who makes the stocking decisions of each product in its own interest.
Figure 1(b) describes three decentralized multi-channel
distribution systems, each involving two manufacturers and two
retailers. Under a partially centralized system (denoted as PC),
[M.sub.1] sells its product exclusively through [R.sub.1] while
[M.sub.2] sells its products exclusively through [R.sub.2]. In addition,
each of the two competing manufacturer-retailer pair is centralized (or
vertically integrated) and the stocking decision within each pair is
coordinated. However, there exists horizontal coordination between the
two channels. Under a minimally coordinated system (denoted as MC)
[M.sub.1] sells its product exclusively through [R.sub.1], and [M.sub.2]
sells its products exclusively through [R.sub.2]. In addition, only one
of the two vertical channels is coordinated. Assume, without loss of
generality, that [M.sub.1] and [R.sub.1] are coordinated, while the
other manufacturer-retailer pair is not. An exclusive system (denoted as
E) is similar to the PC and MC systems except that none of the two
manufacturer-retailer pairs is coordinated. Thus, under an exclusive
system, [M.sub.1] sells its product exclusively through [R.sub.1],
[M.sub.2] sells its products exclusively through [R.sub.2], and all
parties make decisions in self-interest. It is easy to see that the
degree of coordination goes down as moving from PC to MC to E.
[FIGURE 1(a) OMITTED]
[FIGURE 1(b) OMITTED]
Without loss of generality, we assume the common marginal
production cost for each product is 0. No fixed cost of production is
considered and the production and delivery are assumed to be
instantaneous. The manufacturers produce as retailers' orders under
a wholesale price contract. Let [w.sub.1] and [w.sub.2] be the wholesale
prices and [q.sub.1] and [q.sub.2] be the demand of products 1 and 2
respectively. The retailer(s) set the retail prices, denoted by
[p.sub.1] and [p.sub.2] respectively. We model the horizontal
competition between two channels under both price and quantity
competitions.
Price competition model:
[q.sub.i] = 1 - [p.sub.i] -[theta]([p.sub.j] - [p.sub.i]), i, j =
1,2, i [not equal to] j, (1) where 6 is a parameter.
The horizontal competition between the products is captured by
making the demand of a product sensitive to the prices of both products.
The products are perfectly differentiated when
[theta] = 0. The products are nearly identical as [theta]
approaches infinity.
Quantity competition model:
[p.sub.i] = [alpha] - [beta][q.sub.i] - [gamma][q.sub.j], [alpha],
[beta], [gamma] > 0, [gamma] [less than or equal to] [beta]; i, j =
1,2, i [not equal to] j, (1')
where [alpha], [beta], and [gamma] are parameters.
The horizontal competition between the products is captured by
making the price of a product sensitive to the available quantities of
both products. In particular, the products are perfectly substitutable
when [gamma] = [beta]; and are perfectly differentiated when [gamma] =
0. The condition [gamma] [less than or equal to] [beta] implies that the
demand of a product is more sensitive to its own price rather than the
price of the competing product.
These types of demand functions are standard in economics and
marketing literature modeling product substitutability (Gal-Or, 1991;
Raju et al., 1995). Moreover, Lee and Staelin (2000) show that a linear
demand function involving substitutable products is indeed consistent
with reasonable buyer behavior and market characteristics.
[pi], with subscripts and superscripts, is used to denote profit. A
subscript of "M" or "R" is used to refer to a
manufacturer or a retailer respectively. Superscripts are used to denote
a specific SC configuration. Thus, [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] denotes the profit of retailer i under an
exclusive system.
The notation j denotes an index on the SC configurations under
consideration. Clearly, j = C, DS, SM, SR, PC, MC, E. The total SC
profit (i.e. the sum of the profits of retailer(s) and manufacturer(s))
under configuration j will be denoted as [[pi].sup.j] (no subscripts).
The centralized system yields the highest profit and serves as a
benchmark for the decentralized systems noted earlier. The profit
maximization problem of a centralized system is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
The solution of the above optimization problem yields the following
results. Price competition model:
Inserting equation (1) into (2) and the 1st order conditions (the
2nd order conditions are satisfied) yields
[p.sup.*.sub.1] = [p.sup.*.sub.2] = [p.sup.c*] = 1/2;
[q.sup.*.sub.1] = [q.sup.*.sub.2] = [q.sup.c*] = 1/2; and [[pi].sup.c*]
= 1/2. (3)
Quantity competition model:
Similarly, insert equation (1') into (2) and we get
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3')
For the reasons of brevity, among the decentralized SC
configurations only the single retailer (SR) system is described here.
The rest will have similar formulations. Under a single retailer system,
both manufacturers sell their products through a single retailer. The
profit maximization problem of the retailer is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
Price competition model:
The 1st-order conditions (it is easy to verify that the second
order conditions are satisfied) yield:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
Quantity competition model:
[q.sup.SR*.sub.i]([w.sub.1], [w.sub.2]) = [[alpha]([beta] -
[gamma]) - [beta]([w.sub.i] + c) + [gamma]([w.sub.j] +
c)]/[2([[beta].sup.2] - [[gamma].sup.2])], i, j = 1,2, i [not equal to]
j. (5')
The two manufacturers select their wholesale prices by solving the
following problems.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)
The equilibrium wholesale prices [w.sup.*.sub.1] and
[w.sup.*.sub.2] can be found by solving the 1st-order conditions given
by (6). Once [w.sup.*.sub.1] and [w.sup.*.sub.2] are known, the
equilibrium prices, quantities, and profits as well as the total profit
can be calculated accordingly under both price and quantity
competitions. Similarly, we can solve for the equilibrium prices,
quantities, and profits for the other decentralized SC configurations.
Since our focus is efficiencies of SC configurations, only the
equilibrium profits are summarized in Table 1.
RESULTS AND ANALYSIS
This section compares and contrasts the efficiencies of SC
configurations under price competition with those under quantity
competition and also examines the effects of product substitutability on
the comparison. Under quantity competition, the relative magnitudes of
the parameters [beta] and [gamma] determine the degree of
substitutability between the two products. The product substitutability
can be parameterized by defining [lambda] = [gamma] / [beta]. Since
[beta] [greater than or equal to] [gamma], 0 [less than or equal to]
[lambda] [less than or equal to] 1. Recall that the efficiency of
decentralized SC j is defined as the ratio of equilibrium total SC
profit under configuration j to that of the centralized SC; i.e.,
[R.sup.j] = [[pi].sup.j*] / [[pi].sup.c*], [for all]j. Given that the
centralized system yields the highest system profit, 0 [less than or
equal to] [R.sup.j] [less than or equal to] 1, [for all]j.
Table 2 summarizes the efficiency for each SC configuration under
different horizontal competition.
Let [lambda]' = 1 - [e.sup.-[theta]]. Hence
[lambda]'[member of] [0,1] and [theta] = -ln(l - [lambda]').
Now product substitutability under price competition is rescaled from
[0, [infinity]] to [0, 1] and captured by [lambda]'.
Among all SC configurations, C and DS have the same efficiencies.
Figure 2 (a)-(e) compare the efficiencies of other configurations under
price and quantity competitions.
Theorem.
(i) Price and quantity competitions are equivalent only if the two
products are perfectly differentiated.
(ii) Neither price competition nor quantity competition is a
dominant strategy.
(iii) As the product substitutability increases, a large difference
of the efficiencies between price and quantity competition is observed
(except when the two products are almost identical).
Comparing price with quantity competition analytically, we find the
same efficiency is achieved for each configuration only when [lambda] =
[lambda]' = 0. So the two competitions are never equivalent if the
two products are not perfectly differentiated.
It is easy to see that quantity competition is not always better in
terms of higher efficiency for SC configurations. Neither is price
competition. Actually in SM and E SC configurations, price competition
almost always yields higher efficiency (except when the two products are
almost identical in E SC configuration) while in SR, PC, and MC
configurations, quantity competition always yields higher efficiency.
It is also interesting to notice that as the product
substitutability increases, the difference between quantity and price
competitions increases too (except when the two products are almost
identical in SR and E SC configurations).
[FIGURE 2(a) OMITTED]
[FIGURE 2(b) OMITTED]
[FIGURE 2(c) OMITTED]
[FIGURE 2(d) OMITTED]
[FIGURE 2(e) OMITTED]
SUMMARY AND CONCLUSION
Multi-channel distribution systems with differing channel
configurations are widely observed in practice. This paper studies price
and quantity competitions of dual-channel-dualechelon SC systems. Six
decentralized SC configurations with different degree of horizontal and
vertical integration were discussed. We compare and contrast the
equilibrium SC efficiencies of different SC structures under price with
those under quantity competition.
The most important contributions of this paper are that price
competition and quantity competition are not equivalent, and that
neither of them is a dominant strategy for the SC configuration systems
discussed in this paper.
Another important finding is that for each dual-channel (either two
retailers or two manufacturers or both) SC configuration the difference
of efficiencies under price and quantity competitions increases with
increased product substitutability.
The metrics used in this paper for comparison is the efficiency of
SC configurations. It will be interesting to examine what will be the
results if other metrics are used, such as price. It will also be
interesting, although difficult, to investigate the comparison using
more complex SC configurations, such as SC systems with more than two
echelons or with more than two manufacturers/retailers. If SC systems of
three or more echelons are considered, the tractability of the resulting
analytic models significantly decreases. Another extension we consider
pursuing is to relax the assumption in this paper that the demand
functions of two retailers are symmetric. It will be very intriguing to
see how sensitive the results in this article are to the changes in the
demand function structures.
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Bin Shao, West Texas A&M University
Chongqi Wu, California State University, East Bay
Kunpeng Li, Sam Houston State University
TABLE 1: EQUILIBRIUM PROFITS OF SC CONFIGURATIONS.
Configuration [[pi].sub.j] under [[pi].sub.j] under
(j) Price Competition Quantity Competition
C [MATHEMATICAL EXPRESSION [[alpha].sup.2]/
NOT REPRODUCIBLE IN 2([beta] + [gamma])
ASCII]
DS 3/8 [[alpha].sup.2]/
8[([beta] +
[gamma]).sup.2]
SM ([theta] + 3) [[alpha].sup.2]
([theta] + 1)/ (3[beta] + [gamma])/
2[([theta] + 2).sup.2] 2[(2[beta] +
[gamma]).sup.2]
SR ([theta] + 1) [[alpha].sup.2][beta]
([theta] + 3)/2[([theta] (3[beta] - 2[gamma])/
+ 2).sup.2] 2([beta] + [gamma])
(2[beta] -
[gamma]).sup.2]
PC 2([theta] + 1)/ 2[[alpha].sup.2][beta]/
[([theta] + 2).sup.2] [(2[beta] +
[gamma]).sup.2]
MC ([theta] + 1) [[alpha].sup.2]
(13[[theta].sup.4] + (28[[beta].sup.2] +
82[[theta].sup.3] + 8[beta][gamma] -
167[[theta].sup.2] + [[gamma].sup.2])/
12[[theta].sup.6] + 28)/ 16[beta][(2[beta] +
4[([theta] + 2).sup.2] [gamma]).sup.2]
[([[theta].sup.2] +
4[theta] + 2).sup.2]
E 4([theta] + 1) 4[[alpha].sup.2][beta]
([[theta].sup.2] + (6[[beta].sup.2] -
4[theta] + 2) [[gamma].sup.2])/
(2[[theta].sup.2] + [(2[beta] +
6[theta] + 3)/ [gamma]).sup.2]
[([theta] + 2).sup.2] (4[beta] -
([[theta].sup.2] + [gamma]).sup.2]
7[theta] + 4).sup.2]
TABLE 2: EFFICIENCIES OF SC CONFIGURATIONS
Configuration [R.sup.j] under [R.sup.j] under
(j) Price Competition Quantity Competition
C 1.0 1.0
DS 0.75 0.75
SM ([theta] + 3) 1 - 1/2 (2 +
([theta] + 1)/ [lambda]).sup.2]
[([theta] + 2).sup.2]
SR ([theta] + 3) (3 - 2[lambda])/
([theta] + 1)/ (2 - [lambda]).sup.2]
[([theta] + 2).sup.2]
PC 4([theta] +1)/ 4(1 + [lambda])/
[([theta] + 2).sup.2] [(2 + [lambda]).sup.2]
MC ([theta] +1) (1 + [lambda])(28 +
(13[[theta].sup.4] + 8[lambda] -
82[[theta].sup.3] + [lambda].sup.2])/
167[[theta].sup.2] +
120[theta] + 28)/
2[([theta] + 2).sup.2] 8(2 + [lambda]).sup.2]
([[theta].sup.2] +
4[theta] + 2).sup.2]
E 8([theta] +1) 8(1 + [lambda])([theta] -
([[theta].sup.2] + [[lambda].sup.2])/
4[theta] + 2) [(4 - [lambda]).sup.2]
(2[[theta].sup.2] + [(2 + [lambda]).sup.2]
6[theta] + 3)/
[([theta] + 2).sup.2]
[([[theta].sup.2] +
7[theta] + 4).sup.2]
