A FRAMEWORK FOR INVENTORY MANAGEMENT IN SUPPLY NETWORK
Qian-nong Gua , John K. Visichb
Department of Management and Marketing, Sam Houston State University, Huntsville, TX 77341, USA
Department of Management, Bryant University, Smithfield, RI 02917, USA
The supply network, as a more practical extension of supply chain, comprises of multiple interconnected
supply chains. We first illustrate the difference between supply chain and supply network in structures. Then,
propose a research framework for managing production and inventory under a supply network setting.
Numerical examples are provided for the purpose to illustrate the miscalculation for the supply network when
the inventory control decisions are made under a supply chain setting.
Keywords: Supply Network, Supply Chain, Inventory Management, Game Theory
Researches on the supply chain have been extensively conducted since 1980s because of the expected benefits
of supply chain coordination. A general definition for supply chain is “the global network used to deliver
products and services from raw materials to end customers through an engineered flow of information,
physical distribution, and cash” (APICS, 2008). While the supply chain has been recognized as a network,
most research in the literature usually considers it as a series of partners along the material flow. A two- or
three-tier structure has been broadly used to explore the issues in supply chain. Lummus and Vokurka (1999)
summarized various definitions of supply chain in the literature and concluded that the supply chain is “all the
activities involved in delivering a product from raw material through to the customer including sourcing raw
materials and parts, manufacturing and assembly, warehousing and inventory tracking, order entry and order
management, distribution across all channels, delivery to the customer, and the information systems necessary
to monitor all of these activities” (p. 11 ). In the early stage of supply chain research, the major concerns and
motivations were how to smooth the material flow and how to collaborate the activities of different functional
partners along the supply chain. A well accepted concept is that the competition between companies will be
replaced by competition between their separate supply chains. All rivals in a competitive market are presented
as a series of upstream partners who have added value to the final products. In this case, the competition
between supply chains is assumed to happen only at the last stage of the supply chain, which is usually
between the retailers facing the demand market, such as Wal-Mart, K-Mart and Target. Supply chain
collaboration is expected to increase a supply chain’s competitive capability.
In practice, however, a supply chain that comprises a group of firms which are exclusively dedicated
to one supply chain does not exist. Indeed, different supply chains may involve common parties, particularly
when they are targeting the same or relevant markets. In other words, one firm could be involved in multiple
supply chains at the same time. This supplier will allocate and balance its capacity between two (or more)
supply chains to maximize its own profit rather than maximize any supply chain’s profit. In fact, supply chains
are interconnected by these common partners to form a supply network. For example, Wal-Mart, K-Mart and
Target are competing for slightly different markets (Graff, 2006) and the competition among them is usually
considered as competition among three supply chains represented by Wal-Mart, Target, and K-Mart. However,
many of Wal-Mart’s suppliers provide products to K-Mart and Target as well. Hence, Wal-Mart, Target, and
K-Mart compete not only for the customers in the demand market, but also for the supply resources.
Therefore, a firm should position itself in a setting of a supply network that includes all the supply
chains it belongs to. Any strategic business decision must be made under such a consideration. Harland et al.
(2001) defined supply network as “Supply networks are nested within wider inter-organization networks and
consist of interconnected entities whose primary purpose is the procurement, use, and transformation of
resources to provide packages of goods and service” (p.22 ). The concept of supply network proposed by
Harland et al. has a focal firm. Lambert et al. (1998) illustrated this kind of supply network in Figure 1, though
they still called it supply chain. The noteworthy feature of this structure is the multiple upstream and
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downstream partners involved. We will refer this structure as a focused supply network in this paper to
distinguish from the supply network structure we propose.
FIGURE 1: Structure of a Focused Supply Network
Source: Lambert et al. (1998)
The managers in the focal company need to collaborate with multiple upstream and downstream partners
to optimize its performance e.g. cost minimization, profit maximization. The imperfect assumption here is that
all its partners are assumed to follow the focal company’s decisions which are assumed to benefit the whole
supply chain eventually. Contrastively, there are multiple entities at any stage in a general supply network (see
Fig. 2(b)). With the setting of supply network, firms need to make decisions in a more complex network
because of its roles in different supply chains. Horizontal and vertical competitions are inevitable in a supply
network. The lack of sufficient research on supply network management prevents managers and practitioners
from making decisions using assumptions that are closer to practice. In Figure 2, we present a general structure
of supply network and compare it with the structure of supply chain side by side.
FIGURE 2: Supply chain competition
(a) Two independent supply chains competing (b) A supply network composing of two supply
for one market chains
S1 M1 R1 S1 M1 R1
S2 M2 R2 S2 M2 R2
: Competition : Competition
S: supplier, M: manufacturer, R: retailer.
In Figure 2-a, the supply chain comprises of one supplier (S), one manufacturer (M) and one retailer
(R). Two supply chains, S1-M1-R1 and S2-M2-R2 are competing for the same market. Most supply chain
research focuses on how to improve the retailers’ competition capability by coordinating supply chain
partners’ operations, e.g. sharing information, VMI. The competition between the two supply chains is
represented as the competition between the two retailers. Note that in Figure 2(a), supply chain partners are
exclusive. Simply speaking, two supply chains are separated. But, in practice, a firm most likely has multiple
suppliers, customers, and competitors, and competition occurs between the parties at all stages (see Figure 2-
In supply chain research, the competition and/or collaboration between upstream and downstream
partners is the major concern. Under a supply network setting, we emphasize the inter supply chains
competition and coordination. In Figure 2(b), both suppliers S1 and S2 serve manufacturers M1 and M2.
Similarly, both manufacturers M1 and M2 serve retailers R1 and R2. The competitions not only occur between
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two retailers as shown in Figure 2(a), but also exist between two manufacturers and two suppliers as in Figure
2(b). In a supply network, two retailers compete for the same market. Meanwhile, they are also competing for
the upstream resources. Apparently, the structure of the supply network is closer to practice than that of the
supply chain. Because of the complexity of a supply network, the achievements in research on the supply
chain cannot be simply implemented for a supply network without any changes. This study proposes a
framework for extending existing research in supply chain management to a supply network. Our model and
results can also support managers and decision-makers in practice.
This paper is organized as follows. We review relevant literature in the field in section 2. The
difference in structures of supply chain and supply network is illustrated in section 3. A research framework
for inventory management in a supply network is also proposed in section 3. Section 4 includes a numerical
example to demonstrate the necessity of shifting perspective from a supply chain to a supply network in
research. We conclude the paper with section 5.
Research on supply chain management has attracted widespread attention because of the potential benefit from
coordination among supply chain partners. Various quantitative models have been proposed to analyze
business issues from different perspectives in a supply chain, such as inventory management, supply
contracting, information sharing, and so on. Several publications have presented extensive literature surveys in
this field (Tayur et al. (1998 and Simchi-Levi et al. (2004)). In this study, we do not intend to review more
supply chain literature. There is a series of research (Nagurney et al., 2002; Zhang et al., 2003, Dong et al.,
2004; Nagurney and Matsypura, 2005; and Nagurney 2006) focusing on a similar supply network structure
that we are interested in. This research is introduced in next subsection.
Nagurney et al. (2002) developed an equilibrium model for a supply network by establishing a
variational inequality formulation. The market demand is assumed price-elastic and the retailer price is one of
the decision variables. In the Nash equilibrium condition derived from Nagurney et al. (2002), the total
shipments from retailers to customers is equal to the total shipments from manufacturers to retailers. These
results present an ideal situation without extra products storage (inventory). Any future study in a dynamic
demand case can be evaluated by comparing it with this static benchmark. Dong et al. (2004) replaces the
price-elastic demand in Nagurney et al. (2002) by random demands with known distribution pattern.
Zhang et al. (2003) extends the work of Nagurney et al. (2002) to a multiple markets setting where
intra supply chain cooperation and inter supply chain competition are studied accordingly. The relationship
between two business entities is defined as an interface link in. In contrast, the internal operations such as
manufacturing and storage are defined as an operations link. This special treatment furnishes a means to
consider both cooperation and competition in a supply network.
Nagurney and Matsypura (2005) extended the static problem studied in Nagurney et al. (2002) to a
dynamic situation by developing a multicriteria decision making process for a three-tier supply chain. In the
model, both risk minimization and profit maximization are objectives for the manufacturers and the
distributors. Both of them are facing the political risk and the currency risk, while demand uncertainty is
considered as the risk for retailers.
The afore-mentioned research thread contributes a set of equilibrium states under different scenarios in
which each party in a supply network will not have an incentive to deviate. However, Cachon (1998) stated
that”the optimal policies are never a Nash equilibrium, hence competition always deteriorates supply chain
performance” (p.114 ) In this study, while adopting the similar structure of supply network, we are concerned
with the influence of environmental change on the companies’ performance. Note that the environment is
actually not changed, but instead we model an environment which is closer to practice.
Competition in a supply chain has appeared in the literature as a supplement to supply chain
coordination. Under a supply network setting, competition occurs not only between two sequential operation
owners (e.g. supplier and buyer) but also between two business competitors (e.g. two retailers). Therefore,
game theory is essential for supply network modeling. In next subsection, we briefly review the applications of
game theory in supply chain.
Supply Network Model
In this study, we consider a single-product supply network that consists of two suppliers, two manufacturers,
and two retailers. All suppliers support both manufacturers and all manufacturers provide product to both
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retailers. Without loss of generality, the setting of two parties (competitors) at each level indicates that there
are multiple choices for any resources to avoid different negotiation power among supply network partners.
Both coordination and competition are considered as the major objectives in supply network research.
Figure 4-a below demonstrates the structure of supply network adopted in this study. One supply
network can be considered as two focused supply networks as shown in Figure 4-b. Figure 4-c lists all supply
chains for each manufacturer embedded in the supply network. Note that a supply network is not a simple
summation of all the possible supply chains. In next section, a numerical example will demonstrate the
difference between the results derived under a supply network setting and under a supply chain setting
We choose a manufacturer (M1) as an example to show how to manage a company’s inventory in
supply network. The conclusions and strategies for M1 can be easily extended to any party in supply network
as well. Market demand (y) is assumed price-elastic, i.e. y=m-np, where m ≥ 0 and n ≥ 0 are known parameters
based on the knowledge about the market. For the purpose of simplicity, we assume the prices charged by M1
to retailers are the same as the selling prices charged by retailers to their external customers. Similarly, M1’s
purchasing prices to each supplier are assumed to be the same as the supplier’s production cost.
FIGURE 4: Decomposition of supply network
S1 M1 R1
S1 R1 S1 R1
S2 M2 R2
S2 R2 S2 R2
(a) supply network (b-1) focused supply network for M1 (b-2) focused supply network for M2
SC1: S1 M1 R1 SC5: S1 M2 R1
SC2: S1 M1 R2 SC6: S1 M2 R2
SC3: S2 M1 R1 SC7: S2 M2 R1
SC4: S2 M1 R2 SC8: S2 M2 R2
(c-1) all supply chains for M1 (c-2) all supply chains for M2
In a static one-period problem, the total shipment from suppliers to M1 should be equal to the total
delivery from M1 to all retailers. In a multiple period problem, at the end of each period, there will be leftover
(inventory) or stock out (backordering if allowed). We use xij to denote the shipment from supplier i (i=1, 2)
to manufacture j (j=1, 2). Notation y jl is used to denote the shipment from manufacturer j (j=1, 2) to retailer l
(l=1, 2). The inventory cost for each period is h * (∑ x − ∑ y ) + . The backordering (if allowed) cost is
i =1 l =1
b * (∑ xi1 − ∑ y1l ) . Where, h is the holding cost rate per unit for one period; b is the backordering rate per unit
i =1 l =1
per period. All notations used in this paper are summarized below and Figure 5 illustrates the material flow
xij : Amount of product shipped from supplier i to manufacturer j
y jl : Amount of products shipped from manufacturer j to retailer l
PMj : Selling price manufacturer j charged to retailer l for one unit of product
C Mj : Purchasing price manufacturer j paid to supplier i for one unit of product
h: Inventory holding cost rate per unit per period
b: Backordering cost rate per unit per period
K Si : Supplier i’s production capacity
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DRl : Total market demand retailer l facing
FIGURE 5: Material flow through manufacturer 1 (M1)
x 21 y12
The shipment from one supplier to M1 is not only determined by the price that M1 is willing to pay. It
is also influenced by the production capacity of this supplier as well. The supplier will allocate its limited
capacity among manufacturers based the prices offered in order to maximize its total profit. Hence, even
though there is not direct material flow between the two manufacturers, they are interacted because of
competition for resources and market demand. This effect is indicated by the two-directional vertical arrow in
C M 1 is the price M1 offered to supplier i. It is also equal to the supplier i’s production cost.
C M 1 = C M 1 ( x11 , x 21 , K Si )
∀i ∈ (1, 2)
Here, C M1 is the price M1 offered to supplier 1 but it is also assumed to be equal to supplier 1’s
production cost. Therefore, M1’s total purchasing cost is ∑ (C
M1 * x i 1 ) . M1’s own production cost is defined
as f 1 ( x11 , x 21 ) = α * ( ∑ x i1 ) 2 . Where, α is a pre-defined parameter based on the knowledge about the
production. The M1’s total revenue is ∑ (P
M1 * y1l ) . Therefore, the model for maximizing M1’s total profit is
2 2 2
Max ∏ M 1 = ∑ ( PM 1 * y1l ) − α * (∑ xi1 ) 2 − ∑ (C M 1 * xi1 )
l =1 i =1 i =1
xi1 = xi1 (C M 1 , C M2 , K Si )
∀ i ∈ (1, 2) , y1l = y1l ( PM 1 , PM 2 , DRl )
∀ i ∈ (1, 2)
All x, y, P are non-negative.
In next section, we use a numerical example to demonstrate the above model under a specific cost
structure for supply network. The results in three different scenarios (supply chain, focused supply network,
and supply network) are also compared.
In this section, a one-period single product problem is examined. Consider that two suppliers (S1 and S2 in
Fig. 5) to M1 are identical and that the two retailers (R1 and R2 in Fig. 5) are identical too. The total market
demand to M1 depends on the price M1 offered to R1, PM 1 , and the price to R2, PM 1 . Because the system is
symmetric, we let PM 1 = PM 1 = P1 .
The total market demand for M1 is set as y = 1000 − 2 * P1 − P2 , where P2 is the price M2 offered to
retailers. The involvement of M2’s offer in M1’s demand function indicates the competition between two
manufacturers on market demand. In this example, we assume M1 and M2 are identical. So in an equilibrium
situation, P1 = P2 = P . Therefore, we have total demand y = 1000 − 3 * P for M1. Because of the symmetry
of the structure, y11 = y12 = y / 2 . Similarly, we also have x11 = x 21 = y / 2 . Let y / 2 = q . The total
production cost function for supplier one (S1) is
f1 ( x11 , x12 ) = 0.2( x11 − 100) 2 + 0.2( x11 − 100)( x12 − 100) + 10 * x11 + 10 * x12 . The involvement of x12 in S1’s
production cost function presents the interaction between M1 and M2 when competing on supply resource.
Hence, similarly, S2’s production cost is
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f 2 ( x 21 , x 22 ) = 0.2( x 21 − 100) 2 + 0.2( x 21 − 100)( x 22 − 100) + 10 * x 21 + 10 * x 22
We define M1’s production cost as M 1 = 0.2 * ( x11 + x12 ) 2 + 10 * ( x11 + x12 ) . There are four transportation
costs associated with M1. We assume M1 is in charge of all these transportation costs. They are
TS1 = 0.2 * y11 + 2 * y11 (to R1), TS 2 = 0.2 * y12 + 2 * y12 (to R2), TS 3 = 0.2 * x11 + 2 * x11 (from S1) ,
2 2 2
TS 4 = 0.2 * x 21 + 2 * x 21 (from S2). Because of the symmetry of the structure, we have
x11 = x 21 = y11 = y12 = q and TS 1 = TS 2 = TS 3 = TS 4 = 0.2q 2 + 10q .
We use this numerical example to study three scenarios. The first one is under the supply network
setting as described above. The second scenario is under the setting of a focused supply network in which the
competition between M1 and M2 is ignored. Therefore, the supplier’s production cost functions in the second
scenario are f1' ( x11 ) = 0.2( x11 − 100) 2 + 10 * x11 , f 2' ( x 21 ) = 0.2( x 21 − 100) 2 + 10 * x 21 for S1 and S2
respectively. The third scenario is based on a one-to-one supply chain setting. There are four supply chains
associated with M1 as indicated in Fig. 4-c. In the third scenario, the competition between the two
manufacturers and the interactions among the supply chains are ignored.
Table 1 shows the results under three different scenarios. Although the magnitude of the results in
Table 1 depends on the setting in the example, the trend in real profit is consistent with our expectations. The
solution from a focused supply network setting is close (98%) to the supply network’s optimal solution. Under
the supply chain setting, the total expected profit from the four supply chains associated with M1 is much
higher than the optimal solution derived from a supply network setting. However, when adopting the supply
chain strategy based on optimization in a supply network environment, the real profit is much lower than the
supply network’s optimal solution. It is only 13.98% of the optimal result under supply network setting.
Table 1: Numerical example results
selling price market demand expected profit real profit* % of optimal value
supply chain (4) 219.08 342.76 55783.68 4582.18 13.98%
focused supply network 263.81 208.57 36601.90 32158.64 98.08%
supply network 270.20 189.41 13395.60 32788.33 100.00%
Under the supply chain setting, as we mentioned early, the summation of the four supply chains is not
equivalent to a supply network. In fact, the four supply chains are interconnected and influence each other’s
performance. The ignorance of inter supply chain competition results in a much lower profit than expected.
The profit in a focused supply network is still lower than in the case of supply network, but much better than
under supply chain setting, because the joint effect of multiple suppliers and retailers are considered. This
example shows the necessity for moving from a supply chain oriented research to a supply network oriented
In this study, we propose a supply network model to study inventory management. The structure of a supply
network is closer to practice than that of supply chain. Our model is built on the extensive research in supply
chain management to explore a better way for strategic decision-makers to position them in a complicated
setting. A two-tier or three-tier setting for supply chain is dominant in literature. However, our numerical
example shows that when adopting a supply chain strategy in a supply network environment, the result (total
profit) is lower than both its original expectation and the results based on a supply network oriented strategies.
A supply network can be decomposed into multiple focused supply network or supply chains
conceptually. However, the ignorance of inter supply chain effects (coordination and competition) makes it
impossible to implement a strategy originated in a supply chain to a supply network environment.
The concept and research framework proposed in this research can be extended to solve other
production and operations management issues with the consideration of supply network. For future research,
we can retest existing achievement in supply chain management in supply network and see what necessary
changes need to be made once we move to the next generation of supply chain, the supply network.
References available upon request from Qian-nong Gu at email@example.com
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