مسائل مربوط به ثبات در شبکه های زنجیره تامین : مفاهیمی برای ساز و کارهای هماهنگی

Stability is essential for long term sustainability of supply chain networks. The literature on supply chain coordination focuses on enhancing network efficiency, and stability issues are largely unexplored. In this paper, we consider a two-tier supply chain network with a marketing agent coordinating activities among the network players using a price and profit sharing based coordination mechanism. Our non-cooperative game theoretic model shows that a unique subgame perfect Nash equilibrium exists that facilitates development of structural results characterizing network stability from the perspectives of costs, number of players and parameters of the coordination mechanism. In particular, we obtain ranges for cost, number of players and the profit sharing parameter over which the network is internally and/or externally stable. Our results suggest that cooperation among the network players is not always necessary; network efficiency can be achieved in some situations with the coordination mechanism adopted here.

During the past two decades, supply chains have evolved into complex networks involving diverse players, each with its own rights and individual interests. In this environment, supply chain coordination with focus on mechanisms to align decisions of members for improving the overall effectiveness of the network has emerged as a key management capability (see Cachon, 2003 and Li and Wang, 2007). For long-term sustainability, it is important that such networks remain stable with little incentives for players to alter their existing alliances. The issue is particularly important in networks with exclusive participation constraints due to restrictions on network players from competing simultaneously outside the network. Franchises, exclusive dealerships, captive facilities (such as manufacturing plants, distribution units, etc.) and cooperatives are typical examples of supply chain networks that exhibit such restrictions. The presence of competing supply chains often provides players in the network with alternate avenues that may undermine stability of the network. While coordination issues have received much attention in supply chain management literature (see Whang, 1995, Tsay et al., 1998 and Kouvelis et al., 2006), implications of coordination mechanisms for network stability have not been studied in detail. In this paper, we aim to bridge this gap and develop a modeling approach to examine the impact of coordination mechanisms on stability of supply chain networks. The motivation for our work comes from mixed results in the cooperative sector of India. Over the last seven decades, AMUL, a milk producers’ cooperative, has led a dairy revolution that has resulted in India becoming one of the largest producers of milk in the world (Bellur et al., 1990). The success of AMUL is achieved within the framework of a network of cooperatives organized in a hierarchical manner. The network structure has been subsequently replicated in various other sectors—such as oil, sugar, wheat, fertilizer, etc. However, similar success has eluded many of these cooperatives, and in some cases the networks have disintegrated ( Bandyopadhyay, 1996 and Das et al., 2006). Recently, the AMUL network has also come under strain with competition from private players with alternate avenues for the players in the network that include changing supply chain alliances, terminating network membership, establishing independent production units, etc. (Chandra and Tirupati, 2003). In particular, in 2006, the Mehsana union, the largest of the 17 members in GCMMF, and in 2010, the Kaira union, the oldest producer in the network threatened to pull out of the network in self interest (see Sriram, 2010 and PTI, 2010). As a result sustainability of the India's largest and most admired brand had become uncertain. In a competitive environment such as that in the Indian dairy industry, network formation by the competing players may counteract individual objectives of the network players causing instability in the network. A clear understanding of the interplay between objectives of the individual players and the parent network is necessary in order to eliminate any incentives threatening network stability and to ensure network sustainability. The literature examining stability issues in the context of supply chains is primarily based on cooperative networks which do not adequately capture the AMUL environment (elaborated in 2 and 3). Hence, our objective in this paper is to bridge this gap and develop a model based approach to understand stability issues. It may be noted that similar competitive setting may be observed in network structures such as Independent Grocers Association (IGA)—a group of independent retailers (www.iga.com), Unified Western Grocers Inc.—a purchasing cooperative of independent grocers (www.unifiedgrocers.com) and European Social Franchising Network, CAP Market in Germany—cooperatives of sheltered workshops (www.socialfranchising.coop, www.cap-markt.de). Specifically, in this paper, we examine stability issues in a two-tier supply chain network comprising several producers operating in a competitive market. While some of the producers operate independently and supply their product in the market directly, the rest form a cooperative network (hereafter referred to as network) and supply through a marketing agent that acts as a coordinator. Production decisions by the network producers are driven by self interest and are influenced by the coordination mechanism used for sharing the revenues generated. In this paper, we analyze a profit sharing based mechanism that is popular both in practice (see Azfar and Danninger, 2001 and Heywood and Jirjahn, 2009) and literature (see Chen et al., 2001 and Foros et al., 2009). The coordination mechanism involves procurement price paid by the marketing agent to the network producers and surplus sharing. We develop a game theoretic model to describe the problem context and characterize the decisions of both network and independent producers. Our development involves integration of (i) principles of coordination from supply chain management literature, and (ii) literature on network stability from economics and industrial organization. We derive response functions for the players involved and show that optimal decisions lead to a Nash equilibrium for the supply chain. In addition, we show that there exists a range of procurement prices in which both network and independent producers compete together, i.e., optimal production quantities are non-zero for both types of producers. For procurement price below a threshold value, the network producers do not produce. Similarly, for procurement price beyond an upper bound, the independent producers do not produce. We also develop structural results to characterize stability of the network. Our results show that the profit sharing parameter has no impact on network surplus; however, it has implications for network stability. Also, cooperation among network producers is not always necessary to obtain efficient performance and the coordination mechanism considered in this paper is adequate for this purpose. The results bring out relationship between the factors of interest and provide insights for determining the decision parameters of the coordination mechanism. Our main contribution in the existing literature is linking stability and efficiency of supply chain networks within the framework of supply chain coordination. The remainder of the paper is organized as follows. In Section 2, we describe the problem context in our motivating example. We review the relevant literature in Section 3 and position the work described in this paper. We build the game theoretic model in Section 4. Section 5 covers model analysis. Section 6 discusses network stability. We conclude in Section 7 with a summary of the key findings of the paper. All proofs are relegated to appendix.

In this paper, we have developed a non-cooperative game theoretic model to study stability issues in a two-tier supply chain comprising two types of producers—independent producers who compete directly in the market and network producers that compete through a marketing agent who acts as a coordinator. The model is appropriate for supply chains with exclusivity contracts – such as franchises, cooperatives, exclusive dealership, etc. – that operate in a competitive environment and are governed by profit sharing coordination mechanism that influences individual players’ decisions. While coordination mechanisms and related issues on performance and efficiency have received much attention in the literature, implications for stability have largely remained unexplored. The work reported in this paper bridges this gap and it is complementary in nature. Our results can be broadly classified into two categories: (i) characterizing the equilibrium solutions resulting from the parameter choices of the coordination mechanism and describing the impact of cost parameters and the number of independent producers on the network surplus, prices, production, etc. (ii) Network stability: here we identify conditions under which the network is stable and develop bounds on parameters for assuring stability. The equilibrium solutions are primarily characterized as a function of profit sharing parameter. We show that there exists a range of procurement prices in which both network and independent producers compete together. For procurement price below the threshold value represented by the lower limit of the range, network producers do not produce. Similarly, for procurement price above the upper limit of the range, independent producers do not produce. The model presented in this paper is based on a real life network and recognizes the impact of potential non-cooperative behavior by the network producers. Our results show that under certain conditions, with appropriate choice of parameters, the profit sharing based coordination mechanism considered in the paper results in efficient network performance. Our results also show that the network surplus is independent of the profit share parameter, αα. This is not surprising since the coordination mechanism is internal to the network producers and reasonable coordination mechanisms with consistent parameter choices should not compromise the ability of the network producers to compete with independent producers. However, the choice of αα has implications for stability. We show that, similar to procurement price, there exists a range of αα over which the network is stable and for αα below a lower threshold (above an upper threshold) the network is externally (internally) stable. Likewise, we show that there exists a range for cost parameters and the number of independent producers over which the network is stable either internally and/or externally. Our results are based on several simplifying assumptions; nevertheless they are useful and provide insights and guidelines for managerial decision making. The model and the results presented in this paper may be interpreted as a building block in the development of richer and more comprehensive framework, and we conclude the paper with some remarks in this regard. First, our analysis is based on one particular coordination mechanism. While the one analyzed in the paper is common and popular both in practice and literature, it may be useful to extend the analysis to other mechanisms and to the extent possible generalize the results. Second, we ignored capacity constraints and assumed that the producers are identical. The model can be enriched with a more elaborate, realistic cost structure and permit producers with non-identical costs. Further, it may be useful to consider scale economies in marketing and distribution costs associated with the marketing agent. Third, it may be useful to analyze the network with alternative objectives mentioned briefly in Section 4. Finally, incorporating entry/exit decisions by individual players will expand the scope of the model significantly and enhance its applicability.