Mean-Variance Analysis of Supply Chain Contracts

According to the Council of Supply Chain Management Professionals (September 2007), we have the following description for supply chain management: “supply chain management encompasses the planning and management of all activities involved in sourcing and procurement, conversion, and all logistics management activities. Importantly, it also includes coordination and collaboration with channel partners, which can be suppliers, intermediaries, third-party service providers, and customers. In essence, supply chain management integrates supply and demand management within and across companies.” From this description, it is obviously true that a supply chain in general has multiple channel members (usually called stages) and the coordination and collaboration among these members is a crucial task in supply chain management. In the literature, various policies for supply chain optimization and channel coordination have been proposed. Among them, setting a supply chain contract between individual parties has received much attention in recent years (Tsay et al. 1999, Cachon 2003). Contracts such as buy-back contract, revenue sharing contract, quantity flexibility contract and rebates contract are all known forms of contract which can help to achieve channel coordination in a supply chain. However, in the majority of the literature works, the channels' and supply chain’s objectives are either maximizing the expected profit or minimizing the expected cost. There is no discussion on the level of risk associated with these contracts. As a result, the contract parameters under which coordination is achieved may be viewed as unrealistic by decision makers. In light of this, we conduct in this paper a mean-variance analysis on some popular forms of supply chain contracts such as buy-back contract. By including a constraint on profit uncertainty, we illustrate how decision makers can make a scientifically sound and tailored decision with respect to their degrees of risk aversion. Managerial implications are discussed. The organization of the rest of this chapter is as follows: We briefly review some related literature in Section 2, the discussion of the supply chain’s structure is presented in Section 3. The mean-variance analyses on the buy-back contract and wholesale pricing profit sharing contract are conducted in Sections 4 and 5, respectively. We conclude with some discussions on managerial implications in Section 6. For a notational purpose, we use the following notation in many places throughout this chapter: P = profit, EP = expected profit, SP = standard deviation of profit, MV = mean-