Mean-Risk Analysis of Supply Chain Coordination Problems

Supply chain coordination is an important topic in supply chain management. In the literature, under a stochastic demand, contracts such as returns contract (Pasternack 1985; Wu 2011), revenue sharing contract (Cachon and Lariviere 2005; Krishnan and Winter 2011; Sheu 2011), markdown money contract (Elmaghraby et al. 2008; Yin et al. 2009), quantity flexibility contract (Sethi et al 2004; Lian and Deshmukh 2009), and sales rebate contract (Taylor 2002; Arcelus et al. 2012) have been shown to be successful in coordinating a supply chain with risk neutral agents (see Cachon 2003; Tsay et al. 1999). Even though the studies with risk neutral agents can provide insights into supply chain coordination mechanisms, they lack precision in the sense that the agents could have different degrees of risk aversion. In this chapter, we consider a two-echelon supply chain with a single risk-neutral manufacturer and a single risk-averse retailer, and we study via a mean-risk analysis how target sales rebate (TSR) contract can help to coordinate a supply chain in this setting. In the literature, there are several ways to define supply chain coordination with risk-averse supply chain agents (see Gan et al. 2004). Here, we adopt the definition of supply chain coordination as follows: supply chain coordination is achieved when the expected profit of the supply chain is maximized. We first apply the mean-risk approach to study the problem of supply chain coordination with a risk-averse retailer via TSR contracts. We then extend the mean-risk analysis to study the challenging case that includes sales effort-dependent demand.