Innovative menu of contracts for coordinating a supply chain with multiple mean-variance retailers

We consider the coordination challenge with a risk-neutral manufacturer which supplies to multiple heterogeneou retailers. We find that the manufacturer can maximize its expected profit only if the expected profit of the supply chain is maximized, or equivalently supply chain coordination (SCC) is achieved. The target sales rebate (TSR) contract is commonly used in practice to achieve SCC. However, as we found in this paper, the presence of heterogeneity in retailers' minimum expected profit requirements is the major cause that a single TSR contract and the related single hybrid contracts all fail to achieve SCC and maximize the manufacturer's expected profit simultaneously. Thus, we develop an innovative menu of TSR contracts with fixed order quantity (TSR-FOQ). Although there are multiple contracts in a menu, we find that the manufacturer only needs to decide one basic TSR contract and two newly developed parameters termed as the risk-level indicator and the separation indicator, in applying the sophisticated menu of TSR-FOQ. By adjusting the two indicators, the manufacturer can control the profit variance of the retailers and the separations of the component contracts of the menu. We further propose another sophisticated menu of TSR with minimum order quantity and quantity discount contracts which can give each retailer a higher degree of freedom in the selection of order quantity. Differences between the two menus are analytically examined. Some meaningful managerial insights are generated.