Study on a Revenue Sharing Contract with Risk-Averse Agent

Abstract

Considering a supply chain with the risk-neutral supplier and the risk-averse retailer, the revenue sharing contract is studied. Firstly, the risk-averse behavioral preference of the retailer over random profit is represented in a Conditional Value-at-Risk (CVaR) framework. Then we obtain the supply chain's optimal solution and study the property of contract parameter. It is analyzed that the degree of risk aversion is influential to the contract parameter. Finally, an illustrative example is given to demonstrate that the revenue sharing contract may not coordinate the operation of the supply chain when the retailer is risk averse. Under a revenue-sharing contract, a retailer pays the supplier a wholesale price for each unit purchased, plus a percentage of the revenue the retailer generates. Such contracts have become more prevalent in the network economy. Dana and Spier (2001) showed that revenue sharing is valuable in vertically separated industries in which demand is either stochastic or variable, downstream inventory is chosen before demand is realized and downstream firms engage in intra-brand competition. Gerchak and Wang (2004) investigated a vendor-managed inventory with revenue sharing and found that the assembler can achieve channel coordination and increase the profits of all parties involved by using the revenue sharing contract. Giannoccaro and Pontrandolfo (2004) proposed a model of the supply chain contract aimed at coordinating a three-stage supply chain, which is based on the revenue sharing mechanism. Cachon and Lariviere (2005) studied the coordination of the fixed-price news vendor problem and price-setting news vendor problem in a neutral risk situation, and they demonstrated that revenue sharing coordinates both of the cases and arbitrarily allocates the supply's profit. The model in the above mentioned papers assumes that the agents in the supply chain are risk neutral, and maximize their respective expected profits. However, these papers do not take into consideration the issue of a supply chain consisting of risk-averse agents. It has been pointed out that maximizing the expected profit is not satisfactory from a practical point of view, and the agents in the real world are more concerned with other objectives. There are a number of papers containing the situation with one or more risk-averse agents, such as Lau and Lau (1999), Tsay