Mean-risk analysis of wholesale price contracts with stochastic price-dependent demand

In supply chain management, it is prevalent to design contract for coordination or proper risk-sharing in the supply chain. However, when a supply chain contract is developed based on the concept of expectation (e.g., expected profit), there is uncertainty risk with respect to the contract value which arises from various uncertainties inherent in the supply chain, such as demand uncertainty, price uncertainty, etc. We call such uncertainty risk associated with the contract value risk since it relates to the true value of the contract. Value risk is obviously an important factor in the design and analysis of a supply chain contract. In addition, individual supply chain agents with different risk preferences will have different risk attitudes towards the contract value risk, which affects their decisions under the contract. Motivated by the above, we conduct in this paper a mean-risk analysis for the commonly adopted wholesale price contracts with a supplier–retailer supply chain facing a stochastic price-dependent downward-sloping demand curve, taking into account contract value risk and the retailer’s degree of risk-aversion. Formulating the problem under study as a supplier-led Stackelberg game, we characterize the wholesale price contract model analytically in terms of only the retailer’s risk preference structure, and derive all the results in closed-form. This study makes the first attempt to assess the efficiency of wholesale price contracts incorporating contract value risk, and thereby some interesting managerial and academic insights are obtained. Our research provides a new perspective of looking at the performance of a supply chain contract.