Coordination of Supply Chains with Risk‐Averse Agents

TLDR

Supply‑chain coordination has not been studied for risk‑averse agents in the existing literature. The study defines a coordinating contract that yields a Pareto‑optimal outcome acceptable to all agents. The authors generalize the standard risk‑neutral definition, develop contracts for three scenarios—risk‑neutral supplier with retailer subject to downside risk, mean‑variance trade‑offs for both parties, and expected‑utility maximization for both—and show how to identify Pareto‑optimal solutions and design contracts to achieve them, including explicit sharing rules in a particular case. In the expected‑utility case the contract coincides with the Nash Bargaining solution, and the authors also provide explicit Pareto‑optimal sharing rules and a procedure for obtaining such solutions.

Abstract

The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk‐averse agents. We take up this issue and begin with defining a coordinating contract as one that results in a Pareto‐optimal solution acceptable to each agent. Our definition generalizes the standard one in the risk‐neutral case. We then develop coordinating contracts in three specific cases: (i) the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint; (ii) the supplier and the retailer each maximizes his own mean‐variance trade‐off; and (iii) the supplier and the retailer each maximizes his own expected utility. Moreover, in case (iii), we show that our contract yields the Nash Bargaining solution. In each case, we show how we can find the set of Pareto‐optimal solutions, and then design a contract to achieve the solutions. We also exhibit a case in which we obtain Pareto‐optimal sharing rules explicitly, and outline a procedure to obtain Pareto‐optimal solutions.