Pareto optimality and contract dependence in supply chain coordination with risk‐averse agents

In recent years, research on supply chain coordination (SCC) with risk‐averse agents has received much attention. Previous studies are primarily concerned with the coordination of a single manufacturer–single retailer supply chain using different definitions of SCC. What is lacking is a comprehensive analysis of the achievability of SCC. In this paper, we provide a systematic analysis of SCC with risk‐averse agents. We see that three definitions of SCC have been proposed in the literature to investigate SCC with risk‐averse agents, among which the one based on Pareto optimality (PO) stands out. Here we explore the challenges of using the PO criterion. Specifically, we first examine the standard two‐agent supply chain under the mean–variance (MV) and mean‐downside‐risk (MDR) objectives. What we find is that the achievability of PO depends on the contract type. The wholesale price contract even with a side payment may not lead to PO. Also, unlike under MV where risk sharing is Pareto optimal, we observe that the least risk‐averse agent must take all the risk to achieve SCC under MDR. Importantly, we extend our analysis to multiretailer, multimanufacturer, and multitier supply chains. In each case, we characterize the efficient Pareto‐optimal manifold in the multidimensional space and design coordinating contracts that result in Pareto‐optimal actions acceptable to all agents. We also discover that identifying PO across all the contract forms is difficult when some other risk‐aversion criteria are considered. We conclude by providing suggestions and methods for SCC when we are unable to identify PO.