Optimal decisions of a supply chain with a risk-averse retailer and portfolio contracts

In this paper, we investigate a supply chain involving one risk-neutral supplier and one risk-averse retailer, where the retailer adopts the conditional value-at-risk (CVaR) criterion as his performance measure. To hedge against high risk, the retailer purchases call options from the supplier to adjust his firm orders. We derive the optimal order and production policies, with and without a call option contract and demonstrate that the call option contract can benefit both the retailer and the supplier. In addition, we also generate insights regarding how the contract parameters, level of risk aversion and shortage cost impact the retailer's optimal policy, highlighting the importance of considering the risk aversion and shortage cost simultaneously. Finally, we derive the condition for the supply chain to be coordinated and show that compared to non-coordinating contracts, the wholesale price and call option portfolio contracts proposed in this paper can achieve Pareto optimality. Numerical experiments are conducted to demonstrate theoretical results and observations.