Abstract
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.
Highlights
Products characterized by long lead times, a short sales season and high demand uncertainty (‘‘seasonal products’’) are both well-researched and common in practice [1]
We propose portfolio contracts by introducing the call option contract into a traditional wholesale price contract, and investigate the benefits when the retailer is risk-averse and faces a non-trivial shortage cost
(2) We find that the retailer’s optimal total ordering quantity is independent of the wholesale price, and does not have a monotonic relationship with the risk aversion and exercise price which does not occur when risk aversion and shortage costs are considered in isolation
Summary
Products characterized by long lead times, a short sales season and high demand uncertainty (‘‘seasonal products’’) are both well-researched and common in practice [1]. When retailer’s are risk averse, they may order less than supply chain optimal quantities in an effort to minimize losses in the event that demand is low This behavior occurs even under traditionally contracts, leading to decreased profits [16]. When the retailer is risk-averse, a non-trivial shortage cost magnifies the risk of under-ordering relative to over-ordering and may lead to over-ordering In this scenario, a contract that allows for both firm and option orders may present a risk-averse retailer with the necessary flexibility to balance this trade-off while maintaining high levels of supply chain performance [17]–[19]. (1) We add to supply chain research by analyzing the portfolio contracts under two practically relevant assumptions: that the retailer is risk-averse and there is a non-trivial shortage cost.
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