Option Contract Design for a Multi-period VMI Supply Chain

This paper studies the role of option contracts in a multi-period VMI supply chain consisting of one supplier and one retailer, where an emergency production is allowed to be carried out to replenish unmet demand. By using dynamic programming approach, we formulate two groups of recursive models to characterize the optimal production and ordering policies of two members without and with option contracts, and provide a tractable algorithm to approximate the corresponding policy parameters in two cases. By benchmarking the case without option contracts, we prove that the supplier’s service level in each period is always higher with option contracts than without them. In addition, the supplier is always better off with option contracts than without them. However, the retailer prefers option contracts when the option or exercise price is low, while prefers wholesale price contracts when the option or exercise price is high. Moreover, through the numerical examples, we find that the decisions and performances of two members are decreasing in the demand risk. Finally, we derive the explicit condition on which option contracts can help the multi-period VMI supply chain achieve the optimum under the stationary parameter situation.