Measuring a value of contract flexibility in the third-party warehousing

This paper considers the value of warehousing contract under probabilistic demands. We consider a supply chain consisting of a supplier, a retailer and its third-party warehousing partner who provides the warehousing service to the retailer through an outsourcing contract. A typical contract is specified by initial space commitment and modification schedule. The retailer decides the order quantity for the supplier and space commitment for the outsourcing contract. Since there is close relationship between order quantity and space commitment to minimize the total cost including ordering cost, inventory carrying cost, shortage cost, and warehousing cost, we develop an analytical model under probabilistic demands, where the retailer can determine the optimal order size and space commitment level jointly. We found the closed-form optimum for a single-period case and the optimal conditions for a two-period case. To evaluate the value of contract flexibility for the two-period case, we compared the total cost under two policies; one with modification, under which the base commitment can be changed at the start of each period and the other without modification. From results of our numerical analysis, we showed that the modification policy is more cost-effective as the variability of demand increases.