Capacity reservation and utilization for a manufacturer with uncertain capacity and demand

We consider an OEM (Original Equipment Manufacturer) that has outsourced the production activities to a CM (Contract Manufacturer). The CM produces on a non-dedicated capacitated production line, i.e., the CM produces for multiple OEMs on the same production line. The CM requires that all OEMs reserve capacity slots before ordering and responds to these reservations by acceptance or partial rejection, based on allocation rules that are unknown to the OEM. Therefore, the allocated capacity for the OEM is not known in advance, also because the OEM has no information about the reservations of the other OEMs. We study this problem from the OEM's perspective who faces stochastic demand and stochastic capacity allocation from the contract manufacturer. A single-item periodic review inventory system is considered and we assume linear inventory holding, backorder, and reservation costs. We develop a stochastic dynamic programming model for this problem and characterize the optimal policy. We conduct a numerical study where we also consider the case that the capacity allocation is dependent on the demand distribution. For this case, we show the structure of the optimal policy based on a numerical study. Further, the numerical results reveal several interesting managerial insights, such as the optimal reservation policy is being little sensitive to the uncertainty of capacity allocation. In that case, the optimal reservation quantities hardly increase, but the optimal policy suggests increasing the utilization of the allocated capacity. Moreover, we show that for the contract manufacturer, to achieve the desired behavior, charging small reservation costs is sufficient.