Dual-sourcing of capacity

Problem Definition. Dual-sourcing, a strategy that diversifies supply sources to manage uncertainty, is widely used in supply chain management. We explore this concept in new contexts of transportation and manufacturing, introducing a new notion of “dual-sourcing of capacity.” Unlike traditional dual-sourcing, which focuses on the supply of goods, we use the term sourcing to mean using a resource’s capacity to provide a service, e.g., using seats on vehicles to transport passengers or slots in heating equipment to process semiconductor wafers. In these contexts, we model the classic trade-off between cost and responsiveness using two capacity sources: a cheaper batched source that provides service at a fixed frequency and a more expensive unit source that provides service instantly on-demand. The dual-sourcing of capacity problem aims to determine a sourcing policy that minimizes the service cost while ensuring that the average waiting time does not exceed a responsiveness guarantee. A sourcing policy includes determining the batched source’s service frequency and when to serve using the on-demand source. Methodology/Results. We prove sufficient conditions for the optimality of “Q-policies,” a class of simple threshold policies. In these policies, the on-demand source is only used when the order queue length reaches the threshold Q. This approach prevents the queue from exceeding Q by instantly serving new orders with the on-demand source when this threshold is reached. Managerial insights. Conventional wisdom in sourcing literature suggests increasing the use of the “responsive” on-demand source to reduce the average waiting time. Lowering the threshold Q in Q-policies achieves this in our setting; however, we find that lowering Q below the batched source’s batch size is never optimal for any choice of responsiveness guarantee. Furthermore, we show that a range of responsiveness guarantees exists where the optimal threshold Q is fixed at the batched source’s batch size, and waiting time for orders is reduced by increasing the batched source’s service frequency, which decreases the use of the on-demand source. Our findings provide useful insights for managing responsiveness in transportation and manufacturing contexts when multiple levers of responsiveness are available.