On the Almost Threshold Policy for Multisourcing Under Uncertain Supplies

With extended supply chains and increased global sourcing, the uncertainty in supply streams has become a major consideration in formulating procurement strategies. Many studies in the existing literature characterize the optimal procurement policies under specific assumptions of the supply and demand distributions. In several special cases, a threshold policy or an almost threshold policy is shown to be optimal. A recent study by Feng and Shathikumar [Feng Q, Shanthikumar JG (2018) Supply and demand functions in inventory models. Oper. Res. 66(1):77–91] generalizes the previous results by establishing the optimality of an almost threshold policy under any demand distribution and a set of conditions on the stochastic supply functions, including stochastic linearity in midpoint, stochastic increasing in the dispersive order, and vanishing of the no-delivery probability. In this note, we significantly enhance this result and for the first time, fully characterize the optimal multisourcing policy for general stochastic supply functions that are stochastically linear in midpoint, the weakest known condition to ensure the concavity of the associated dynamic program. Using an iterative constructive approach, we prove that an almost threshold policy is optimal. This result is extended to price-dependent demands and positively dependent supplies.