On a replenishment coordination model in an integrated supply chain with one vendor and multiple buyers

In this paper, we consider an integrated supply chain model in which one vendor supplies items for the demand of multiple buyers. The objective of this model is to minimize the vendor's total annual cost subject to the maximum cost that the buyer may be prepared to incur. We explore the optimality structure of this integrated model and assert the optimal cost curve is piece-wise convex. Especially, the theoretical results on the breakpoints of the optimal cost curve provide useful insights that establish important foundation for the design of our search algorithm. By our numerical experiments, we demonstrate that our search algorithm is very efficient since its run time is extremely short, it obviously out-performs other heuristics, and impressively, it secures the global optimal solution for each of the 20 experimental problems.