Scheduling of multi-buyer joint replenishments

It is a common practice for a multi-branch firm to have its branches ordering a group of items from a single supplier. Obviously, co-ordinating the replenishments among the branches would reduce the firm's ordering and inventory costs. In response to the co-ordinated replenishments of buyers (i.e., the branches), the supplier faces a problem of how to schedule the deliveries according to the buyers' basic order cycle time, and the number of basic order cycles that an item in a branch will be replenished. This supplier's scheduling problem has received little attention in the literature. This paper addresses the deliveries scheduling issue, once the optimal replenishment cycles are determined, by formulating four problems according to four different objectives in cost and resource minimisation. The problems are large integer programming problems which are not easy to solve. This paper proposes to convert the problems into network flow problems whose sizes can be reduced dramatically and hence solved readily.