| Summary: | This paper deals with the problem of shipping multiple commodities from a single vendor to a single buyer. Each commodity is assumed to be constantly consumed at the buyer, and periodically replenished from the vendor. Furthermore, these replenishments are restricted to happen at discrete time instants, e.g., a certain time of the day or a certain day of the week. At any such time instant, transportation cost depends on the shipment quantity according to certain discount scheme. Specifically, we consider two transportation quantity discount schemes: LTL (less-than-truckload) incremental discount and TL (truckload) discount. For each case, we develop MIP (mixed integer programming) mathematical model whose objective is to make an integrated replenishment and transportation decision such that the total system cost is minimized. We also derive optimal solution properties and give numerical studies to investigate the problem.
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