Relatively optimal production-distribution plans for stock management in supply chains over a finite time horizon

Abstract

A model of the centralized dynamic production - distribution control is considered. In a supply chain a vendor supplies a product to a buyer, sending the products to the buyer’s warehouse in equal-size batches. Costs are attached to manufacturing the batch, the delivery of shipment and stockholding at both agents, and defined on production-distribution cycles (PDCs). There is only one production setup in a cycle with the restriction that in each warehouse the beginning and the ending inventory levels are the same. It is shown that the average cost of “sensible” PDCs is a continuous piece-wise convex function of their production batch sizes. For infinite time horizon the optimal production distribution plan is a constant sequence of PDCs with lowest average cost - economic production-distribution cycles (EPDCs).