The optimal production and shipment policy for the single-vendor singlebuyer integrated production-inventory problem

TLDR: In this paper, the problem of minimizing the mean total cost per unit time of manufacturing set-up, stock transfer, and stock holding is considered, and the structure of the globally optimal solution is derived and an algorithm for obtaining it is presented.

Abstract: This paper considers the problem of a vendor (manufacturer) supplying a product to a buyer (customer). The vendor manufactures the product in batches at a finite rate and ships the output to the buyer. The buyer then consumes the product at a fixed rate. The objective is to minimize the mean total cost per unit time of manufacturing set-up, stock transfer and stock holding. Previously published work has concentrated on finding optimal solutions from within given classes of policy. We derive the structure of the globally-optimal solution, set out an algorithm for obtaining it and illustrate the process with two numerical examples.