Optimizing a production system with a fixed delivery schedule

This note considers a model in which a manufacturing company purchases a raw material, manufactures a product (at a finite rate) and ships a fixed quantity of the product to a single customer at fixed and regular intervals of time, as specified by the customer. In general there are several shipments made during each production run. The objective is to determine a purchasing and production schedule which minimises the total cost of purchasing, manufacturing and stockholding. It extends previously published work by considering the possibility that a single raw material purchase provides stock for several production runs or that several raw material purchases provide stock for a single production run.