The common cycle economic lot scheduling problem with backorders: Benefits of controllable production rates

In this paper, we deal with the production scheduling of several products that are produced periodically, in a fixed sequence, on a single machine. In the literature, this problem is usually referred to as the Common Cycle Economic Lot Scheduling Problem. We extend the latter to allow the production rates to be controllable at the beginning of as well as during each production run of a product. Also, we assume that unsatisfied demand is completely backordered. The objective is to determine the optimal schedule that satisfies the demand for all the products and that realizes the minimum average setup, inventory holding and backlog cost per unit time. Comparison with previous results (when production rates are fixed) reveals that average costs can be reduced up to 66% by allowing controllable production rates.