A Model for Resource Constrained Production and Inventory Management

We present a general model for multi‐item production and inventory management problems that include a resource restriction. The decision variables in the model can take on a variety of interpretations, but will typically represent cycle times, production batch sizes, number of production runs, or order quantities for each item. We consider environments where item demand rates are approximately constant and performing an activity such as producing a batch of a product or placing an order results in the consumption of a scarceresource that is shared among the items. Some examples of shared resources include limited machine capacity, a restriction on the amount of money that can be tied up in stock, orlimited storage capacity. We focus on the case where the decision variables must be integer valued or selected from a discrete set of choices, such as when an integer number of production runs is desired for each item, or in order quantity problems where the items come in pack sizes containing more than one unit and, therefore, the order quantities must be an integer multiple of the pack sizes. We develop a heuristic and a branch and bound algorithm for solving the problem. The branch and bound algorithm includes reoptimization procedures and the heuristic to improve its performance. Computational testing indicates that the algorithms are effective for solving the general model.