A Multiproduct Inventory System with Interactive Set-Up Costs

We present a branch and bound algorithm for finding the optimal ordering policy for a multiproduct inventory system with deterministic demand, infinite horizon, and no backlogging. Ordering costs are assumed to include a separate set-up cost for each product ordered, but with a fixed savings each time all products are simultaneously ordered. Holding costs accrue at a constant rate per unit of each product. We first restrict our search to policies of a certain type, and then prove several theorems which lead to an efficient algorithm. For the two-product case, a special algorithm is developed to give more precise results than earlier authors.