A Heuristic With Lower Bound Performance Guarantee For The

A multiple product version of the dynamic lot-size problem is examined. The simplest nontrivial joint structure, that of joint setup costs, is considered. A variety of heuristics have been suggested for solving the single product problem. One of these is the Silver Meal heuristic. A simple extension of the Silver Meal heuristic to the multiple product case is given. The same may be done with other single product heuristics. It is shown that the calculations needed for the heuristics automatically give one information that can be used to generate an a posteriori lower bound on the (unknown) optimal, a lower bound whose running time is only linear in a number of products. Thus, whenever one uses the heuristic, one can also get a guarantee of closeness to the optimal. Computational experience on realistically sized problems (30 products, 24 periods) shows performance usually within 5% of the (unknown) optimum.