Minimizing the expected total value of shortages for a population of itemssubject to practical restrictions on the reorder points

We address a problem of setting reorder points (expressed as time supplies) of a population of items, subject to a restricted set of possible time sup plies as well as a budget on the total amount of safety stocks, both import ant practical constraints. We provide a branch-and-bound algorithm for obta ining the optimal solution. In addition, a simple and efficient heuristic a lgorithm has been developed. Computational experiments show that the perfor mance of the heuristic is excellent based on a set of realistic examples. H owever, the typical set of possible time supplies may significantly degrade performance compared with the situation where a continuum of choices are p ossible. (C) 2001 Elsevier Science B.V. All rights reserved.