Minimizing the expected total value of shortages for a population of items subject 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 supplies as well as a budget on the total amount of safety stocks, both important practical constraints. We provide a branch-and-bound algorithm for obtaining the optimal solution. In addition, a simple and efficient heuristic algorithm has been developed. Computational experiments show that the performance of the heuristic is excellent based on a set of realistic examples. However, the typical set of possible time supplies may significantly degrade performance compared with the situation where a continuum of choices are possible.