Eeective Heuristics for Multi-product Shipment Models

We consider two shipment models (motivated by a real application) where multiple customers asking for sets of products are to be satissed from inventory in the best manner possible. The restrictions posed by the customers include that the rst shipment be at least a minimum fraction of the total demand, and that the second shipment (if any) should not be too small nor be further split. We rst show that solving these problems to optimality requires considerable computational eeort. Thus, the performance of commercially available packages, applied directly on these problems, is unsatisfactory. Adapting the latest developments in computational integer programming, we are able to solve several instances to optimality. However, this can also require considerable computational eeort with some instances not solvable within 10 hours. So we develop and analyze two heuristics: these are easy to implement, run very quickly and provide good solutions. In a test bed of 50 problems of industrial size, one heuristic solves Model 1 and Model 2 under 30 seconds and 10 seconds respectively, with an average error of 0.86% and 2.1%. The average relative error of the second heuristic is 0.18 % and 1.05 % for Model 1 and Model 2 respectively and solves these in an average of 142 seconds and 321 seconds.