Effective heuristics for multiproduct partial shipment models

Motivated by real applications, we consider the problem of shipping products to multiple customers from limited inventory. After formulating the optimization problems under different restrictions on partial shipments, we find that commercially available packages, applied directly, are unsatisfactory, as are simple greedy approaches. We develop a scheme of heuristics that enables the user to select a good balance between computation time and effectiveness. A detailed computational study of one- and two-period industrial-sized problems indicates that these heuristics are computationally practical and generate solutions that are, on average, within 3%-4% of the optimum.