Determining the best shipper sizes for sending products to customers

A distribution company has to send products, packed into shippers, from the warehouse to retail shops. The number of different shipper types is regarded as a parameter given by the user, who is looking for a balance between transportation costs and stock and procurement costs. The problem is to decide the sizes of the shipper types to keep at the warehouse so as to minimize the cost of meeting the forecasted demand over the planning horizon. In this paper, we describe an integer linear programming formulation for the problem and obtaining feasible solutions. Other models, based on multiknapsack and p‐median and facility location models, are for obtaining lower bounds. We study several ways of reducing the set of possible shipper types in order to obtain models of a manageable size. The feasible solutions obtained are improved by using a reduced model and metaheuristic algorithm. A computational study conducted on real instances provided by the company is presented and discussed.