The Generalized Bin Packing Problem with bin-dependent item profits

In this paper, we introduce the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), a variant of the Generalized Bin Packing Problem. In GBPPI, various bin types are available with their own capacities and costs. A set of compulsory and non-compulsory items are also given, with volume and bin-dependent profits. The aim of GBPPI is to determine an assignment of items to bins such that the overall net cost is minimized. The importance of GBPPI is confirmed by a number of applications. The introduction of bin-dependent item profits enables the application of GBPPI to cross-country and multi-modal transportation problems at strategic and tactical levels as well as in last-mile logistic environments. Having provided a Mixed Integer Programming formulation of the problem, we introduce efficient heuristics that can effectively address GBPPI for instances involving up to 1000 items and problems with a mixed objective function. Extensive computational tests demonstrate the accuracy of the proposed heuristics. Finally, we present a case study of a well-known international courier operating in northern Italy. The problem approached by the international courier is GBPPI. In this case study, our methodology outperforms the policies of the company.