A linear programming approach for the three-dimensional bin-packing problem

Abstract

In this paper we consider the three-dimensional bin packing problem (3D-BPP), when the bins are identical with the aim of minimizing the number of the used bins. We introduce a mixed-integer linear programming formulation (MILP1). Some special valid inequalities will be presented in order to improve the relaxed lower bound of MILP1. A large set of experimental tests has been carried out. The obtained results show that our method provides a satisfactory performance. © 2010 Elsevier B.V.