New Symmetry-less ILP Formulation for the Classical One Dimensional Bin-Packing Problem

In this article, we address the classical One-Dimensional Bin Packing Problem (1D-BPP), an \(\mathcal {NP}\)-hard combinatorial optimization problem. We propose a new formulation of integer linear programming for the problem, which reduces the search space compared to those described in the literature, as well as two families of cutting planes. Computational experiments are conducted on the data-set found in BPPLib and the results show that it is possible to solve more instances and to decrease the computation time by using our new formulation.