A variable neighborhood search algorithm for the bin packing problem with compatible categories

• Published in: Expert systems with applications Vol. 124; pp. 209 - 225
• Main Authors: Santos, Luiz F.O. Moura, Iwayama, Renan Sallai, Cavalcanti, Luísa Brandão, Turi, Leandro Maciel, Morais, Fabio Emanuel de Souza, Mormilho, Gabriel, Cunha, Claudio B.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 15-06-2019; Elsevier BV
• Subjects: Bin packing problem with compatible categories; Categories; Compatibility; Computation; Developing countries; Formulations; Heuristic methods; Incompatibility; Last mile distribution; LDCs; Matrix methods; Nanostores; Operations research; Optimization; Production scheduling; Search algorithms; Shaking; Variable neighborhood search; Nanostores; Bin packing problem with compatible categories; Last mile distribution; Variable neighborhood search
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2019.01.052

•A new variant of the Bin Packing Problem is introduced.•It is motivated by last mile delivery to tiny stores.•Items to be delivered belong to categories that may not be transported together in the same vehicle.•Extensive computational tests are performed on instances derived from the literature.•Results show that our VNS algorithm can effectively solve the BPCC in very short CPU times.
In this paper, we address the Bin Packing Problem with Compatible Categories (BPCC), a challenging optimization problem that arises in the context of last mile distribution to nanostores in large cities, particularly in developing countries. By introducing the concept of incompatible categories of items to be delivered (i.e., types of items that cannot be transported together, such as food and cleaning products), as opposed to the item-by-item incompatibility found in previous literature, we aim to determine the best assignment of deliveries of distinct products to a homogeneous fleet of capacitated vehicles in order to minimize the number of required vehicles (bins). To solve large instances of the BPCC that are commonly found in practice, we propose an efficient variable neighborhood search (VNS) metaheuristic that relies on a simple greedy heuristic to generate initial solutions and on simple and efficient neighborhoods as well as problem-tailored shaking procedures. We perform extensive computational experiments on a very large set of 8000 instances derived from benchmark datasets. The tested instances differ in terms of number of items (ranging from 201 to 1002), bin capacities, compatibility matrices and proportion of items that belong to the different categories. We also present two new mathematical formulations for the BPCC and compare them to the item-by-item bin packing formulation (Gendreau et al., 2004) using a high performance computer (HPC). The computational experiments indicate that our VNS algorithm can effectively solve the BPCC in very short CPU times.