Hybrid greedy heuristics based on linear programming for the three-dimensional single bin-size bin packing problem

In this paper, we propose to solve the three-dimensional single bin-size bin packing problem (3D-SBSBPP) using a simple strategy based on integer linear programming (ILP) heuristics, without using any improvement based on metaheuristics. We first propose an ILP that is converted into a series of three-dimensional single knapsack problems (3D-SKP). Then, the first tailored heuristic can be viewed as a hybrid approach in which both selection and positioning phases are combined. The first phase serves to select a subset of items where each of these items is susceptible to belonging to an active container. The positioning phase serves to pack a subset of items already preselected by the selection phase. Then, both phases cooperate till packing all items into their corresponding containers. The second heuristic can be viewed as an extended version of the first one. Indeed, before deciding whether the current container is closed or a new container is activated, a local reoptimization phase is considered. Finally, both proposed heuristics are evaluated on a set of random instances obtained by using the standard generator scheme of the literature. The provided results show that both proposed heuristics remain competitive when compared to the results obtained by one of the best methods of the literature.