Multi-period bin packing model and effective constructive heuristics for corridor-based logistics capacity planning

The bin packing problem is one of the most studied combinatorial optimization problem. This paper proposes two novel bin packing problem settings with many practical applications, in particular in logistics capacity planning. Both problems explicitly consider, besides the classical bin-selection costs, the item and bin-specific item-to-bin assignment costs. These assignment costs depend not only on the physical, e.g., item and bin size, and economic, e.g., bin selection fixed cost and the cost of item "transport" by the bin, but also on the temporal attributes of items and bins, e.g., availability of regular bins for selection and utilization and of items to be assigned to such a regular bin. Special, item-specific in terms of size, spot-market bins may be used at higher cost for the items one cannot fit into the selected bins. Single and a multi-period formulations are proposed, both aiming to minimize the total cost of the system computed as the sum of the fixed costs of the selected bins and the total item-to-bin assignment cost using regular and spot-market bins. The multi-period formulation optimizes the cost over all the time periods considered. Several constructive heuristics are proposed, three for the single-period model, and four for the multi-period formulation. The heuristics are evaluated and compared through an extensive computational experimentation. The numerical results show the high level of performance of the proposed heuristics in terms of solution quality and computational efficiency, as well as the potential benefits of using the new models in practical applications.