Decision Support For Bundle Shipment Choices: Orthogonal Two-Dimensional Bin Packing With Practical Constraints

In this paper, we study a real life application of an orthogonal two dimensional bin packing problem (2DBPP) with a small assortment of different shapes of bins and items. A telecommunication equipment company ships its products to customers several times daily by trucks and it currently uses the less-than-truckload (LTL) shipping option which is priced as unit price per volume times the total volume of products. However, depending on scale of products to be shipped, full-truckload (FTL) shipping which is priced as a single price per truck may be cheaper. In this paper we aim to help the company to decide on the delivery choice as well as on how to pack the truck optimally when FTL shipping is selected. We model the problem as a variant of an orthogonal 2D-BPP using mixed-integer linear programming (MIP) with the objective to minimise the total cost of delivery. Practical conditions influencing the feasibility of packing patterns are also considered. Practical guidance such as those on some modelling techniques and the application of the model, are applied to enhance the solving efficiency. The problems are solved by commercial solver CPLEX to optimality up to 34 pallets within an acceptable time. For lager problems, we adopt an approach to combine same items into larger rectangles and then pack them. This increases the solvability to 154 pallets. On average, our method help the company save 26% shipping cost.