Multiple bin-size bin packing problem considering incompatible product categories

Optimizing the order-fulfillment process is crucial to the logistics industry. Replacing experience-based judgment with intelligent methods in the packing process not only improves work efficiency but also eliminates resource wastage. This study focuses on the three-dimensional multiple bin-size bin packing problem with compatible categories (3D-MBSBPPCC) and different size of the boxes. An algorithm is developed to achieve the best packing pattern while minimizing the number of boxes required and the total unused space in the boxes. In the algorithm, we first use the first-fit decreasing algorithm to find an initial solution. Next, the carton configuration algorithm is applied to perform packing and evaluate the solution. Subsequently, a simulated annealing (SA)-based algorithm is employed to improve the solution by moving the products among the subsets of the solution. Finally, hybrid metaheuristics based on both SA and the genetic algorithm, are proposed to improve the solution quality. We tested the proposed packing algorithms on real-world scenarios. The experimental results demonstrate that the proposed algorithms are effective in solving 3D-MBSBPPCC.