A two-step evolutionary algorithm for the distributor's pallet loading problem with multi-size pallets

Abstract

A two-step evolutionary algorithm for solving a real-life Distributor's Pallet Loading Problem (DPLP) is presented. Previous literature considers multiple sizes of boxes to be loaded on the same size pallet for the DPLP. However, in this research, multiple-size pallets are allowed. Allowing multi-size pallets is new to the problem and makes it even harder to solve, because the DPLP with the same size pallet is NP-Hard already. Because of the complexity and size of the problem, a two-step algorithm, based on an Evolutionary Algorithm and a Differential Evolution Algorithm, is developed to solve the problem. The first step is to determine the number of pallets of each type, and to assign boxes onto each pallet. The second step is used for improving the solutions obtained from the first step. The effectiveness of the algorithm is evaluated by using a benchmark problem set based on 3D bin-packing problem, and real-life cases from a factory. For the benchmark problem set, the total number of pallets used, as suggested by the newly developed algorithm, is 0.42% higher than the worst results of the exact algorithm on average. However, the results, regarding computation time show that the proposed algorithm is able to find sufficiently good solutions with 78.54% less average calculation time of all problems which the algorithm performed better. As for the real-life cases, the solutions obtained by the algorithm are better both in terms of calculation time and the number of pallets required, which are 26.76% and 28.02% less of the average total occupied cross-section area, and 7 and 29 min of the average total computation time with alpha = 0.7 and alpha = 0.8, respectively.