Algorithms for the variable-sized bin packing problem with time windows

Abstract

This paper introduces and studies the variable-sized bin packing problem with time windows, a real problem in the logistics industry. Given a set of items with different volume and time window, and several types of bins with variable size and cost, the objective is to select bins with the minimum cost to pack all the items. The total volume packed in the same bin must not exceed the volume capacity, and there must be one common time point among the time windows of the items in the same bin. We first formulate the problem as an integer programming model and then propose three heuristics to solve this problem. Firstly, the classical best-fit heuristic is modified to find an initial solution. An iterative local search based on the shortest path decoder is employed to find more solutions. Lastly, a primal heuristic based on the column generation is utilized. These three heuristics are different and independent. Two categories of instances are generated to test the performance of our approach. The results demonstrate that the proposed approach is effective in solving this problem and finds near-optimal solutions in a short time.