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.

本文介绍并研究了带有时间窗的可变尺寸垃圾箱包装问题，这是物流业中的一个实际问题。给定一组具有不同体积和时间窗口的物品，以及具有不同大小和成本的几种类型的垃圾箱，目标是选择成本最低的垃圾箱来包装所有物品。同一箱柜中包装的总体积不得超过其容量，并且同一箱柜中各个项目的时间窗口之间必须有一个公共时间点。我们首先将问题表述为整数规划模型，然后提出三种启发式方法来解决该问题。首先，对经典的最佳拟合启发式进行了修改以找到初始解。采用基于最短路径解码器的迭代局部搜索来找到更多解决方案。最后，利用基于列生成的原始启发式算法。这三种启发式方法是不同且独立的。生成了两类实例来测试我们方法的性能。结果表明，所提出的方法可以有效地解决该问题，并在短时间内找到接近最优的解决方案。