The Fragility-Constrained Vehicle Routing Problem with Time Windows
研究了一种新的带时间窗车辆路径问题变种，其中车辆容量分为多个相同堆栈，易碎品不能放在非易碎品下方，且途中不能重新装载。开发了精确分支定价切割算法，并验证了其有效性。
We study a new variant of the well-studied vehicle routing problem with time windows (VRPTW), called the fragility-constrained VRPTW, which assumes that (1) the capacity of a vehicle is organized in multiple identical stacks; (2) all items picked up at a customer are either “fragile” or not; (3) no nonfragile items can be put on top of a fragile item (the fragility constraint); and (4) no en route load rearrangement is possible. We first characterize the feasibility of a route with respect to this fragility constraint. Then, to solve this new problem, we develop an exact branch-price-and-cut (BPC) algorithm that includes a labeling algorithm exploiting this feasibility characterization to efficiently generate feasible routes. This algorithm is benchmarked against another BPC algorithm that deals with the fragility constraint in the column generation master problem through infeasible path cuts. Our computational results show that the former BPC algorithm clearly outperforms the latter in terms of computational time and that the fragility constraint has a greater impact on the optimal solution cost (compared with that of the VRPTW) when vehicle capacity decreases, stack height increases, and for a more balanced mix of customers with fragile and nonfragile items. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN 2015-06289 and RGPIN 2022-03916]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1168 .