Generalized Riskiness Index in Vehicle Routing Under Uncertain Travel Times: Formulations, Properties, and Exact Solution Framework
针对不确定行驶时间下的带时间窗车辆路径问题，提出广义风险指数（GRI）作为迟到风险度量，并开发了结合路径枚举与分支定价切割的精确求解框架，可求解多达100个节点的实例。
We consider a vehicle routing problem with time windows under uncertain travel times where the goal is to determine routes for a fleet of homogeneous vehicles to arrive at the locations of customers within their stipulated time windows to the maximum extent while ensuring that the total travel cost does not exceed a prescribed budget. Specifically, a novel performance measure that accounts for the riskiness associated with late arrivals at the customers, called the generalized riskiness index (GRI), is optimized. The GRI covers several existing riskiness indices as special cases and generates new ones. We demonstrate its salient managerial and computational properties to motivate it better. We propose alternative set partitioning-based models of the problem. To obtain the optimal solution, we develop an exact solution framework combining route enumeration and branch-price-and-cut algorithms, in which the GRI is dealt with in route enumeration and column generation subproblems. We mainly reduce the solution space by exploiting the GRI and budget constraints’ properties without losing optimality. The proposed method is tested on a collection of instances derived from the literature. The results show that a new instance of the GRI outperforms several existing riskiness indices in mitigating lateness. The exact method can solve instances with up to 100 nodes to optimality. It can consistently solve instances involving up to 50 nodes, outperforming state-of-the-art methods by more than doubling the manageable instance size. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72101187, 72371204, 72021002, and 71901180], the Qatar National Research Fund [Grant ARG01-0430-230029], Natural Science Foundation of Sichuan Province [24NSFSC6232], and Guanghua Talent Project of the Southwestern University of Finance and Economics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0345 .