一种面向带时间窗取送货问题的机组调度元启发式算法
A metaheuristic for crew scheduling in a pickup-and-delivery problem with time windows
AI总结：
针对带时间窗取送货场景下车辆与机组路径独立的VRCSP，提出两阶段求解框架，第二阶段采用带扰动与修复机制的GRASP元启发式算法，可高效求解大规模算例，且双驾驶员机组能显著降低外部班车成本。
摘要：
车辆路径与机组调度问题（VRCSP）需要同时规划车队的行驶路线并安排机组人员调度，且车辆与机组人员的对应关系并非固定不变。这一特性提升了规划灵活性与车队利用效率，但同时也要求高度的同步性。本文研究了一类VRCSP：在给定规划周期内，需通过卡车与驾驶员完成带时间窗的取送货需求。机组可由1名或2名驾驶员组成，任意驾驶员均可在指定的一组地点换班。此外，驾驶员可乘坐非公司班车在不同地点间通勤，由此产生的额外成本将被最小化。由于本问题中卡车与驾驶员的路径相互独立，相比现有文献中将机组视为不可分割单元的VRCSP，我们拥有额外的规划灵活性。\n我们采用两阶段顺序方法求解该问题：第一阶段计算一组卡车路径，第二阶段生成与卡车路径相匹配的驾驶员路径。本文针对第二阶段设计了一种基于元启发式的算法并评估其性能。该算法以GRASP（贪婪随机自适应搜索算法）为核心，引入扰动机制：当搜索新解陷入困境时，可复用已找到的解。该机制与不可行解修复机制共同作用，可在1小时内，对分布于15座城市的100个需求、配备12-32辆卡车（数量依规划周期而定）的算例，求得高质量解。我们还得出结论：与单人机组相比，配备额外驾驶员的方案可使外部班车成本平均降低约60%，部分场景下可完全消除该成本。
英文摘要：
A vehicle routing and crew scheduling problem (VRCSP) consists of simultaneously planning the routes of a fleet of vehicles and scheduling the crews, where the vehicle-crew correspondence is not fixed through time. This allows a greater planning flexibility and a more efficient use of the fleet, but in counterpart, a high synchronisation is demanded. In this work, we present a VRCSP where pickup-and-delivery requests with time windows have to be fulfilled over a given planning horizon by using trucks and drivers. Crews can be composed of 1 or 2 drivers and any of them can be relieved in a given set of locations. Moreover, they are allowed to travel among locations with non-company shuttles, at an additional cost that is minimised. As our problem considers distinct routes for trucks and drivers, we have an additional flexibility not contemplated in other previous VRCSP given in the literature where a crew is handled as an indivisible unit. We tackle this problem with a two-stage sequential approach: a set of truck routes is computed in the first stage and a set of driver routes consistent with the truck routes is obtained in the second one. We design and evaluate the performance of a metaheuristic based algorithm for the latter stage. Our algorithm is mainly a GRASP with a perturbation procedure that allows reusing solutions already found in case the search for new solutions becomes difficult. This procedure together with other to repair infeasible solutions allow us to find high-quality solutions on instances of 100 requests spread across 15 cities with a fleet of 12-32 trucks (depending on the planning horizon) in less than an hour. We also conclude that the possibility of carrying an additional driver leads to a decrease of the cost of external shuttles by about 60% on average with respect to individual crews and, in some cases, to remove this cost completely.
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