This paper explores a problem related to both the Traveling Salesman Problem and Scheduling Problem where a traveler moves through n locations (nodes), visits all locations and each location exactly once to assign and initiate one of n jobs, and then returns to the first location. After initiation of a job, the traveler moves to the next location immediately and the job continues autonomously. This is representative of many practical scenarios including autonomous robotics, equipment maintenance, highly automated manufacturing, agricultural harvesting, and disaster recovery. The goal is to minimize the time of completion of the last job, i.e. makespan. Although the makespan objective typically is used in scheduling problems, the transportation times can be significant relative to the processing time, and this changes the optimization considerations. We refer to this problem as the Traveling Salesman Problem with Job-times (TSPJ) and present a mathematical formulation and local search improvement heuristics for it. Computational experience in solving the TSPJ using both commercial solvers and heuristics is reported.

本文探讨了与旅行商问题和日程安排问题相关的问题，其中旅行者在n个位置（节点）中移动，仅拜访所有位置和每个位置一次，以分配和启动n个作业，然后返回到第一个位置。在开始工作后，旅行者立即移动到下一个位置，并且工作自动进行。这代表了许多实际情况，包括自主机器人，设备维护，高度自动化的制造，农业收割和灾难恢复。目标是最大程度地减少完成上一个作业（即制造时间）的时间。尽管通常将makepan目标用于计划问题，但运输时间相对于处理时间而言可能很重要，这改变了优化注意事项。我们将此问题称为带工作时间的旅行推销员问题（TSPJ），并提出了数学公式和本地搜索改进方法。报告了使用商业求解器和启发式方法求解TSPJ的计算经验。