Arrival and service time dependencies in the single- and multi-visit selective traveling salesman problem
研究了选择性旅行商问题中利润依赖于服务时间或服务时间依赖于到达时间的两种情况，分别构建了单次和多次访问顶点的连续时间与离散时间模型，并用Gurobi求解。
We analyze several time dependency issues for the selective traveling salesman problem with time-dependent profits. Specifically, we consider the case in which the profit collected at a vertex depends on the service time, understood as the time spent at this vertex, and when the service time at each vertex depends on the arrival time at the vertex. For each of these two cases, we formulate two continuous-time problems: (i) a vertex can be visited at most once, and (ii) vertices may be visited more than once. In each case, we consider general profit functions at the vertices, i.e., the profit functions are not limited to monotonic functions of time. We also formulate the problems as discrete-time problems using appropriate variants of an auxiliary time-extended graph, and we solve them with Gurobi. We apply our methodology to two sets of instances. First, we use a set of artificial instances to illustrate the main differences amongst the different versions of the problem. We then solve several instances adapted from TSPLIB to evaluate the computational capabilities of the methodology.