Arrival and service time dependencies in the single- and multi-visit selective traveling salesman problem

David Canca, Eva Barrena, Gilbert Laporte

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number106632
JournalComputers and Operations Research
Early online date27 Mar 2024
Publication statusE-pub ahead of print - 27 Mar 2024

Data Availability Statement

Data will be made available on request.


  • Selective traveling salesman problem
  • Service time-dependent profit
  • Single- and multi-visit
  • Time-dependent service time

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research


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