Analysis of the selective traveling salesman problem with time-dependent profits

We consider a generalization of the selective traveling salesman problem (STSP) in which the benefit of visiting a location changes over time. This new problem, called the selective travelling salesman problem with time-dependent profits (STSP-TDP), is defined on a graph with time-dependent profits...

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Bibliographic Details
Published in:TOP 2023-04, Vol.31 (1), p.165-193
Main Authors: Barrena, Eva, Canca, David, Coelho, Leandro C., Laporte, Gilbert
Format: Article
Language:English
Subjects:
Apexes
Business and Management
Circuits
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Graph theory
Industrial and Production Engineering
Insurance
Mailboxes
Management
Operations Research/Decision Theory
Optimization
Original Paper
Profits
Statistics for Business
Time dependence
Traveling salesman problem
Water sampling
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Summary:We consider a generalization of the selective traveling salesman problem (STSP) in which the benefit of visiting a location changes over time. This new problem, called the selective travelling salesman problem with time-dependent profits (STSP-TDP), is defined on a graph with time-dependent profits associated with the vertices, and consists of determining a circuit of maximal total profit. In the STSP-TDP the tour length must not exceed a maximum value, and its starting and ending times must both lie within a prespecified planning horizon. This problem arises in planning tourist itineraries, mailbox collection, military surveillance, and water sampling, where the traveler accumulates different profits upon visiting the locations throughout the day. We focus on analyzing several variants of the problem depending on the shape of the time-dependent profit function. If this function is not monotonic, it may be worth visiting a site more than once. We propose formulations for the single-visit case and for when multiple visits are allowed, in which case the problem reduces to an STSP, which is adapted to be solved as a longest path problem. These formulations are then solved for piecewise-linear profit functions using a general-purpose solver, and tested on several artificially created instances and on four TSPLib instances involving up to 535 vertices. A detailed analysis of the problem and the solution is performed.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-022-00632-6