Journal of the Operational Research Society

, Volume 56, Issue 4, pp 439–452 | Cite as

Algorithms for a stochastic selective travelling salesperson problem

Theoretical Paper


In this paper, the selective travelling salesperson problem with stochastic service times, travel times, and travel costs (SSTSP) is addressed. In the SSTSP, service times, travel times and travel costs are known a priori only probabilistically. A non-negative value of reward for providing service is associated with each customer and there is a pre-specified limit on the duration of the solution tour. It is assumed that not all potential customers can be visited within this tour duration limit, even under the best circumstances. And, thus, a subset of customers must be selected. The objective of the SSTSP is to design an a priori tour that visits each chosen customer once such that the total profit (total reward collected by servicing customers minus travel costs) is maximized and the probability that the total actual tour duration exceeds a given threshold is no larger than a chosen probability value. We formulate the SSTSP as a chance-constrained stochastic program and propose both exact and heuristic approaches for solving it. Computational experiments indicate that the exact algorithm is able to solve small- and moderate-size problems to optimality and the heuristic can provide near-optimal solutions in significantly reduced computing time.


selective travelling salesperson problem stochastic travelling salesman chance constraints orienteering problem 


  1. Golden B, Levy L and Vohra R (1987). The orienteering problem. Naval Res Logist 34: 307–318.CrossRefGoogle Scholar
  2. Laporte G and Martello S (1990). The selective traveling salesman problem. Discrete Appl Math 26: 193–207.CrossRefGoogle Scholar
  3. Ramesh R, Yoon Y and Karwan M (1992). An optimal algorithm for the orienteering tour problem. ORSA J Comput 4: 155–165.CrossRefGoogle Scholar
  4. Fischetti M, Salazar J and Toth P (1998). Solving the orienteering problem through branch-and-cut. INFORMS J Comput 10: 33–148.CrossRefGoogle Scholar
  5. Gendreau M, Laporte G and Semet F (1998). A branch-and-cut algorithm for the undirected selective traveling salesman problem. Networks 32: 263–273.CrossRefGoogle Scholar
  6. Tsiligirides T (1984). Heuristic methods applied to orienteering. J Opl Res Soc 35: 797–809.CrossRefGoogle Scholar
  7. Wren A and Holliday A (1972). Computer scheduling of vehicles from one or more depots to a number of delivery points. Opl Res Quart 23: 333–344.CrossRefGoogle Scholar
  8. Golden B, Wang Q and Liu L (1988). A multifaceted heuristic for the orienteering problem. Naval Res Logist 35: 359–366.CrossRefGoogle Scholar
  9. Ramesh R and Brown K (1991). An efficient four-phase heuristic for the generalized orienteering problem. Comput Opns Res 18: 151–165.CrossRefGoogle Scholar
  10. Chao I (1993). Algorithms and solutions to multi-level vehicle routing problems. PhD dissertation, University of Maryland, College Park.Google Scholar
  11. Chao I, Golden B and Wasil E (1996). A fast and effective heuristic for the orienteering problem. Eur J Opl Res 88: 475–489.CrossRefGoogle Scholar
  12. Golden B, Wasil E, Kelly J and Chao I (1998). The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results. In: Crainic T and Laporte G (eds). Fleet Management and Logistics. Kluwer Academic Publishers, Boston, pp 33–56.CrossRefGoogle Scholar
  13. Gendreau M, Hertz A and Laporte G (1992). New insertion and postoptimization procedures for the traveling salesman problem. Opns Res 40: 1086–1094.CrossRefGoogle Scholar
  14. Gendreau M, Laporte G and Semet F (1998). A tabu search heuristic for the undirected selective traveling salesman problem. Eur J Opl Res 106: 539–545.CrossRefGoogle Scholar
  15. Laporte G, Louveaux F and Mercure H (1992). The vehicle routing problem with stochastic travel times. Transport Sci 26: 161–170.CrossRefGoogle Scholar
  16. Laporte G and Louveaux F (1993). The integer L-shaped method for stochastic integer programs with complete recourse. Opns Res Lett 13: 133–142.CrossRefGoogle Scholar
  17. Fischetti M, Salazar J and Toth P (1997). A branch-and-cut algorithm for the symmetric generalized travelling salesman problem. Opns Res 45: 378–394.CrossRefGoogle Scholar
  18. Gendreau M, Laporte G and Semet F (1997). The covering tour problem. Opns Res 45: 568–576.CrossRefGoogle Scholar
  19. Padberg M and Hong S (1980). On the symmetric travelling salesman problem: a computational study. Math Prog Study 12: 78–107.CrossRefGoogle Scholar
  20. Barnhart C et al (1998). Branch-and-cut: column generation for solving huge integer programs. Opns Res 46: 316–329.CrossRefGoogle Scholar
  21. Laporte G, Louveaux F and Mercure H (1994). A priori optimization of the probabilistic traveling salesman problem. Opns Res 42: 543–549.CrossRefGoogle Scholar
  22. Tsubakitani S and Evans J (1998). An empirical study of a new metaheuristic for the traveling salesman problem. Eur J Opl Res 104: 113–128.CrossRefGoogle Scholar
  23. Or I (1976). Travelling salesman-type combinatorial optimization problems and their relation to the logistics of regional blood banking. PhD dissertation. Northwestern University, Evanston.Google Scholar
  24. Rosenkrantz D, Stearns R and Lewis P (1977). An analysis of several heuristics for the traveling salesman problem. SIAM J Comput 6: 563–581.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan Ltd 2004

Authors and Affiliations

  1. 1.Operations Research and Spatial Applications, FedEx Express CorporationMemphisUSA
  2. 2.The University of Maryland, College ParkUSA

Personalised recommendations