Abstract
In this chapter, single vehicle routing problems with profits are introduced and defined. Three variants are considered: the profitable tour problem, the prize-collecting traveling salesperson problem, and the orienteering problem. The difference between these variants is the way in which the profit and the travel cost, mostly distance or time, are modeled. Profit and travel cost can be modeled as (part of) the objective or as a constraint. All three problems differ from the well-known traveling salesperson problem, for which the only objective is to find the shortest route to visit all customers in a given set. In vehicle routing problems with profits, some customers will be selected to be visited and others will not, based on the objective considered. In this chapter, each single vehicle variant will be defined and an appropriate mathematical model will be presented, together with a discussion on the differences and similarities with the other variants. First, the profitable tour problem is discussed, then the prize-collecting traveling salesperson problem and finally the orienteering problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Achuthan N, Caccetta L, Hill S (1996) A new subtour elimination constraint for the vehicle routing problem. Eur J Oper Res 91(3):573–586
Archetti C, Feillet D, Hertz A, Speranza MG (2009) The capacitated team orienteering and profitable tour problems. J Oper Res Soc 60:831–842
Archetti C, Speranza MG, Vigo D (2014) Vehicle routing problems with profits. In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications. MOS-SIAM series on optimization. SIAM, Philadelphia, pp 273–298
Feillet D, Dejax P, Gendreau M (2005) Traveling salesman problems with profits. Transp Sci 39(2):188–205
Golden BL, Levy L, Vohra R (1987) The orienteering problem. Naval Res Logist 34(3):307–318
Gunawan A, Lau HC, Vansteenwegen P (2016) Orienteering problem: a survey of recent variants, solution approaches and applications. Eur J Oper Res 255(2):315–332
Miller C, Tucker A, Zemlin R (1960) Integer programming formulations and travelling salesman problems. J ACM 7:326–329
Vansteenwegen P, Mateo M (2014) An iterated local search algorithm for the single-vehicle cyclic inventory routing problem. Eur J Oper Res 237(3):802–813
Vansteenwegen P, Souffriau W, Van Oudheusden D (2011) The orienteering problem: a survey. Eur J Oper Res 209(1):1–10
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Vansteenwegen, P., Gunawan, A. (2019). Definitions and Mathematical Models of Single Vehicle Routing Problems with Profits. In: Orienteering Problems. EURO Advanced Tutorials on Operational Research. Springer, Cham. https://doi.org/10.1007/978-3-030-29746-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-29746-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29745-9
Online ISBN: 978-3-030-29746-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)