Definitions and Mathematical Models of Single Vehicle Routing Problems with Profits

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.