Definitions and Mathematical Models of OP Variants

Abstract

We have described the basic orienteering problem (OP) in Chap. 2, as one known variant of the single vehicle routing problems with profits (VRPP). In this chapter, we introduce the best-known variants of the OP. The first one is the team orienteering problem (TOP). In the TOP multiple routes can be composed to visit a subset of customers. In the context of the game of orienteering, the TOP corresponds to several players of the same team, each collecting profits in parallel, during the same time span. Another well-known variant of the basic OP is the OP with time windows (OPTW), imposing time windows for each customer. If we consider, for example, an application in tourism, we should account for the fact that most tourist attractions are only open within certain opening hours. Arriving at an attraction after it has closed or long before it will open, should be avoided. Both variants, the TOP and the OPTW come together in the third well-known variant, the team OP with time windows (TOPTW), where time windows are considered together with multiple vehicles (or a multiple day trip). The TOP, OPTW, and TOPTW will be presented in detail in this chapter, together with an appropriate mathematical model. Other variants and extensions of the OP, modeling more complex and complicated optimization problems from practice, will be explained in Chap. 8.