Study on the Time-Dependent Orienteering Problem

In the orienteering problem (OP) a set of locations is given, each with a score. The goal is to determine a route, limited in length, that visits some locations and maximize the sum of the collected scores. The orienteering problem is often used as a starting point for modeling many combinatorial optimization problems. This paper studies the time-dependent orienteering problem taking into account the travel cost varying with time and stay time constraints. After a mixed integer programming model is proposed, a novel optimal pre-node labeling algorithm is designed based on the idea of network planning and dynamic programming. Finally, a numerical example is presented to show the validity and feasibility of this algorithm.