Team Orienteering Problem with Time Windows and Variable Profit

This paper introduces the Team Orienteering Problem with Time Windows and Variable Profits (TOPWPVP), which is a variant of the classical Orienteering Problem (OP) and an NP-hard optimization problem. It consists in determining the optimal route for a vehicle to traverse to deliver to a given set of nodes (customers), where each node has a predefined time window in which the service must start (in case this node is visited), and the vehicle may spend an amount of time given by a predefined interval so that the profit collected at this node depends on the time spent. We first propose a mathematical model for the TOPTWVP, then propose an algorithm based on Iterated Local Search to solve modified benchmark instances. The results show that our approach can solve difficult instances with good quality.