An iterated local search for a multi-period orienteering problem arising in a car patrolling application

This paper addresses a real-world multi-period orienteering problem arising in a large Italian company that needs to patrol an area in order to provide security services to a set of customers. Each customer requires different services on a weekly basis. Some services are mandatory, while others are optional. It might be impossible to perform all optional services, and each of them is assigned a score when performed. The challenge is to determine a set of routes, one per day, that maximizes a weighted sum of the total collected score and total working time, while meeting several operational constraints, including hard time windows, maximum riding time, minimum number of services performed, and minimum time between two consecutive visits for the same service at the same customer. To solve the problem, we propose an iterated local search that invokes at each iteration an inner variable neighborhood descent procedure. Computational tests performed on a large number of real-world instances prove that the developed algorithm is very efficient, and finds in a short time solutions that are consistently better than those produced by a mathematical model, and those in use at the company.