An improved formulation for the maximum coverage patrol routing problem

We present an improved formulation for the maximum coverage patrol routing problem (MCPRP). The main goal of the patrol routing problem is to maximize the coverage of critical highway stretches while ensuring the feasibility of routes and considering the availability of resources. By investigating the structural properties of the optimal solution, we formulate a new, improved mixed integer program that can solve real life instances to optimality within seconds, where methods proposed in prior literature fail to find a provably optimal solution within an hour. The improved formulation provides enhanced highway coverage for both randomly generated and real life instances. We show an average increase in coverage of nearly 20% for the randomly generated instances provided in the literature, with a best case increase over 46%. Similarly, for the real life instances, we close the optimality gap within seconds and demonstrate an additional coverage of over 13% in the best case. The improved formulation also allows for testing a number of real life scenarios related to multi-start routes, delayed starts at the beginning of the shifts, and taking a planned break during the shift. Being able to solve these scenarios in short durations help decision and policy makers to better evaluate resource allocation options while serving public.