Modeling the emergency service network of police special forces units for high-risk law enforcement operations

Abstract

In this paper, we propose a mathematical model that arises from the problem of establishing the network of Police Special Forces Units (PSFUs) for high-risk law enforcement operations. The goal of the considered problem is to locate certain number of PSFUs at the nodes of a given network, in order to minimize the maximal load of an established emergency unit. The uncertainty of the number of criminal acts and other conditions that arise from practice are considered. We propose a robust integer programming formulation of the problem that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. We present computational results obtained by CPLEX solver for the set of real-life test instances including 165 cities and 234 potential PSFU sites in the Republic of Serbia. We examine the impact of different protection levels on the objective value and the tradeoff between the probability of constraint violation and solution's optimality. The CPLEX solver could not provide solutions for some of the largest instances, and therefore, we have designed an efficient evolutionary-based heuristic method (EA) for solving the considered problem. The proposed EA is enhanced with an improvement local search method (LS) that helps the EA to converge to high-quality solutions. Conducted computational study shows that the proposed hybrid method EA-LS quickly reaches all known optimal solutions and provides solutions for the instances unsolved to optimality by CPLEX. We believe that the results presented in this study may help to identify a sustainable security strategy and to improve the efficiency of a security system. The proposed mathematical model may be applicable in designing and management of other emergency-service networks as well.