An Integer Nonlinear Goal Programming Model for the Deployment of State Highway Patrol Units

Abstract

A number of models have been developed in recent years for the allocation and deployment of urban police units. However, these models are not directly applicable to the state highway patrol counterparts. Although urban police and the state highway patrol are both law enforcement agencies, an urban police force typically operates by reacting to crimes already committed (i.e., a reactive mode of operation) while the state highway patrol attempts to maintain a visible presence to prevent infractions (i.e., a proactive mode of operation). This paper describes a modeling approach that can be used to deploy state highway patrol cars to the road segments comprising a highway patrol district. Specifically, an integer nonlinear goal programming model is described and demonstrated within the context of a hypothetical case example. The model reflects the fact that the relationships between unit deployment and performance measures are often nonlinear—as additional patrol units are assigned to a road segment, performance will increase but at a decreasing rate. The model's goal constraints reflect the proactive nature of patrol deployment. The model is solved using a modified multi-criteria pattern/gradient search technique, and the results are analyzed to test their sensitivity to goal levels and priority structures.