A mixed integer knapsack model for allocating funds to highway safety improvements

This paper presents a methodology for allocating funds to highway safety improvements. Besides the commonly used binary variables that represent discrete interventions at specific points of a highway, continuous variables are introduced to represent the lengths of a highway over which continuous improvements, such a pavement resurfacing or lighting, are implemented. The problem is formulated as a mixed integer knapsack model with linear multiple choice constraints. Some insight into its solution properties is provided and an efficient branch and bound algorithm is proposed for its solution. A case study that illustrates the application of the model is also presented.