This paper presents an optimization model that minimizes the crash costs of highway networks, while the total safety improvement cost is limited. The crash prediction models for which this optimization model is developed have a base model and a series of Accident Modification Factors (AMFs). The main objective of this paper is to combine the Empirical Bayes (EB) method with the crash cost optimization model that uses the predicted number of highway crashes. The goal of using EB analysis in conjunction with the crash prediction model is to eliminate the effect of the regression-to-mean phenomenon that creates biases in the estimation of the expected number of crashes. In the EB approach presented here, the observed number of crashes for each segment of each highway of the network is combined with the model prediction for that segment. This model is presented in the context of crash prediction models contained in the Interactive Highway Safety Design Model (IHSDM).
This study presents the application of the presented model on a large scale case study containing the network of two-lane rural highways of Washington State. A priority strategy is presented that chooses 44 stretches of highways for safety improvements. Optimization problems are solved using CPLEX software and analyses are conducted on different budget limitations looking at absolute Benefit/Cost ratios as well as for incremental Benefit/Cost ratios. It is shown that for some improvement combinations, even though the absolute Benefit/Cost ratio may justify the improvements, the incremental Benefit/Cost ratio rejects part of those improvements.