This paper presents a Linear Programming model that in conjunction with an Empirical Bayes (EB) method minimizes the crash costs related to highway segments given limited budgets for improvements. The crashes are predicted by using a base model and productive Accident Modification Factors (AMFs). In this type of model a base model prediction of crashes for each segment is multiplied by AMFs for different highway features, resulting in an expected number of crashes for that segment.
The EB method is used to deal with the regression-to-mean phenomenon that creates biases in the estimation of the expected number of crashes. In this method, crash history data are used to take the effect of available crash data into consideration. In an EB analysis the model prediction for each segment is combined with the previously observed number of crashes for that segment. A weighting factor determines what fractions of the model prediction and crash observation should be used in the final prediction of crashes. The optimization model is presented in the context of crash prediction models contained in the Interactive Highway Safety Design Model (IHSDM).
A test case study is presented containing five highways from Washington State. All possible improvement combinations for these highways are considered. Optimization problems with different budget limitations are solved using CPLEX software. Variations of the crash costs savings vs. improvement costs are studied and the results are discussed.