Combining Worst Case and Average Case Considerations in an Integrated Emergency Response Network Design Problem

We study an emergency response network design problem that integrates relief (supply) and evacuation (demand) sides under disaster location and intensity uncertainties which, in turn, dictate uncertainty in terms of the location and amount of demand. Representing these uncertainties by discrete scenarios, we present a stochastic programming framework in which two second stage objectives, the average and worst case costs, are combined. In our model, we minimize, over all of the scenarios, the fixed costs of opening supply centers and shelters, and the weighted sum of average and worst case flow costs. Thus, the model gives the decision maker the flexibility to put relative emphasis on the worst case and average flow cost minimization and explore outcomes in terms of total costs and network configurations. To solve large scale instances with varying relative weights, we devise alternative Benders Decomposition approaches. We implement these by using an advanced callback feature of the solver while simultaneously incorporating several performance-enhancing steps that help to improve runtimes significantly. We conduct a detailed computational study to highlight the efficiency of our proposed solution methodology. Furthermore, we apply our approach in a realistic case study based on Geographical Information Systems data on coastal Texas and present interesting insights about the problem and the resulting network structures for varying weights assigned to objectives.