Integration of fuzzy linear optimization and scenario analysis in network flow problems: disaster response perspective

In this paper, we address the problem of transporting vital commodities and emergency personnel during the response stage of a disaster relief operation by integrating fuzzy linear optimization and the principles of scenario analysis. We treat this transportation system as a probabilistic multi-commodity multi-modal network flow problem and first develop a fuzzy model that allows the satisfaction of demand requirements through different supply nodes over a fuzzy network. Since the available information in case of disasters is generally vague and imprecise about the values of model parameters, fuzzy linear optimization is employed to deal with this uncertainty and to generate different scenarios depending upon the preferences of the decision maker. Then these scenarios are handled within the framework of the scenario analysis by defining a scenario as a joint realization of the uncertain parameters. Here, scenario analysis method can be considered as a search for a robust solution that guarantees the maximum satisfaction of demands with the minimum transportation cost.