A multi-objective distributionally robust model for sustainable last mile relief network design problem

Natural disasters not only inflict massive life and economic losses but also result in psychological damage to survivors, at times even causing social unrest. It is necessary to design a sustainable last mile relief network for distributing relief supplies regarding social factors, disaster relief efficiency as well as the economic cost of three perspectives in terms of sustainability. We establish a multi-objective distributionally robust optimization model for a sustainable last mile relief network problem that maximizes the equitable distribution of relief supplies and simultaneously minimizes the transportation time and operation cost. Under the partial probability information of uncertainties, such as the disaster situation, transportation time, freight, road capacity, and demand, we characterize the uncertain variables in an ambiguity set incorporating the bounds, means and the mean absolute deviations. Then, the bounds on the objective values and the safe approximations of the chance constraints are deduced under the ambiguity sets. Based on a revised multi-choice goal programming approach, we obtain a computationally tractable framework of the multi-objective model. To verify the effectiveness of the model and methods, a case study of the Banten tsunami is illustrated. The results demonstrate our proposed model can obtain a trade-off between the equitability, timeliness and economics for relief distribution in a relief network.