Models for a fair relief distribution: A network design problem

The emergency logistics field is a new and particular challenge for logistics' managers. In these networks, the satisfaction of the affected people's demand is much more important than the cost minimization. Moreover, crisis managers are looking for networks that ensure an equitable distribution of resources over affected people. We propose a new mathematical formulation that reflects this interest. First, we define a multi-period formulation for the network design problem, where the opening decisions are reconsidered at every period. In addition, this model includes different features of the realistic challenges of emergency logistics, like the possible shortage in capacity and the backorder of demand. Finally, three different formulations of a “fair” distribution problem are proposed. These formulations are tested on random generated instances and the analysis of the distribution plans obtained with each formulation is presented at the end of this paper.