A Branch-and-Price Algorithm for the Risk-Equity Constrained Routing Problem

We study a multi-criteria variant of the problem of routing hazardous material on a geographical area subdivided in regions. The two objective functions are given by a generally defined routing cost and a risk equity equal to the maximum, over each region, of the risk perceived within a region. This is a multicommodity flow problem where integer variables are used to define the number of trucks used for the routing. This problem admits a straightforward path formulation, for which a branch-and-price problem where, for each node of the branch-and-bound tree, column generation is used to obtain a lower bound.