The bi‐objective stochastic covering tour problem

We formulate a bi‐objective covering tour model with stochastic demand where the two objectives are given by (i) cost (opening cost for distribution centers plus routing cost for a fleet of vehicles) and (ii) expected uncovered demand. In the model, it is assumed that depending on the distance, a certain percentage of clients go from their homes to the nearest distribution center. An application in humanitarian logistics is envisaged. For the computational solution of the resulting bi‐objective two‐stage stochastic program with recourse, a branch‐and‐cut technique, applied to a sample‐average version of the problem obtained from a fixed random sample of demand vectors, is used within an epsilon‐constraint algorithm. Computational results on real‐world data for rural communities in Senegal show the viability of the approach.