The bi-objective stochastic covering tour problem

Authors:
Fabien Tricoire;Alexandra Graf;Walter J. Gutjahr
Affiliations:
Department of Business Administration, University of Vienna, Bruenner Strasse 72, 1210 Vienna, Austria and NICTA/UNSW, Sydney, Australia;Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria;Department of Statistics and Operations Research, University of Vienna, Universitaetsstrasse 5, 1010 Vienna, Austria
Venue:
Computers and Operations Research
Year:
2012

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Abstract

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.