Intl. Trans. in Op. Res. 00 (2015) 1–27 DOI: 10.1111/itor.12163 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH Bi-objective stochastic programming models for determining depot locations in disaster relief operations Stefan Rath a,b , Michel Gendreau a,c and Walter J. Gutjahr b a Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Canada b Department of Statistics and Operations Research, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria c Department of Mathematics and Industrial Engineering, ´ Ecole Polytechnique de Montr´ eal, P.O. Box 6079, Station Centre-ville, Montreal, Canada H3C 3A7 E-mail: stefan.rath@univie.ac.at [Rath]; michel.gendreau@cirrelt.ca [Gendreau]; walter.gutjahr@univie.ac.at [Gutjahr] Received 20 September 2013; received in revised form 6 February 2015; accepted 12 February 2015 Abstract This paper presents two-stage bi-objective stochastic programming models for disaster relief operations. We consider a problem that occurs in the aftermath of a natural disaster: a transportation system for supplying disaster victims with relief goods must be established. We propose bi-objective optimization models with a monetary objective and humanitarian objective. Uncertainty in the accessibility of the road network is modeled by a discrete set of scenarios. The key features of our model are the determination of locations for intermediate depots and acquisition of vehicles. Several model variants are considered. First, the operating budget can be fixed at the first stage for all possible scenarios or determined for each scenario at the second stage. Second, the assignment of vehicles to a depot can be either fixed or free. Third, we compare a heterogeneous vehicle fleet to a homogeneous fleet. We study the impact of the variants on the solutions. The set of Pareto-optimal solutions is computed by applying the adaptive Epsilon-constraint method. We solve the deterministic equivalents of the two-stage stochastic programs using the MIP-solver CPLEX. Keywords: humanitarian logistics; disaster management; stochastic programming; multiobjective optimization 1. Introduction Natural disasters, such as floods, fires, earthquakes, and hurricanes, destroy the infrastructure of the affected region. A transportation system for disaster relief must be established to transport food, medicine, blankets, tents, hygiene products, and other relief goods to the victims. This is usually done by nonprofit aid organizations that rely on external funding. The transportation system that we con- sider is as follows. Relief goods are transported from suppliers to intermediate depots (sometimes also called warehouses or distribution centers). Suppliers are local or international suppliers who C  2015 The Authors. International Transactions in Operational Research C  2015 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA.