A Three-Stage Stochastic Facility Routing Model for Humanitarian Logistics Planning

This paper presents a humanitarian logistics decision model to be used in the event of a disaster. The operations under consideration span from opening of local distribution facilities and initial allocation of supplies, to last mile distribution of aid. A mathematical model is developed aiming to enable efficient decision making, maximizing the utility of distribution of aid amongst beneficiaries. This model is formulated as a three-stage mixed-integer stochastic programming model to account for the difficulty in predicting the outcome of a disaster. Accessibility of new information implies initiation of distinct operations in the humanitarian supply chain, be it facility location and supply allocation, or last mile distribution planning and execution. The realized level of demand, in addition to the transportation resources available to the decision maker for execution of last mile aid distribution and the state of the infrastructure, are parameters treated as random due to uncertainty. An assessment of the applicability and validity of the stochastic program is made through extensive computational testing based on several test instances. The results show that instances of considerable size are challenging to solve due to the complexity of the stochastic programming model but, still, optimal solutions may be found within a reasonable time frame. Moreover, findings prove the value of the stochastic programming model to be significant as compared with a deterministic expected value approach. Finally, the model is also applied to a case study based on the earthquake that hit Haiti in January of 2010, showing how it could be used in a realistic operation framework.