A quantitative model proposal for location routing problem inhumanitarian logistics

The increasing number of disasters causes loss of life and property. To minimize these losses, humanitarian aid logistics activities need to be managed effectively. Accordingly, facility locations should be determined, and a distribution plan should be created to meet the needs of disaster victims in the fastest and most cost-effective way. In making facility location and vehicle routing decisions in humanitarian logistics, uncertainties such as infrastructure damage caused by the disaster and the uncertainty of demand should be considered. The aim of this study is to propose a decision support model to organizations engaged in humanitarian aid activities. In this context, a probabilistic bi-objective mixed integer linear programming model is proposed for a facility location routing problem confronted in humanitarian logistics. One of the objectives of this model is to minimize total cost, and the other one is to minimize total travel time. Cost minimization includes vehicle fixed cost, facility fixed cost and fuel cost. Therefore, evaluations are made regarding the calculation of fuel consumption. The proposed model considers the heterogeneous vehicle fleet structure and the closure of roads after a disaster. Moreover, the uncertainty of the demands of the victims is also respected. The accuracy and applicability of the model are demonstrated by a case study and subsequent numerical analysis. The case study is about a possible earthquake in the Kartal district of Istanbul. The numerical analyses emphasize the situations that can be encountered in real life as a support for decision-makers. The obtained results reveal the tradeoff between total cost and travel time. In addition, the advantages of using a heterogeneous vehicle fleet, the uncertainty of demand and road closure are evaluated.