Shelter site location under demand uncertainty : a chance-constrained multi-objective modeling framework

Abstract

Shelters have a very critical role in disaster relief since they provide accommodation and necessary services for the disaster victims who lost their homes. The selection of their locations among many candidate points is a task that should be carried out with a proper methodology that generates applicable and fairnessbased plans. Since this selection process is done before the occurrence of disasters, it is important to take demand variability into account. Motivated by this, the problem of determining shelter site locations under demand uncertainty is addressed. In particular, a chance-constrained mathematical model that takes demand as a stochastic input is developed. By using a linearization approach that utilizes special ordered set of type 2 (SOS2) variables, a mixed-integer linear programming model is formulated. Using the proposed formulation, instances of the problem using data associated with Istanbul are solved. The results indicate that capturing uncertainty in the shelter site location problem by means of chance constraints may lead to solutions that are much different from those obtained from a deterministic setting. During these computational analysis, it is observed that the single-objective model is prone to generate many alternative solutions with different characteristics of important quality measures. Motivated by this, a multi-objective framework is developed for this problem in order to have a stronger modeling approach that generates only non-dominated solutions for the selected performance measures. The ε-constraint method is used for scalarization of the model. Bi-objective and 3-objective algorithms are presented for detecting all the efficient solutions of a given setting. Unlike the single-objective configuration, the decision makers could be supplied with much richer information by reporting many non-dominated solutions and allowing them to evaluate the trade-offs based on their preferences.