Afete hazırlık ve müdahale konusunda eşitsizlikten bağımsız optimizasyon

While efficiency, e.g. minimizing total cost, is the major concern in commercial operations, equity comes forward as an essential requirement in humanitarian operations such as response services. In humanitarian operations, models that address inequity-averseness have received insignificant attention. In this thesis, we aim to incorporate both efficiency and equity objectives into disaster preparedness and response operations. The Gini coefficient has been utilized in the economics literature for assessing income inequity among individuals. In this work, we develop models that incorporate measures of equity based on the Gini coefficient from the economics literature, to balance efficiency and equity. First, we study the problem of selecting a set of shelter locations in preparation for natural disasters. We incorporate uncertainties concerning demand locations, demand amounts, and road network accessibility into the problem. Our goal is to minimize a measure derived from individual distances that take both efficiency and inequity into account. We use a stochastic model with a set of possible disaster scenarios. Demand, affected population, and traversable road distances between population nodes and facility locations depend on the scenarios. A chance constraint is defined on the total cost of opening the shelters and their capacity expansion. In this stochastic context, a weighted mean of the so-called ex ante and ex post versions of the inequity-averse objective function under uncertainty are optimized. Since the model can be solved to optimality only for small instances, we developed a tailored genetic algorithm (GA) that utilizes a mixed integer programming subproblem to solve this problem heuristically for larger instances. We compared the performance of the mathematical program and the GA via benchmark instances. It turns out that the GA yields small optimality gaps in a much shorter time for these instances. We run the GA also on real data of the Kartal district in Istanbul to drive insights to guide decision-makers for preparation. We also implement a bi-objective analysis to approximate the Pareto frontier considering efficiency and equity as separated objectives. Furthermore, we compared ex-ante and ex-post approaches in the objective function. Second, we study the distribution of relief supplies to the shelters as part of humanitarian relief logistics in response to a natural disaster. We consider the problem of planning vehicle routes between a depot and shelters as well as assigning relief supply delivery amounts to the shelters. We assume the prepositioned relief supply amount will not be sufficient enough to meet all shelters' demands. We define two objectives for the problem: minimization of the total time of relief item distribution and the Gini index related inequity measure on the unsatisfied demand percentages among the shelters. We develop a mathematical formulations for the problem based on the VRP formulation in the literature. We adopt the epsilon-constraint approach to handle our multi-objective problem. We solve the linear relaxation of the problem with column generation, which ensures a good quality lower bound. Moreover, a branch-and-price (B&P) algorithm is proposed to solve the problem efficiently to optimality. Our computational results show the superior performance of the B&P algorithm to solving the alternative models with commercial solvers. Finally, we execute the B&P algorithm on real data of Istanbul and provide some insights to be considered by the decision makers.