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. Optimization problems addressing operational aspects should aim at providing equitable services to victims in order to make the suggested solutions acceptable. In the Operations Research literature, equity has been addressed in problems such as resource allocation, facility location, scheduling and transportation in various contexts such as bandwidth allocation in telecommunications; cost/benefit allocation in collaborative logistics; organ, blood, and drug allocation in health care; public facility location. However, in humanitarian operations, models that address inequity-averseness have received relatively less attention. We aim to incorporate both efficiency and equity objectives into disaster preparedness and response operations.
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. A chance constraint is defined on the total cost of opening the shelters and their capacity expansion. 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 run the GA also on real data of the Kartal district in Istanbul to drive insights to guide decision-makers for preparation. 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 formulation for the problem based on the VRP formulation in the literature. 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.
Mahdi Mostajabdaveh is a Postdoctoral fellow at Kühne Logistic University. He received his Ph.D. in Industrial Engineering and Management Science from the College of Engineering at Koç University in Istanbul, Turkey. His M.Sc. and B.Sc. degrees are in Industrial Engineering from Sharif University of Technology, Tehran, Iran. His research interests include humanitarian logistics, facility location, vehicle routing, heuristic algorithms, and packing problems.