A MATHEMATICAL FRAMEWORK FOR OPTIMIZING DISASTER RELIEF LOGISTICS
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In today's society that disasters seem to be striking all corners of the globe, the importance of emergency management is undeniable. Much human loss and unnecessary destruction of infrastructure can be avoided with better planning and foresight. When a disaster strikes, various aid organizations often face significant problems of transporting large amounts of many different commodities including food, clothing, medicine, medical supplies, machinery, and personnel from several points of origin to a number of destinations in the disaster areas. The transportation of supplies and relief personnel must be done quickly and efficiently to maximize the survival rate of the affected population.
The goal of this research is to develop a comprehensive model that describes the integrated logistics operations in response to natural disasters at the operational level. The proposed mathematical model integrates three main components. First, it controls the flow of several relief commodities from sources through the supply chain until they are delivered to the hands of recipients. Second, it considers a large-scale unconventional vehicle routing problem with mixed pickup and delivery schedules for multiple transportation modes. And third, following FEMA's complex logistics structure, a special facility location problem is considered that involves four layers of temporary facilities at the federal and state levels. Such integrated model provides the opportunity for a centralized operation plan that can effectively eliminate delays and assign the limited resources in a way that is optimal for the entire system.
The proposed model is a large-scale mixed integer program. To solve the model, two sets of heuristic algorithms are proposed. For solving the multi-echelon facility location problem, four heuristic approaches are proposed. Also four heuristic algorithms are proposed to solve the general integer vehicle routing problem. Overall, the proposed heuristics could efficiently find optimal or near optimal solution in minutes of CPU time where solving the same problems with a commercial solver needed hours of computation time.
Numerical case studies and extensive sensitivity analysis are conducted to evaluate the properties of the model and solution algorithms. The numerical analysis indicated the capabilities of the model to handle large-scale relief operations with adequate details. Solution algorithms were tested for several random generated cases and showed robustness in solution quality as well as computation time.