Modeling and Optimization of Supply Chain Operations during Emergency Response

The global increase in the number of natural or man made disasters highlights the need for a better planning and operation of the responding agencies. In case of these emergencies various organizations 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 numerous 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 and minimize the cost of such operations. Current research offers a mathematical model that describes the FEMA's supply chain operations in response to natural disasters. The model is able to find the optimal location for temporary facilities and fully consider the flow of relief commodities from sources to the recipients. The model also considers optimal vehicle routings for each vehicle in each transportation mode for the duration of the operations as well as detailed pick-up and drop-off itinerary for each vehicle. The proposed model is tested for numerical case studies which showed the model's ability to help decision makers during the large emergency relief operations. Also, this research introduces a set of solution techniques and heuristic algorithms to solve the MIP problem for large cases in short times. It is shown in the analysis of numerical results that for large scale problems, commercial solvers are not able to find the optimal solution for proposed model or the running time is so long that it is not practical for disaster response management at the operational level. Two main approaches are followed to develop heuristic solution techniques. First, the model is decomposed into a number of smaller/easier problems and then the results are aggregated. The decomposition can be spatial or temporal or both. In the second approach, the idea is to develop heuristics that find near optimal solutions for the entire model in a short time. Various relaxation techniques are used for this type of heuristics. At the end, the results of the two approaches are compared to each other for different numerical cases. This research offers a tight lower bound for the MIP problem, in order to evaluate the quality of solutions provided by the heuristic algorithms. It is very important to have a relatively close bound because for the large numerical problems, a theoretical bound is the only benchmark to compare the quality of different heuristics. The proposed lower bound provides the opportunity to try more ambitious heuristics that can potentially be very rewarding. In addition, a set of real-world-size case studies and simulation experiments are constructed to analyze the model behavior in the large scale disaster response operations. The disaster relief operations can happen in large and disperse geographical areas which requires management tools capable of handling the large scale operations. The dynamic environment after the disaster strike will be best replicated through a set of well-designed simulation experiments that covers a wide range of possible scenarios and test the model's ability to react to variations of data over time. Finally, in this research major sensitivity analysis is performed on both the model structure and the solution algorithms. The proposed model includes several parameters and variables that can affect the quality of solution as well as the solution time. A major sensitivity analysis on all of the related parameters is essential in order to thoroughly investigate the properties of the model and solution algorithms.