In the aftermath of a disaster, a part of the population of the affected region are forced to move out of their homes that have been damaged during the onset of the disaster and to head to shelters provided by the relief agencies. Evacuees usually go the nearest shelter they could find without the knowledge of the available sheltering capacities at those shelters. This type of behavior could result in some shelters being overflown with evacuees while other shelters possess an unused capacity. Furthermore, those shelters are usually pre-stocked with supplies in anticipation of a disaster but there is no guarantee that there would be a perfect match between the number of evacuees that head to a shelter and the amount of supplies that are present there (i.e. having too many evacuees and low levels of supplies or vice versa). This dissertation introduces a strategy for alleviating the effects of overcrowding in shelters and of the mismatch between number of evacuees and amount of supplies in shelters in the aftermath of a disaster through the new concept of Relief Supplies and Evacuees Redistribution. This concept, to the extent of our knowledge, has not been addressed in the literature for disaster operations management. The Relief Supplies and Evacuees Redistribution problem consists of managing a fleet of vehicles to redistribute relief supplies and evacuees among shelters in the aftermath of a disaster in order to minimize shelter overcrowding and the impact of supply mismatches experienced by evacuees during the period they have to spend in shelters.
A mathematical formulation of the Relief Supplies and Evacuees Redistribution problem is presented in the form of a Mixed Integer Linear Programming model which was used to solve small instances of the problem using commercial solvers. The results of these runs were used to analyze the effect of the new concept of allowing evacuees redistribution and investigate its value. The results of those tests confirmed the benefit of introducing the concept of evacuees redistribution and its potential in reducing overcrowding and shortages of relief supplies in shelters. Solving larger instances of the problem was achieved through the development of a problem specific solution procedure built upon the framework of Branch and Price methodology. The solution procedure developed was successful in solving instances of practical size to optimality and it was demonstrated that this approach for solving the problem has the potential to provide efficient solutions to even larger instances of the problem. The solution algorithm developed for the problem through the Branch and Price framework was expanded and used to solve even larger instances of the problem which considered multiple modes of transportation (i.e. boats and helicopters) in moving relief supplies and evacuees between shelters.