Two-stage network design in humanitarian logistics.

Natural disasters such as floods and earthquakes can cause multiple deaths, injuries, and severe damage to properties. In order to minimize the impact of such disasters, emergency response plans should be developed well in advance of such events. Moreover, because different organizations such as non-governmental organizations (NGOs), governments, and militaries are involved in emergency response, the development of a coordination scheme is necessary to efficiently organize all the activities and minimize the impact of disasters. The logistics network design component of emergency management includes determining where to store emergency relief materials, the corresponding quantities and distribution to the affected areas in a cost effective and timely manner. In a two-echelon humanitarian relief chain, relief materials are pre-positioned first in regional rescue centers (RRCs), supply sources, or they are donated to centers. These materials are then shipped to local rescue centers (LRCs) that distribute these materials locally. Finally, different relief materials will be delivered to demand points (also called affected areas or AAs). Before the occurrence of a disaster, exact data pertaining to the origin of demand, amount of demand at these points, availability of routes, availability of LRCs, percentage of usable pre-positioned material, and others are not available. Hence, in order to make a location-allocation model for pre-positioning relief material, we can estimate data based on prior events and consequently develop a stochastic model. The outputs of this model are the location and the amount of pre-positioned material at each RRC as well as the distribution of relief materials through LRCs to demand points. Once the disaster occurs, actual values of the parameters we seek (e.g., demand) will be available. Also, other supply sources such as donation centers and vendors can be taken into account. Hence, using updated data, a new location-allocation plan should be developed and used. It should be mentioned that in the aftermath of the disaster, new parameters such as reliability of routes, ransack probability of routes and priority of singular demand points will be accessible. Therefore, the related model will have multiple objectives. In this dissertation, we first develop a comprehensive pre-positioning model that minimizes the total cost while considering a time limit for deliveries. The model incorporates shortage, transportation, and holding costs. It also considers limited capacities for each RRC and LRC. Moreover, it has the availability of direct shipments (i.e., shipments can be done from RRCs directly to AAs) and also has service quality. Because this model is in the class of two-stage stochastic facility location problems, it is NP-hard and should be solved heuristically. In order to solve this model, we propose using Lagrangian Heuristic that is based on Lagrangian Relaxation. Results from the first model are amounts and locations of pre-positioned relief materials as well as their allocation plan for each possible scenario. This information is then used as a part of the input for the second model, where the facility location problem will be formulated using real data. In fact, with pre-positioned items in hand, other supplies sources can be considered as necessary. The resulting multi-objective problem is formulated based on a widely used method called lexicography goal programming. The real-time facility location model of this dissertation is multi-product. It also considers the location problem for LRCs using real-time data. Moreover, it considers the minimization of the total cost as one of the objectives in the model and it has the availability of direct shipments. This model is also NP-hard and is solved using the Lagrangian Heuristic. One of the contributions of this dissertation is the development of Lagrangian Heuristic method for solving the pre-positioning and the real- time models. Based on the results of Lagrangian Heuristic for the pre-positioning model, almost all the deviations from optimal values are below 5%, which shows that the Heuristics works acceptably for the problem. Also, the execution times are no more than 780 seconds for the largest test instances. Moreover, for the real-time model, though not directly comparable, the solutions are fairly close to optimal and the execution time for the largest test instance is below 660 seconds. Hence, the efficiency of the heuristic for real-time model is satisfactory