Doyen et al. (Döyen 2012) elaborate on necessity of pre- and post-disaster planning in humanitarian logistics for earthquakes. In their study, they consider a two-echelon logistics system, which facilitates the transshipment of the relief items to the demand points. In the top echelon, the relief items are stored in (uncapacitatd) regional rescue centers (RRCs) prior to the incident (e.g., an earthquake). Depending on the severity of the incident, which is realized through a set of probabilistic scenarios, the relief items are transmitted to (capacitated) local rescue centers (LRCs), where they are delivered to the demand points. Accordingly, the authors suggest a two-stage stochastic program for pre-positioning and post-distribution of the relief items. In the first stage, the location of the RRCs and their stock level is determined in pre-disaster phase. In the second stage, the decisions regarding the locations of the LRCs are made and the flows of relief items between echelons are determined. The model seeks minimization of facilities locating costs, inventory holding costs for RRCs, the necessary transportation costs, and the shortage costs. To solve this problem, the authors have developed a Lagrangian relaxation-based heuristics (LH) equipped with local search algorithm. To apply LH, the inter-relating constraints for the echelons are relaxed and lower and upper bounds are computed accordingly. Next, the solution technique performs iterative local search algorithm to improve the quality of the solution.
locating + allocation
Noyan et. al (Noyan 2015) mention the importance of the relief items distribution in the last mile, i.e., where the items are delivered to the affected people. They state that, although a lot of donations and relief items are often collected once any disaster occurs, the challenge is how to deliver the items where it is needed and to the amount that is needed. They focus on the so-called “last mile” relief network, which is depicted as a two-echelon network with the following structure: 1) a local distribution center (LDC), which is a large warehouses storing relief items, and 2) multiple points of distribution (PODs), where the relief items are delivered demand points (i.e., to the affected people). Recognizing the need to design the relief network rather than focusing only on the distribution problems, the authors suggest a mathematical program to determine the locations and capacities of PODs as well as the flow of a single package supply from LDC to PODs and the assignment of demand points to PODs. To help formulating a real-world problem, they incorporate the inherent uncertainty in the demand as well as in the transportation network through post-disaster link capacities. Hence, they formulate the problem as a two-stage stochastic optimization with finite number of scenarios, where the locations and capacities of PODs are determined in the first stage, while the flow of supply from LDC to PODs and the assignment of demand