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Rahman Khorramfar Deleted File
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\section{A multi-objective relief chain location distribution model for urban disaster management}
Barzinpour and Esmaeili \cite{BarzinpourEsmaeili2014} study the mitigation of consequences of natural disasters on affected people. They argue the importance of location/allocation models in humanitarian supply chains that aim to provide quick relief items in the right time and the right place. In particular, they suggest a multi-objective mixed-integer linear program (MILP) solved on a grid representation of the city (using geographic information system (GIS)), which determines the location of distribution centers (DCs) and the assignment of DCs to the demand points. The authors suppose that the demand of each grid is a function of its population and its potential damage severity. To provide the necessary input for their model, they have employed a special-purposed software that assess the seismic vulnerability in cities. In their model, the authors consider various type of costs such as setup costs, holding costs, transportation costs, and shortage costs. They also consider three objective functions: 1) maximization of the cumulative coverage of population, 2) minimization of the total setup costs, and 3) minimization of the total transportation, holding, and shortage costs. To solve the problem, the authors have used the goal-programming approach. In particular, they have used expert judgments for the ideal values of the objective function. Furthermore to be able to tackle problem, the authors have assumed that the district can be divided into ten subregions, where the DC in each subregion will only serve within the subregion. This results in a significant reduction into the model size and allows the usage of standard optimization solvers. In particular, they report the result of their model for the district with 350,000 inhabitants, 10 subregions, and four types of relief products.
