One of the main critical steps that should be taken during natural disasters is the assignment and distribution of resources among affected people. In such situations, this can save many lives. Determining the demands for critical items (i.e., the number of injured people) is very important. Accordingly, a number of casualties and injured people have to be known during a disaster. Obtaining an acceptable estimation of the number of casualties adds to the complexity of the problem. In this paper, a location-routing problem is discussed for urgent therapeutic services during disasters. The problem is formulated as a bi-objective Mixed-Integer Linear Programming (MILP) model. The objectives are to concurrently minimize the time of offering relief items to the affected people and minimize the total costs. The costs include those related to locations and transportation means (e.g., ambulances and helicopters) that are used to carry medical personnel and patients. To address the bi-objectiveness and verify the efficiency and applicability of the proposed model, the ε-constraint method is employed to solve several randomly-generated problems with CLEPX solver in GAMS. The obtained results include the objective functions, the number of the required facility, and the trade-offs between objectives. Then, the parameter of demands (i.e., number of casualties), which has the most important role, is examined using a sensitivity analysis and the managerial insights are discussed.
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