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3.1. Formulation and Applications An economic problem of great practical importance is to choose the location of facilities, such as industrial plants or warehouses, in order to minimize the cost (or maximize the profit) of satisfying the demand for some commodity. In general there are fixed costs for locating the facilities and transportation costs for distributing the commodities between the facilities and the clients. This problem has been extensively studied in the literature and is commonly referred to as the plant location problem, or facility location problem. when each potential facility has a capacity, which is the maximum demand that it can supply, the problem is called the capacitated facility location problem. when the capacity hypothesis is not needed, we have the simple or uncapacitated facility location problem, or, for short, the UFL Problem.

The mathematical formulation of these problems as integer programs has …