Imprecise weights in Weber facility location problem

This paper presents a method for locating multiple facilities on a plane bounded by a convex polygon under the criterion minimize the sum of all the transportation cost, where the cost per unit distances are known imprecisely. Assuming some (fuzzy) aspiration levels for each of the goals and basing these on a comparison of (flat) fuzzy numbers, the original fuzzy problem is transferred into a crisp satisfactory model. To determine a suitable solution the authors will maximize the minimum of the surpluses over the aspiration levels. Rectilinear distance norm has been taken as the scenario and may be considered as in an urban setting. This induces the problem with a non-linear objective function, which is equivalent to a linear program. A numerical example has been given to illustrate the solution procedure.