Bicriteria location of a semi-obnoxious facility

The problem of locating a new semi-obnoxious facility in an existing layout is considered. The facility interacts with the existing facilities, so that on one hand, it is desired to be placed close to them in order to minimize total transportation cost, but on the other hand it is not desired to be placed too close to them because it has certain undesirable effects. For this problem, a maximin-minisum bicriteria location model with rectilinear distances is developed. The resulting nonconvex bicriteria problem is decomposed into a series of linear bicriteria problems which are solved by an adaptation of the Fourier–Motzkin Elimination Method. An algorithm that constructs the entire nondominated and efficient sets is presented and it is illustrated in an example problem.