Contour line construction for a new rectangular facility in an existing layout with rectangular departments

In a recent paper, Savas, Batta and Nagi (Operations Research, Nov.-Dec. 2002) consider the optimal placement of a finite size facility in the presence of arbitrarily shaped barriers under rectilinear travel. Their model applies to a layout context, since barriers can be thought to be existing departments and the finite size department can be viewed as the new department to be placed. In a layout situation, the existing and new departments are typically rectangular in shape. This is a special case of the Savas et al. paper. However the resultant optimal placement may be infeasible due to practical constraints like aisle locations, electrical connections, etc. Hence there is a need for the development of contour lines, i.e. lines of equal objective function value. With these contour lines constructed, one can place the new facility in the best manner. This paper deals with the problem of constructing contour lines in this context. A comparison is made to the well-studied infinitesimal facility size case via an example.