Integer programming approaches to facilities layout models with forbidden areas

The facilities layout problem is concerned with a given number of facilities of some systems which are to be laid out in a plane region such as a factory floor or a flat building site. The problem has applications, beyond manufacturing, in the design of various types of government and other public facilities, as well as of buildings for commercial activities. The aim of the classical facilities layout problem is to produce a plan drawn to scale which shows the relative positions of the facilities to be laid out in order to optimise some measure of the performance of the system, We assume that the region P, in which the facilities are to be laid out, is a rectangle of integer dimensions and that each of the facilities to be laid out in it is to be a connected subregion of given area, or arbitrary shape, whose boundaries are parallel to the perimeter of P. In many practical layout scenarios, there are regions in which it is forbidden to locate facilities. This sometimes occurs when a factory is to be redesigned and certain existing facilities are to remain where they are. In other scenarios, the forbidden regions represent areas which cannot contain any facilities at all, e.g. for security, transport, technical, or other reasons. We devise integer programming models for the facilities layout problem with forbidden areas. As a result, we believe that the approaches described represent a useful addition to the facilities planner’s toolkit.