Integer programming approaches tofacilities layout models with forbidden areas

Abstract

The facilities layout problem is concerned with a given number of facilities of somesystem which are to be laid out in a plane region such as a factory floor or a flat buildingsite. The problem has applications, beyond manufacturing, in the design of various types ofgovernment 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 whichshows the relative positions of the facilities to be laid out in order to optimise some measureof the performance of the system. We assume that the region P, in which the facilities are tobe laid out, is a rectangle of integer dimensions and that each of the facilities to be laid outin it is to be a connected subregion of given area, of arbitrary shape, whose boundaries areparallel to the perimeter of P. In many practical layout scenarios, there are regions in whichit is forbidden to locate facilities. This sometimes occurs when a factory is to be redesignedand certain existing facilities are to remain where they are. In other scenarios, the forbiddenregions 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 layoutproblem with forbidden areas. As a result, we believe that the approaches described representa useful addition to the facilities planner's toolkit.