Continuous global optimization: Applications; Genetic algorithmsContinuous global optimization: ApplicationsFORECASTING
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10 Fig. 1: A block plan with 11 facilities, including the exterior region, indicated as facility 1.
The identification of effective plans depends upon interfacility relationships, which may be quantitative (e.g. transportation costs) or qualitative (e.g. utility scores, called REL chart scores, based on facility adjacency). Each FL problem involves optimizing one or more objective functions based on the given interfacility relationship. FL is an important application area of optimization. This is partly because increased global competition in manufacturing has spurred renewed efforts to reduce production costs. Efficient physical layout design of manufacturing plants is critical in the quest to achieve and maintain competitive productivity. Indeed, up to 70% of the operating costs of a manufacturing system are related to materials handling and layout. This is because improved layout design often brings about reductions in materials handling, transportation, congestion, and work-in-process. There are applications of FL techniques in areas other than manufacturing plant design. Examples include the design of office blocks and other commercial buildings, hospitals and other public services, and university campuses, government agencies, and sports complexes. As will become evident in the following discussion, most FL models are NP-hard in the strong sense (cf. also C o m p l e x ity t h e o r y ; C o m p l e x i t y classes in o p t i m i z a tion). This has reinforced the search for effective heuristics for them. One of the earliest and best-known FL heuristics is termed CRAFT (coordinate relative allocation of facilities technique) [1]. It requires an initial block plan as input, which it attempts to improve by exchanging the positions of two or three facili-
Facilities layout problems
ties at a time. In contrast to this improved procedure, many other early FL heuristics are construction procedures which build up the final block plan iteratively, by placing facilities sequentially. The serial decision process requires, at each step: i) a selection of which facility is to be placed next in the block plan being constructed, and ii) a decision as to where this facility is going to be placed. Early construction procedures include: CORELLAP [23] and A L D E P [32]. One of the major FL optimization models is based on the quadratic assignment problem (QAP; cf. also Q u a d r a t i c a s s i g n m e n t p r o b l e m ) . For overviews on this subject see [4], [5], [29]. Formulations of various FL problems based on the QAP involve minimizing the total transportation cost between all pairs of facilities. This total cost comprises a sum of components calculated according to the distance and the amount of work flow between each pair of facilities. The constraints of the QAP model are based on the assumption that the block plan is tessellated into a grid of unit squares (called l o c a t i o n s ) and that no two facilities are to be assigned the same location. Many of these models assume that all th
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