Note—On the Complexity of Facilities Layout Problems

Abstract

Please scroll down for article-it is on subsequent pages With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

On the use of flow dominance in complexity measures for facility layout problems

“…The flow-cost they refer to, however, is not necessarily syn~etr In other words, Block (!977, 1979) and Aneke and Carrie ( 1983) use the flow definition Eqs. Block (1979) has recently formalized the observations already made by Vollmann and Buffa ( 1966)…”

“…Vollmann and Buffa (1966) conducted a computational experiment on four example layout problems which, in comb th the reported flow dominance values, paved the way for many confusing and utmost conflicting papers, replies and rejoinders on the potential use of flow dominance and some derived complexity measures to determine the choice between computer algorithms and visual based layout methods (Block ( 1977(Block ( , 1979. Buffa' (1976b), Coleman (1977Coleman ( ), S and (1975Coleman ( , 1976Coleman ( , 1981, Trybus and Hopkins (1980)).…”

“…The inclusion of cost is also implici suggested by Block (1977Block ( ,1979 who defines f as the " tmental cost between departments i and j" in Block (1977) and as "the cost re between the ith and jth facili Block (1979). J.…”

“…Flow dominance was defined as the coefficient of variation of the flow data, computed from the flow matrix elements as (100 :x standard deviation/mean). The conclusion sugwhich its a coefficient of variation, gested was that a flow the flow on or by us one of the so-called sible use of flow dominance in comp ty ratings to determine the choice between computer algorithms and visual based plant layout methods (Block (1977(Block ( , 1979, Buffa (1976), Coleman (1977), Gupta and Deisenroth (1981), Lewis and Block (1980), Scriabin and Vergin (1981), Trybus and Hopkins (1980)), to determine the extent to which flow dominance and other complexity measures can affect the computational time of a branchand-bound algorithm for the quadra~ic assignment problem (Mojena, Vollmann…”

“…In particular the shortcomings of the complexity rating factor suggested by Block (1979) are critically examined, Due to these shortcomings, it would be infeasible to use the complexity measure for its intended purpose, which is to de visual based methods for the choice between computer algorithms and ant layout. We conclude that section with a discussion of the idiosyncracies of the line dominance concept, suggested by Scriabin and Vergin (1981) in order to overcome the drawbacks of Block's complexity rating.…”