Efficiency in integral facility design problems |
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Authors: | L. G. Chalmet R. L. Francis J. F. Lawrence |
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Affiliation: | (1) Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida;(2) Department of Mathematics, University of Kentucky, Lexington, Kentucky |
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Abstract: | An example of design might be a warehouse floor (represented by a setS) of areaA, with unspecified shape. Givenm warehouse users, we suppose that useri has a known disutility functionfisuch thatHi(S), the integral offiover the setS (for example, total travel distance), defines the disutility of the designS to useri. For the vectorH(S) with entriesHi(S), we study the vector minimization problem over the set {H(S) :S a design} and call a design efficient if and only if it solves this problem. Assuming a mild regularity condition, we give necessary and sufficient conditions for a design to be efficient, as well as verifiable conditions for the regularity condition to hold. For the case wherefiis thelp-distance from warehouse docki, with 1<p<, a design is efficient if and only if it is essentially the same as a contour set of some Steiner-Weber functionf=1f1++mfm,when the i are nonnegative constants, not all zero.This research was supported in part by the Interuniversity College for PhD Studies in Management Sciences (CIM), Brussels, Belgium; by the Army Research Office, Triangle Park, North Carolina; by a National Academy of Sciences-National Research Council Postdoctorate Associateship; and by the Operations Research Division, National Bureau of Standards, Washington, D.C. The authors would like to thank R. E. Wendell for calling Ref. 16 to their attention. |
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Keywords: | Multiobjective optimization efficiency facilities design design problems |
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