ISSN:
1573-2878
Keywords:
Multiobjective optimization
;
efficiency
;
facilities design
;
design problems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 functionf isuch thatH i(S), the integral off iover the setS (for example, total travel distance), defines the disutility of the designS to useri. For the vectorH(S) with entriesH i(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 wheref iis thel p-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 λ=λ1 f 1+⋯+λ m f m ,when the λ i are nonnegative constants, not all zero.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934720
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