On Characterizing Supremum-Efficient Facility Designs.
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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Define a design to be any planar set S of known area A, but unknown shape and location more generally, a design can be any set in R superscript n of measure A. For example, a design might be one floor of a warehouse, or a sports arena of known seating capacity. Suppose the design to have, say, m users, or evaluators, with userevaluator i having a design disutility function f sub i, i or to 1 but or to m, which can be defined for all points in the plane independently of the designs of interest. Given any design S, denote by G sub i S the disutility of S to userevaluator i where, by definition, G sub i S is the supremum of f sub i over the set S, i or to 1 but or to m. Let GS be the vector with entries G sub i S, 1 or i or m, and define a design to be efficient if it solves the vector minimization problem obtained using the set of vectors GSS a design. Given mild assumptions about the disutility functions, and a slight refinement of the design definition to rule out certain pathologies, we give necessary and sufficient conditions for a design to be efficient, and study properties of efficient designs. Author
- Statistics and Probability
- Operations Research