On Characterizing Supremum-Efficient Facility Designs.
Abstract
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 user/evaluator 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 user/evaluator 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 G(S) 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 (G(S):S 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1978
- Accession Number
- ADA059040
Entities
People
- James F. Lawrence
- Luc G. Chalmet
- Richard L. Francis
Organizations
- University of Florida