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A SIMPLIFICATION AND GENERALIZATION OF THE EXCLUSION THEOREM: A TECHNICAL NOTE
Author(s) -
Martinich Joseph S.,
Hurter Arthur P.
Publication year - 1990
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/j.1467-9787.1990.tb00109.x
Subject(s) - trigonometry , generalization , mathematical proof , regular polygon , triangle inequality , mathematics , algebraic number , polygon (computer graphics) , space (punctuation) , production (economics) , facility location problem , algebra over a field , mathematical economics , combinatorics , mathematical optimization , computer science , pure mathematics , geometry , mathematical analysis , economics , telecommunications , frame (networking) , macroeconomics , operating system
Several researchers have proven that for the integrated production‐location problem on the Weberian triangle, intermediate points on the edge of the triangle can never be optimal locations. Authors of previous proofs of this result have used cumbersome trigonometric arguments. We present a much simpler algebraic proof of the result, and present it in terms of the more general n ‐input model, where the feasible location space is a convex polygon rather than a triangle. In addition, the result generalizes immediately to other cases, such as (1) multifacility production‐location problems, (2) stochastic versions of one‐facility and multifacility production‐location problems, and (3) comparable pure location problems (e.g., the Weber problem).