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Assigning output variables to equations using linear programming
Author(s) -
Gupta Prem K.,
Westerberg Arthur W.,
Hendry John E.,
Hughes Richard R.
Publication year - 1974
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690200231
Subject(s) - library science , engine department , computer science , operations research , mathematics , engineering , mechanical engineering
Several papers have occurred in the literature on the subject of assigning output variables to equations in the course of deriving a solution procedure for the equations. Such an assignment is called an output set assignment. Steward (1962) showed that if an output set assignment fails to exist, the equations are singular, that is, redundant or inconsistent. Given an output set assignment, effective algorithms exist to precedence order the equations (Harary, 1960; Steward, 1962; Sargent and Westerberg, 1964) and to locate minimum tear orderings within the irreducible groups found in the precedence order (Barkley and Motard, 1972). For nonsquare equation sets (that is, n equations in m variables, rn > n) , algorithms exist to find the output assignment which minimizes the number of tear variables resulting (Lee, Christensen, and Rudd, 1966) or to avoid singular equation sets being left for subsequent solution (Edie and Westerberg, 1971). The subject has directly or indirectly therefore received considerable attention. The purpose of this note is to point out that the assigning of an output set for several criteria can be formulated as an Assignment Problem or a Bottleneck Problem in linear programming and thus solved by existing, very powerful algorithms for those problems.