 Parametric Objective Function (Part 1)Thomas Saaty and
Saul Gass
Operations Research, 1954, vol. 2, issue 3, 316-319 Abstract: In the linear programming problem where there is a linear function to be optimized (called the objective function), it is desirable to study the behaviour of solutions when the (cost) coefficients in the objective function are parametrized. The problem is then to find the set of x j ( j = 1, 2, ..., n ) which minimizes the linear form (sum)( c j + (lambda) c j ') x j and satisfy the constraints x j (ge) 0 and (sum) a ıj x j = a ı 0 ( i = 1, 2, ..., m ) where c j , c j ', a ıj , and a ı 0 are constants, with at least one c j (ne) 0, and (lambda) a parameter. Using the simplex method, a computational procedure is described which enables one, given a feasible solution, to determine the values of the parameter (if any) for which the solution minimizes the objective function; and given a minimum feasible solution how one can generate by the simplex algorithm all minimum feasible solutions and the corresponding values of the parameter. To a minimum solution there corresponds one interval of values of (lambda) (nondegeneracy assumed). The process indicates how to obtain a new solution and the corresponding interval of values of (lambda) which is contiguous to the previous one both having only one point in common. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984. Date: 1954 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:2:y:1954:i:3:p:316-319 Access Statistics for this article More articles in Operations Research from INFORMS Contact information at EDIRC. |
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