Journal ArticleDOI
An explicit general solution in linear fractional programming
TLDR
The formulations as well as the proofs and the transformations provided by the general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases.Abstract:
: A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowski lemma and the duality relationships which emerge from the Charnes-Cooper linear programming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by our general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.read more
Citations
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Journal ArticleDOI
Measuring the efficiency of decision making units
TL;DR: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs and methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs.
Journal ArticleDOI
Restricting Weight Flexibility in Data Envelopment Analysis
Y.-H. B. Wong,John E. Beasley +1 more
TL;DR: A method, based on the use of proportions, for restricting weight flexibility in data envelopment analysis when the decision-making units being evaluated have multiple inputs and outputs is presented.
Journal ArticleDOI
A Dea Model For Measuring The Relative Eeficiency Of Highway Maintenance Patrols
TL;DR: A pilot application of Data Envelopment Analysis (DEA) for the measurement of the efficiency of highway maintenance patrols is demonstrated and results are compared to those obtained from a conventional DEA model.
Journal ArticleDOI
Fractional programming: Applications and algorithms
TL;DR: This paper surveys applications as well as solution methods in linear, quadratic and concave-convex fractional programming and tries to determine for each method the kind of fractional programs that are solved by it suitably.
Journal ArticleDOI
On the Use of Ordinal Data in Data Envelopment Analysis
TL;DR: A procedure is presented for incorporating an ordinal factor into the DEA structure, with the resulting formulation being a particular form of cone ratio model, which is then applied to the technology installation efficiency problem.
References
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Journal ArticleDOI
Programming with linear fractional functionals
Journal ArticleDOI
A Linear Programming Approach to the Cutting Stock Problem---Part II
P. C. Gilmore,Ralph E. Gomory +1 more
TL;DR: The paper describes a new and faster knapsack method, experiments, and formulation changes, and the introduction of a rational objective function when customers' orders are not for fixed amounts, but rather for a range of amounts.
Journal ArticleDOI
Programming with linear fractional functionals
TL;DR: In this paper, it was shown that if a finite solution to the problem exists, only one linear programming problem must be solved, and this is because the denominator cannot have two different signs in the feasible region except in ways which are not of practical importance.
Journal ArticleDOI
On sequential decisions and markov chains
TL;DR: In this article, the optimal control of dynamic systems is investigated and it is shown that the optimal rules for controlling the system belong to a subclass of all possible rules and, within this subclass, the optimal rule can be derived by solving linear programming problems.
Journal ArticleDOI
On Some Properties of Programming Problems in Parametric form Pertaining to Fractional Programming
TL;DR: This paper presents results which apply to convex programming problem in parametric form and is extended to general non-linear programming problems with special reference to continuous criterion functions.