An effective heuristic for multistage linear programming with a stochastic right-hand side

2014 ◽  
Vol 51 ◽  
pp. 237-250 ◽  
Author(s):  
C. Beltran-Royo ◽  
L.F. Escudero ◽  
J.F. Monge ◽  
R.E. Rodriguez-Ravines
Keyword(s):  
Linear Programming ◽  
Right Hand ◽  
Multistage Linear Programming

A method for solving linear programming with interval-valued trapezoidal fuzzy variables

2018 ◽  
Vol 52 (3) ◽  
pp. 955-979 ◽  
Author(s):  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Auxiliary Problem ◽  
Coefficient Matrix ◽  
Uncertain Parameters ◽  
Fuzzy Variables ◽  
Right Hand ◽  
Fuzzy Cost ◽  
The Right ◽  
Interval Valued

An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem. It is demonstrated that study of LP problems with interval-valued trapezoidal fuzzy variables gives rise to the same expected results as those obtained for LP with trapezoidal fuzzy variables.

scholarly journals Linear programming with interval right hand sides

2010 ◽  
Vol 17 (3) ◽  
pp. 397-408 ◽  
Author(s):  
Virginie Gabrel ◽  
Cécile Murat ◽  
Nabila Remli
Keyword(s):  
Linear Programming ◽  
Right Hand

scholarly journals Postoptimization of the model of water supply for urban and industrial agglomeration

2018 ◽  
Vol 23 ◽  
pp. 00035
Author(s):  
Jacek Wawrzosek ◽  
Szymon Ignaciuk
Keyword(s):  
Linear Programming ◽  
Water Supply ◽  
Programming Models ◽  
Industrial Agglomeration ◽  
Infinitely Many Solutions ◽  
Nodal Solutions ◽  
Parametric Linear Programming ◽  
Right Hand ◽  
The Right

A case study of the tools used by an analyst of the economic aspects of the operation of the water supply network has been undertaken in this paper. All issues discussed here are formulated by using degenerated linear programming models ( PL ). Below, it is noted that the linear dependence of binding constraints ( CO ) distorts standard postoptimization procedures in PL. This observed fact makes postoptimization analysis mostly unhelpful for an average analyst due to problems with the int erpretation of ambiguous sensitivity reports which are obtained from popular computer packages. In standard postoptimization methods, changes to single parameters of the right-hand vector CO are analyzed or referred to parametric linear programming that unfortunately requires prior knowledge of mathematically and economically justified vectors of changes of right-hand sides CO. Therefore, it is suggested that modifications are introduced to some of the postoptimization procedures in this work. For issues in the field of hydrology, the following were presented: interpretation and methods of generating justified vectors of changes of right-hand sides of limiting conditions. And so, the procedure of generating infinitely many solutions of the dual issue based on certain vectors orthogonal to the vector of right-hand sides of constraint conditions was demonstrated. Furthermore, the same orthogonal vectors were used to obtain nodal solutions of the dua0l model and the corresponding vectors of changes of the entire right-hand sides of the constraint conditions. Then, managerial interpretation was applied to this way of proceeding. The methods presented in the work serve to improve the functioning of the system of water supply.

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