Transformation of a multi-choice linear programming problem

Biswal, M. P.; Acharya, Srikumar

doi:10.1016/j.amc.2008.12.080

Cited by 36 publications

(35 citation statements)

References 4 publications

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“…The technique in this paper transforms the right hand side of each constraint to a linear combination with the same number of terms which enable us to treat the problem as a usual linear programming problem. Indeed, using different softwares we found that our technique gives the same results as [8] [9].…”

Section: Discussionsupporting

confidence: 53%

“…In Section 4, we offer a numerical example to show the procedure of our technique. We conclude the paper by a brief discussion to compare our result with other results given by Biswal and Acharya [8] [9]. We end the paper by some helpful references.…”

Section: Introductionmentioning

confidence: 78%

“…Biswal and Acharya [8] treat the problem of multi-choice linear programming problem by replacing the right hand side of each constraint with a specific mathematical expressions involving the multi-choice values multiplied by polynomials of binary variables, those expressions change from one constraint to another according to the number of multi-choice values in that constraint. Moreover, some restrictions are imposed on the binary variable to obtain just one value in the right hand side of each constraint.…”

Section: Discussionmentioning

confidence: 99%

“…The all binary variables are zeros except 6 z take the value one which means that the choice of the goals of first, second and third constraints are 1100 gal, 1450 gal and 400 hours respectively. One can follow the techniques in [8] [9] to obtain the same solution.…”

Section: Illustrative Numerical Examplementioning

confidence: 99%

“…The number of binary variables required for a constraint is same as the total number of choices for that constraint. Biswal and Acharya [8] gave new approach for treating the multi-choice linear programming problem. they used multiplicative terms of binary variables.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Solution of Multi-Choice Mathematical Programming Problem Using a New Technique

Khalil¹,

Raghav²,

Badra³

2016

AJOR

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The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.

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Section: Discussionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Section: Illustrative Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Solution of Multi-Choice Mathematical Programming Problem Using a New Technique

Khalil¹,

Raghav²,

Badra³

2016

AJOR

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Multi-level Nonlinear Programming Problem with Some Multi-choice Parameter

Pradhan

Biswal

2014

Mathematics and Computing 2013

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Decentralized planning is important for modeling a real-life decision-making problem. Multi-level programming is a very powerful tool for modeling such type of decentralized planning problems. In a multi-level programming problem, the decision is taken by several decision makers who are in different levels. In this paper, we studied a multi-level nonlinear programming problem where some (or all) of the coefficients of the objectives and the constraints are multi-choice type. We propose a suitable solution procedure to solve the stated multi-level programming problem. To solve these type of problems, first we tackle each multi-choice parameter of the multi-level programming problem by using interpolating polynomial and obtain a multi-level mixed integer nonlinear programming problem. Then we use the concept of tolerance membership function for the objectives and the control variables of the decision makers and formulate a fuzzy max-min type decision model to obtain a Pareto optimal solution of the transformed multi-level programming problem. We present a numerical example to illustrate the solution procedure of the stated problem.

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