Possibilistic Linear Programming Problems involving Normal Random Variables

Possibilistic Linear Programming Problems involving Normal Random Variables

Suresh Kumar Barik (Department of Mathematics, KIIT University, Bhubaneswar, India) and M. P. Biswal (Department of Mathematics, IIT Kharagpur, Kharagpur, India)
Copyright: © 2016 |Pages: 13
DOI: 10.4018/IJFSA.2016070101

Abstract

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.
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2. Mathematical Programming Model

The proposed mathematical programming model can be stated as:

IJFSA.2016070101.m01
(1) Subject to
IJFSA.2016070101.m02
(2)
IJFSA.2016070101.m03
(3) where, the decision variables IJFSA.2016070101.m04 and IJFSA.2016070101.m05 are assumed to be deterministic. IJFSA.2016070101.m06 are specified probability levels. Also, it is assumed that IJFSA.2016070101.m07 are imprecise with triangular possibility distributions as shown in Figure 1 and IJFSA.2016070101.m08 are normal random variables. IJFSA.2016070101.m09 is the most possible value (possibility = 1 if normalized), IJFSA.2016070101.m10 (the most pessimistic value), and IJFSA.2016070101.m11 (the most optimistic value) are the least possible values.

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