Suresh Barik | IIT Kharagpur (original) (raw)

Papers by Suresh Barik

Research paper thumbnail of Possibilistic Linear Programming Problems involving Normal Random Variables

International Journal of Fuzzy System Applications, 2016

A new solution procedure of possibilistic linear programming problem is developed involving the r... more 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.

Research paper thumbnail of Stochastic programming problems involving Pareto distribution

Journal of Interdisciplinary Mathematics, 2011

ABSTRACT Stochastic programming is a branch of mathematical programming that considers optimizati... more ABSTRACT Stochastic programming is a branch of mathematical programming that considers optimization in the presence of uncertainty. In this paper, both single-objective and multi-objective stochastic programming problems are considered, where the right hand side parameters follow Pareto distribution with known mean and variance. Both the stochastic programming methods namely, chance constrained programming and two-stage stochastic programming are used. In order to solve these stochastic programming problems; we convert these problems into some equivalent deterministic models. Then we use standard mathematical programming techniques for solving single-objective deterministic model. We use fuzzy programming technique to solve the multi-objective deterministic model. The solution procedures are illustrated with an example.

Research paper thumbnail of Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

Advances in Operations Research, 2012

Most of the real-life decision-making problems have more than one conflicting and incommensurable... more Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highl...

Research paper thumbnail of Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters

Advances in Operations Research, 2012

We present a solution procedure for a quadratic programming problem with some probabilistic const... more We present a solution procedure for a quadratic programming problem with some probabilistic constraints where the model parameters are either triangular fuzzy number or trapezoidal fuzzy number. Randomness and fuzziness are present in some real-life situations, so it makes perfect sense to address decision making problem by using some specified random variables and fuzzy numbers. In the present paper, randomness is characterized by Weibull random variables and fuzziness is characterized by triangular and trapezoidal fuzzy number. A defuzzification method has been introduced for finding the crisp values of the fuzzy numbers using the proportional probability density function associated with the membership functions of these fuzzy numbers. An equivalent deterministic crisp model has been established in order to solve the proposed model. Finally, a numerical example is presented to illustrate the solution procedure.

Research paper thumbnail of Two-stage stochastic programming problems involving interval discrete random variables

OPSEARCH, 2012

In this paper, we proposed a solution procedure of a two-stage stochastic programming problem whe... more In this paper, we proposed a solution procedure of a two-stage stochastic programming problem where the right hand side parameters follow either uniform or exponential or normal or log-normal distribution with known mean and variance. To establish the solution of the stated problem, we first convert the problem into an equivalent deterministic model. Then a standard linear/non-linear programming technique is applied to solve the transformed deterministic model. Illustrative numerical examples are provided to demonstrate the solution procedure of the developed methodology.

Research paper thumbnail of Possibilistic Linear Programming Problems involving Normal Random Variables

International Journal of Fuzzy System Applications, 2016

A new solution procedure of possibilistic linear programming problem is developed involving the r... more 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.

Research paper thumbnail of Stochastic programming problems involving Pareto distribution

Journal of Interdisciplinary Mathematics, 2011

ABSTRACT Stochastic programming is a branch of mathematical programming that considers optimizati... more ABSTRACT Stochastic programming is a branch of mathematical programming that considers optimization in the presence of uncertainty. In this paper, both single-objective and multi-objective stochastic programming problems are considered, where the right hand side parameters follow Pareto distribution with known mean and variance. Both the stochastic programming methods namely, chance constrained programming and two-stage stochastic programming are used. In order to solve these stochastic programming problems; we convert these problems into some equivalent deterministic models. Then we use standard mathematical programming techniques for solving single-objective deterministic model. We use fuzzy programming technique to solve the multi-objective deterministic model. The solution procedures are illustrated with an example.

Research paper thumbnail of Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

Advances in Operations Research, 2012

Most of the real-life decision-making problems have more than one conflicting and incommensurable... more Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highl...

Research paper thumbnail of Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters

Advances in Operations Research, 2012

We present a solution procedure for a quadratic programming problem with some probabilistic const... more We present a solution procedure for a quadratic programming problem with some probabilistic constraints where the model parameters are either triangular fuzzy number or trapezoidal fuzzy number. Randomness and fuzziness are present in some real-life situations, so it makes perfect sense to address decision making problem by using some specified random variables and fuzzy numbers. In the present paper, randomness is characterized by Weibull random variables and fuzziness is characterized by triangular and trapezoidal fuzzy number. A defuzzification method has been introduced for finding the crisp values of the fuzzy numbers using the proportional probability density function associated with the membership functions of these fuzzy numbers. An equivalent deterministic crisp model has been established in order to solve the proposed model. Finally, a numerical example is presented to illustrate the solution procedure.

Research paper thumbnail of Two-stage stochastic programming problems involving interval discrete random variables

OPSEARCH, 2012

In this paper, we proposed a solution procedure of a two-stage stochastic programming problem whe... more In this paper, we proposed a solution procedure of a two-stage stochastic programming problem where the right hand side parameters follow either uniform or exponential or normal or log-normal distribution with known mean and variance. To establish the solution of the stated problem, we first convert the problem into an equivalent deterministic model. Then a standard linear/non-linear programming technique is applied to solve the transformed deterministic model. Illustrative numerical examples are provided to demonstrate the solution procedure of the developed methodology.