Two-stage stochastic programming problems involving interval discrete random variables

In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the r...

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Vydáno v:	Opsearch Ročník 49; číslo 3; s. 280 - 298
Hlavní autoři:	Barik, Suresh Kumar, Biswal, Mahendra Prasad, Chakravarty, Debashish
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	India Springer-Verlag 01.09.2012 Springer Nature B.V
Témata:	Business and Management Decision making Expected values Integer programming Intervals Linear programming Long term planning Management Mathematical models Mathematical problems Mathematics Mining engineering Operations research Operations Research/Decision Theory Optimization Probability distribution Programming Random variables Randomness Stochasticity Studies Theoretical Article Waste management Water resources Interval discrete random variables Interval linear programming Two-stage stochastic programming Stochastic programming
ISSN:	0030-3887, 0975-0320
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Abstract	In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the randomness and discrete intervals are simultaneously considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are studied in two-stage stochastic programming. To solve the stated problem, first we remove the randomness from the problem and formulate an equivalent deterministic linear programming model with interval coefficients. Then the deterministic model is solved using the solution procedure of linear programming with interval coefficients. We obtain the upper bound and lower bound of the objective function as the best and the worst value respectively. It highlights the possible risk involved in the decision making process. A numerical example is presented to demonstrate the usefulness of the proposed methodology.
AbstractList	In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the randomness and discrete intervals are simultaneously considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are studied in two-stage stochastic programming. To solve the stated problem, first we remove the randomness from the problem and formulate an equivalent deterministic linear programming model with interval coefficients. Then the deterministic model is solved using the solution procedure of linear programming with interval coefficients. We obtain the upper bound and lower bound of the objective function as the best and the worst value respectively. It highlights the possible risk involved in the decision making process. A numerical example is presented to demonstrate the usefulness of the proposed methodology. In this paper, we propose a two-stage stochastic linear programming problem considering some of the left hand side and right hand side of linear constraints parameters as interval discrete random variables with known probability distribution and rest of the parameters are precisely known. Both the randomness and discrete intervals are simultaneously considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are studied in two-stage stochastic programming. To solve the stated problem, first we remove the randomness from the problem and formulate an equivalent deterministic linear programming model with interval coefficients. Then the deterministic model is solved using the solution procedure of linear programming with interval coefficients. We obtain the upper bound and lower bound of the objective function as the best and the worst value respectively. It highlights the possible risk involved in the decision making process. A numerical example is presented to demonstrate the usefulness of the proposed methodology. [PUBLICATION ABSTRACT]
Author	Barik, Suresh Kumar Biswal, Mahendra Prasad Chakravarty, Debashish
Author_xml	– sequence: 1 givenname: Suresh Kumar surname: Barik fullname: Barik, Suresh Kumar organization: Department of Mathematics, Indian Institute of Technology – sequence: 2 givenname: Mahendra Prasad surname: Biswal fullname: Biswal, Mahendra Prasad email: mpbiswal@maths.iitkgp.ernet.in, mpbiswal@gmail.com organization: Department of Mathematics, Indian Institute of Technology – sequence: 3 givenname: Debashish surname: Chakravarty fullname: Chakravarty, Debashish organization: Department of Mining Engineering, Indian Institute of Technology
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Cites_doi	10.1016/j.jenvman.2005.10.007 10.1016/0165-0114(94)90097-3 10.1016/j.resconrec.2009.09.011 10.1287/mnsc.1.3-4.197 10.1007/s11269-007-9186-8 10.1016/j.compchemeng.2003.09.017 10.1089/ees.2009.0212 10.1137/0115113 10.1111/j.2517-6161.1955.tb00191.x 10.1109/FSKD.2008.465 10.1057/palgrave.jors.2600891
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SubjectTerms	Business and Management Decision making Expected values Integer programming Intervals Linear programming Long term planning Management Mathematical models Mathematical problems Mathematics Mining engineering Operations research Operations Research/Decision Theory Optimization Probability distribution Programming Random variables Randomness Stochasticity Studies Theoretical Article Waste management Water resources
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Title	Two-stage stochastic programming problems involving interval discrete random variables
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