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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Bibliographic Details
Published in:Opsearch Vol. 49; no. 3; pp. 280 - 298
Main Authors: Barik, Suresh Kumar, Biswal, Mahendra Prasad, Chakravarty, Debashish
Format: Journal Article
Language:English
Published: India Springer-Verlag 01.09.2012
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0030-3887
0975-0320
DOI:10.1007/s12597-012-0078-1