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ABSTRACT
This paper considers a linear programming problem involving random interval coefficients. A new random interval programming model is presented by extending the variance model of stochastic programming. The original problem involving random interval parameters is transformed into a deterministic equivalent problem using the proposed model. A variance model which is based on the concept of distance between intervals is provided for solving the problem. The deterministic equivalent problem which is a quadratic convex programming can be solved by convex techniques. Moreover, a comparison between the results of using different distances is presented. A numerical example is carried out to show the efficiency of the proposed model.
Acknowledgments
The authors are very grateful to the editor and anonymous referees for their suggestions in improving the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Notes on contributors
Ziba Arjmandzadeh
Ziba Arjmandzadeh is a Ph.D. student in operations research at the Faculty of Mathematics, Statistics and Computer Science, Semnan University. She received her M.Sc. degree in Optimal Control from Industrial University of Shahrood in 2012. Her research interests include stochastic programming, semidefinite programming, multiobjective Linear programming.
Mohamad Reza Safi
Mohamad Reza Safi is currently an Assistant Professor of operations research at Faculty of Mathematics, Statistics and Computer Science, Semnan University. His current research interests include Stochastic programming, Semidefinite programming, Multiobjective Linear programming.