A New Method for Solving the Fully Interval Bilevel Linear Programming Problem with Equal Constraints

Subject Areas : Statistics

seyyedeh farkhondeh tayebnasab ¹ , farhad hamidi ² , mehdi allahdadi ³

1 - Mathematics Department, Mathematics, University of Sistan and Baluchestan, Zahedan , Iran
2 - Mathematics Department, Mathematics, University of Sistan and Baluchestan, Zahedan , Iran
3 - Department of Mathematics, Sistan and Baluchestan University, Sistan and Baloochestan

Received: 2018-03-11 Accepted : 2018-07-11 Published : 2018-08-01

Keywords: ضرایب بازه‌ای, برنامه‌ریزی خطی دو ترازه, بهترین و بدترین مقدار بهینه,

Abstract :

Most research on bilevel linear programming problem is focused on its deterministic form, in which the coefficients and decision variables in the objective functions and constraints are assumed to be crisp. In fact, due to inaccurate information, it is difficult to know exactly values of coefficients that used to construct a bilevel model. The interval set theory is suitable for describing and solving uncertainty and inaccuracy in these decision-making issues. For this reason, interval bilevel linear programming problem, in which the coefficients in both objective functions and constraints are interval, is an attractive subject. In this paper, we consider a type of interval bilevel linear programming problem full , in which all the coefficients in both objective functions and constraints are interval. The purpose of this paper is to present a new method for solving fully interval bilevel linear programming problem with equality constraints. By providing numerical examples, the implementation of this method is expressed. economics and in the problems that we have certain, converting to interval programming a, is studied problems simply