Linear Programming Problem with Interval Coefficients and an Interpretation for Its Constraints

Abstract – In this paper, we introduce a Satisfaction Function (SF) to compare interval values on the basis of Tseng and Klein’s idea. The SF estimates the degree to which arithmetic comparisons between two interval values are satisfied. Then, we define two other functions called Lower and Upper SF based on the SF. We apply these functions in order to present a new interpretation of inequality constraints with interval coefficients in an interval linear programming problem. This problem is as an extension of the classical linear programming problem to an inexact environment. On the basis of definitions of the SF, the lower and upper SF and their properties, we reduce the inequality constraints with interval coefficients in their satisfactory crisp equivalent forms and define a satisfactory solution to the problem. Finally, a numerical example is given and its results are compared with other approaches.