A generalized division approach for interval fractional programming problems

Abstract

In this paper, an interval fractional programming problem is considered with the generalized division of intervals. A parametric non-fractional interval problem is formulated, and an equivalence between the fractional and parametric non-fractional problems is established. The necessary conditions are derived using the alternative theorem proposed and the linear independence constraint qualification. Moreover, the LU-convexity assumption is used to prove sufficient optimality conditions. The optimality conditions discussed in this study are inclusion relations rather than equations. A Wolfe-type dual is formulated, and the weak, strong, and strict converse duality results are derived using the LU-convexity assumption. Since many other factors are uncertain in the industry sector, a steel blending problem with interval cost and components is formulated as an interval fractional problem. The developed optimality conditions are applied to obtain the optimal choice of base steel combination in order to obtain blended steel of the desired quality at the minimum cost. Throughout the paper, the results are illustrated with non-trivial examples.