Optimality theory of an unconstrained interval optimization problem in parametric form: Its application in inventory control

Abstract

The aim of this work is to establish the optimality conditions of an unconstrained interval optimization problem in parametric form. For this purpose, a new definition of interval order relation is proposed. With the help of the proposed order relation, the definition of maximizer and minimizer of an unconstrained interval optimization problem are introduced. After those the necessary and sufficient conditions for the optimality of both the interval maximization and interval minimization problems are derived separately. Then the established results are applied in the area of inventory control to solve a production inventory problem with time dependent demand in interval environment. Finally, the established results are justified by solving the said inventory problem numerically and the work is concluded with some important findings.