راه حل های بهینه و به شدت بهینه برای مدل برنامه ریزی خطی با پارامترهای متغیر

This paper deals with linear programming (LP) models with variable parameters and introduces two concepts for this class of problems: optimal solution and strongly optimal solution. Also, it seeks necessary and sufficient conditions for a feasible solution to be optimal or strongly optimal.

In the real applications of the field of optimisation, there are linear programming (LP) problems whose parameters (i.e., technological coefficients, requirement values, and cost coefficients) are not precisely fixed and can vary within some prescribed intervals (see [2], [4] and [5] as well as Section 5 of the present paper). In this paper, we deal with this class of LP models, which is a more general class compared to the one discussed in [5], and introduce two key concepts: optimal solution and strongly optimal solution. The main aim of this paper is to find the necessary and sufficient conditions for a feasible solution to be optimal or strongly optimal. The rest of this paper is organized as follows: In Section 2, LP models with variable parameters are defined, and the two concepts of optimal solution and strongly optimal solution are introduced. Section 3 and Section 4 contain necessary and sufficient conditions for optimality and strong optimality, respectively. Section 5 addresses some applications of the results of this paper.