Investigation of the Regularity Conditions in Data Envelopment Analysis

Duality plays a fundamental role in mathematics, especially in optimization. For every linear programming model, there is a corresponding one which called ʹdualʹ. A dual linear programming problem has some special specifications associated with the basic problem in which all characteristics, specially in order to meet the results for the basic problem, is used. Its variables provide extremely useful information about the optimal solution to the original linear program. This leads to rich economic interpretations related to the original linear programming problem. In fact, the roots of this problem lie in the characterization of the optimality conditions for the original linear program. For the sake of expository reference, we shall call the original linear programming problem, the primal (linear programming) problem, and we shall call this related linear program, the dual (linear programming) problem. Actually, the terms primal and dual for this related pair of linear programming problems are only relative, because the dual of the ʹdualʹ is the ʹprimalʹ itself. One of the most interesting specifications of primal-dual, is to investigate the regularity conditions. In this paper, the regularity conditions is going to be inspected in two models, BCC and CCR, and then, the conclusions will be discussed