A note on imposing strong complementary slackness conditions in DEA

A note on imposing strong complementary slackness conditions in DEA

A new DEA model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions. It was claimed that a reference set that contains the maximum number of efficient units can then be determined. The model is very interesting as a theoretical idea. However, not only does the computational burden increase significantly, but it seems...

On the Strictly Complementary Slackness Relation in Linear Programming

Balinski and Tucker introduced in 1969 a special form of optimal tableaus for LP, which can be used to construct primal and dual optimal solutions such that the complementary slackness relation holds strictly. In this paper, first we note that using a polynomial time algorithm for LP Balinski and Tucker’s tableaus are obtainable in polynomial time. Furthermore, we show that, given a pair of pri...

The complementary-slackness class of hybrid systems

In this paper we understand by a `hybrid system' one that combines features of continuous dynamical systems with characteristics of nite automata. We study a special class of such systems which we call the complementary-slackness class. We study existence and uniqueness of solutions in the special cases of linear and Hamiltonian complementary-slackness systems. For the latter class we also prov...

On the control of complementary-slackness juggling mechanical systems

This paper studies the feedback control of a class of complementary-slackness hybrid mechanical systems. Roughly, the systems we study are composed of an uncontrollable part (the “object”) and a controlled one (the “robot”), linked by a unilateral constraint and an impact rule. A systematic and general control design method for this class of systems is proposed. The approach is a nontrivial ext...

Ranking of DMUs on interval data by imposing a minimum weight restriction in DEA