Since the introduction of exible manufacturing systems, researchers have investigated the various planning and scheduling problems that the users of such systems are facing. Several of these problems are not encountered in more classical production settings, and so called tool mamagement problems appear to be among the more fundamental ones of these problems. Many researchers have proposed approximate solution techniques for tool management problems, most of which are hard to solve. In this paper we investigate the quality of these algorithms by means of worst case analysis. We show that all of the polynomial approximation algorithms proposed to date exhibit rather poor worst case behavior. We also investigate the complexity of solving these problems approximately. In this respect, we investigate the interrelationships between tool management problems and their relationships with other well known combinatorial problems, such as Set Covering and Clique, and give several negative results on the approximability of various tool management problems.
