Worst-case performance of approximation algorithms for tool management problems

Since the introduction of flexible manufacturing systems, researchers have investigated various planning and scheduling problems faced by the users of such systems, Several of these problems are not encountered in more classi cal production settings, and so-called tool management problems appear to b e among the more fundamental ones of these problems. Most tool management p roblems are hard to solve, so that numerous approximate solution techniques have been proposed to tackle them. In this paper, we investigate the quali ty of such algorithms by means of worst-case analysis. We consider several polynomial-time approximation algorithms described in the literature, and w e show that all these algorithms exhibit rather poor worst-case behavior. W e also study the complexity of solving tool management problems approximate ly. In this respect, we investigate the interrelationships among tool manag ement problems, as well as their relationships with other well-known combin atorial problems such as the maximum clique problem or the set covering pro blem, and we prove several negative results on the approximability of vario us tool management problems. (C) 1999 John Wiley & Sons, Inc.