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 classical production settings, and so‐called tool management problems appear to be among the more fundamental ones of these problems. Most tool management problems are hard to solve, so that numerous approximate solution techniques have been proposed to tackle them. In this paper, we investigate the quality of such algorithms by means of worst‐case analysis. We consider several polynomial‐time approximation algorithms described in the literature, and we show that all these algorithms exhibit rather poor worst‐case behavior. We also study the complexity of solving tool management problems approximately. In this respect, we investigate the interrelationships among tool management problems, as well as their relationships with other well‐known combinatorial problems such as the maximum clique problem or the set covering problem, and we prove several negative results on the approximability of various tool management problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 445–462, 1999     

Basic scheduling problems with raw material constraints

One of the achievements of scheduling theory is its contribution to practical applications in industrial settings. In particular, taking finiteness of the available production capacity explicitly into account, has been a major improvement of standard practice. Availability of raw materials, however, which is another important constraint in practice, has been largely disregarded in scheduling theory. This paper considers basic models for scheduling problems in contemporary manufacturing settings where raw material availability is of critical importance. We explore single scheduling machine problems, mostly with unit or all equal processing times, and L_max and C_max objectives. We present polynomial time algorithms, complexity and approximation results, and computational experiments. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A queuing model for due date control in a multiserver repair shop

This paper deals with a repair shop with multiple parallel servers, which has to carry out planned overhauls. Each overhaul consists of a large number of maintenance jobs. The overhaul process is interrupted by randomly arriving emergency jobs. To control the delivery performance of the overhauls, knowledge about the overhaul makespan distribution should be available. Using a 2‐dimensional Markov model, we derive the first and second moment of the overhaul makespan analytically for the case that the repair times of all overhaul jobs are identically and exponentially distributed. For the case of nonidentical repair time distributions, an approximation is presented. Simulation shows that the makespan distribution fitted on these moments gives an excellent approximation. © John Wiley & Sons, Inc. Naval Research Logistics 48: 281–282, 2001