Minimizing the expected processing time on a flexible machine with random tool lives

We present a stochastic version of economic tool life models for machines with finite capacity tool magazines and a variable processing speed capability, where the tool life is a random variable. Using renewal theory to express the expected number of tool setups as a function of cutting speed and magazine capacity, we extend previously published deterministic mathematical programming models to the case of minimizing the expected total processing time. A numerical illustration with typical cutting tool data shows the deterministic model underestimates the optimal expected processing time by more than 8% when the coefficient of variation equals 0.3 (typical for carbide tools), and the difference exceeds 15% for single-injury tools having an exponentially distributed economic life (worst case).

Acknowledgements

This research was supported in part by the National Science and Engineering Research Council of Canada, under grant 0105560, and the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche du Québec, under grant 1570. The authors also thank the National Science Foundation for supporting this research through grant DMII: 9813177. Martin Noël's help with some of the computations is also acknowledged.