Minimizing the expected processing time on a flexible machine with random tool lives
Date of Original Version
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). Copyright © "IIE".
IIE Transactions (Institute of Industrial Engineers)
Lamond, Bernard F., and Manbir S. Sodhi. "Minimizing the expected processing time on a flexible machine with random tool lives." IIE Transactions (Institute of Industrial Engineers) 38, 1 (2006): 1-11. doi:10.1080/07408170500346360.