Simulation optimization of buffer allocations in production lines with unreliable machines

We use a recent simulation-based optimization method, sample path optimization, to find optimal buffer allocations in tandem production lines where machines are subject to random breakdowns and repairs, and the product is fluid-type. We explore some of the functional properties of throughput of such systems and exploit these properties to prove the almost sure convergence of our optimization technique, under a regularity condition on the steady state. Utilizing a generalized semi-Markov process representation of the system, we derive recursive expressions to compute one-sided directional derivatives of throughput, from a single simulation run. Finally, we give computational results for lines with up to 50 machines. We also compare results for smaller lines with the results from a more conventional method, stochastic approximation, whenever applicable. In these numerical studies, our method performed quite well on problems that are considered difficult by current computational standards.