Simulation-based production planning for engineer-to-order systems with random yield

We consider an engineer-to-order production system with unknown yield. We model the yield as a random variable which represents the percentage output obtained from one unit of production quantity. We develop a beta-regression model in which the mean value of the yield depends on the unique attributes of the engineer-to-order product. Assuming that the beta-regression parameters are unknown by the decision maker, we investigate the problem of identifying the optimal production quantity. Adopting a Bayesian approach for modeling the uncertainty in the beta-regression parameters, we use simulation to approximate the posterior distributions of these parameters. We further quantify the increase in the expected cost due to the so-called input uncertainty as a function of the size of the historical data set, the product attributes, and economic parameters. We also introduce a sampling-based algorithm that reduces the average increase in the expected cost due to input uncertainty.