Economic production lot sizing with two independent/dependent imperfect key subsystems

This paper applies an economic production quantity model to determine a lot size for manufacturing a product in batches on an imperfect production system. Typically, a single machine is considered for production. Generalising this situation and for providing a wide-range application, a new model is developed where the production system is affected by two key production subsystems (KPSs) that may shift from an in-control state to an out-of-control state. When a shifting happens, a fixed percentage of items produced become defective. Let X and Y denote the time-to-shift of these two KPSs, respectively. They are exponentially distributed random variables. Depending on whether X and Y are statistically independent, two cases are investigated. The objective is to find an optimal production run time so as to minimise the expected total costs including setup, inventory holding, and defective costs. A glass pot production system of a cutting module and a spout forming module is introduced to show the application. Numerical analyses are given at the end to illustrate the models.