Dynamic programming for energy control of machine tools in manufacturing

Controlling the machine state towards the optimum trade-off between cycle time and power demand improves machine sustainability in manufacturing. This paper presents a dynamic programming approach for optimally controlling a single server manufacturing system with finite capacity and Poisson arrivals (M/M/1/K). The admission of parts into the system is controlled together with the service rate of the machine tool. Further, the machine can be triggered in a low power consumption state when the service is interrupted. The structural properties of the optimal control are analyzed when the transition off/on is instantaneous and when a transitory - i.e., warm-up - is necessary to resume the service. The transitory length is considered exponentially distributed. Numerical results are based on value iteration approximation.