Optimal lot-sizing and machining economics

This paper presents a queueing model with the service station subject to breakdown while it is busy, in order to determine analytically the optimal batch size in a machining economics problem. It is shown that departures from the optimal batch size result in moderate waiting-time increases when the batch size is scaled up and in significant waiting-time increases when the batch size is scaled down. It is also shown, through the use of a simulation model with normally distributed tool lives, that the analytical results obtained with exponentially distributed tool lives are quite robust. In the multiple-item case, simulation results show that the time in the system for each item and the average time in the system across all items behave exactly like the time in the system in the single-item case.