Abstract: In the market of online-customized products, demands possess uncertainty in both amount and time.In this paper, a promised lead time and capacity decision-making model is proposed by taking expected profit as the objective function with the Activity Based Costing, considering the demands are sensitivity of promised lead time and stochastic. A recursive mathematical expression of the optimal promised lead time and the optimal capacity is obtained by analyzing the model. On this basis, building up the M/M/1 model by taking the reliability of promised lead time as limiting condition with the queuing theory. It is proved that the M/M/1 model is Concave Programming, and equations of the optimal promised lead time and the optimal capacity are obtained. At last, through numerical example the optimal promised lead time and the optimal capacity are restricted by the reliability of promised lead time, and with the improvement of the reliability of promised lead time, the optimal promised lead time is increasing; the optimal capacity and the optimal expected profit are decreasing. The research shows that the optimal promised lead time and the optimal capacity are got through combining with the reliability of the promised lead time, which can improve the utilization rate of capacity and the accuracy of lead time.

Key words: uncertain demand, capacity, promised lead time, M/M/1