需求不确定下承诺交货时间和产能决策

在网上定制的市场中，需求具有数量和时间两方面的不确定性。本文提出同时考虑需求量具有承诺交货时间敏感性和随机性，采用作业成本法建立以期望利润为目标函数，以承诺交货时间和产能为决策变量的模型。通过模型的分析得到了相互递推的最优承诺交货时间和最优产能数学表达式。在此基础上，运用排队理论建立了以承诺交货时间可靠性为限制条件的M/M/1决策模型。通过模型分析，证明了模型是凹规划，给出了最优承诺交货时间和最优产能满足的方程组。最后，通过算例的分析可知最优承诺交货时间和最优产能受承诺交货时间可靠性限制，而且随着承诺交货时间可靠性的提高，最优承诺交货时间是递增的，最优产能和最优期望利润是递减的。研究表明：结合承诺交货时间可靠性确定最优承诺交货时间和最优产能有助于提高产能的利用率和交货时间的准确性。

Promised Lead Time and Capacity Decision-Making Based on Demand is Uncertain

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.