云制造环境下考虑不确定性的产品配置优化

越来越多的大规模定制企业借助于云制造技术实现产品的个性化定制。针对云制造环境下的产品配置问题，提出了基于鲁棒优化的方法建立最小化配置总成本为目标的优化模型，并考虑了云制造成本和时间的不确定性。运用基于budget和区间的不确定集来刻画参数的扰动性。通过对偶理论，将其转化为鲁棒等价模型，从而可以采用CPLEX进行求解。以一个配置案例为例论证了鲁棒优化模型的有效性。最后，设计了不同的算例进行仿真实验，证明了鲁棒优化解在应对不确定风险时更为稳健、能够显著改善产品的准时交货期。

Product Configuration Optimization Problems in Cloud Manufacturing with Uncertainity

An increasing number of enterprises realize their personalized production by means of cloud manufacturing technology. To deal with the uncertainties in cloud manufacturing, a robust optimization approach to product configuration is proposed with the objective of minimizing the total configuration cost. The uncertainties in cloud manufacturing cost and time are characterized by using budget-based robust representation. The robust model is transformed into a robust counterpart model using the duality theory. As a result, commercial solvers such as CPLEX can be employed to solve the model to optimality. A configuration case is designed to illustrate the effectiveness of the robust model. Numerical experiments are conducted to demonstrate that the proposed model is more robust and can substantially improve the delivery date of products.