不确定彩排时长下节目调度的鲁棒优化

实际节目彩排调度中，节目的表演时长受内外因素影响，具有不确定性。为了合理调度所有节目，控制演员的空闲时间，使得演员的总等待成本最小，采用了鲁棒优化方法进行研究。首先，建立了节目彩排调度的确定型模型；进一步，考虑节目表演时长的不确定性，采用有界区间描述节目表演时长并考虑决策者风险偏好，在确定型模型的基础上构建区间型两阶段鲁棒优化模型；接着，将鲁棒优化模型转化为0-1混合线性规划模型；最后，采用Matlab进行数值实验，结果表明决策者越偏好规避风险，演员的总等待成本越大。

Robust optimization of rehearsal scheduling under uncertain duration

In a dress rehearsal, the duration of a program which is affected by internal and external factors, is uncertain. A robust optimization method is adopted to schedule the programs to minimize the total waiting cost of actors. A deterministic dress rehearsal model is first proposed. Then, based on the above deterministic model, a two-stage robust optimization model is built, considering the uncertainty of the programs. durations and the risk preference of decision makers. Thirdly, the robust optimization model is converted into a 0-1 mixed linear programming. At last, numerical experiments are carried out by Matlab, and the results show that the actors' waiting cost increases with the decreasement of decision makers' risk preference.