Scheduling under Uncertainty

不确定条件下的决策方法有随机规划法、稳健优化法和稳定性分析法。尽管它们有着悠久的研究历史和先进的理论成果，但现有方法的实际适用性往往相当有限。新的弹性分析方法克服了现有方法的一些缺点：它不依赖于不确定参数的概率特征，不依赖于最坏情况或目标解的最优性要求。对经典组合优化问题的初步研究表明，弹性分析不仅可以为不确定情况下的决策提供理论上的严谨，而且在实践上也是可行的方法。本项目将进一步阐述适应性分析的关键方法，并将其应用于研究了60多年的重要调度问题：单机和并行机问题、开放车间、流水作业和作业车间。利用调度理论和组合优化的其他学科之间的联系，我们将采取措施扩大我们的研究，考虑诸如图的优化和指派问题。

The well-known approaches in decision making under uncertainty are Stochastic Programming, Robust Optimisation and Stability Analysis. In spite of their long history of study and advanced theoretical findings, the practical applicability of the existing methods is often quite limited. The new methodology of Resiliency Analysis overcomes some of the drawbacks of the existing methods: it does not rely on probabilistic characteristics of uncertain parameters, on worst-case scenarios or optimality requirements of target solutions. The preliminary study of the classical Combinatorial Optimisation problems has indicated the benefits of Resiliency Analysis, which can provide not only theoretically rigorous, but also practically feasible methods for decision making under uncertainty. The project will elaborate the key methods of Resiliency Analysis further and apply them to important scheduling problems which have been under study for more than 60 years: single- and parallel-machine problems, open-shop, flow-shop and job-shop. Using the links between Scheduling Theory and other disciplines of Combinatorial Optimisation, we will make steps towards extending our study, considering such problems as optimisation on graphs and the assignment problem.