Scheduling under Uncertainty

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.