Quantified Combinatorial Optimization
MIP and IP programming are state-of-the-art modeling techniques for computer-aided optimization. However, companies observe an increasing danger of disruptions that prevent them from acting as planned. One reason is input data being assumed as deterministic, but in reality, data is afflicted with uncertainties. Incorporating uncertainty in existing models, however, often pushes the complexity of problems that are in P or NP, to the complexity class PSPACE. Quantified integer linear programming (QIP) is a PSPACE-complete extension of the IP problem with variables being either existentially or universally quantified. With the help of QIPs, it is possible to model board-games like Gomoku as well as traditional combinatorial OR problems under uncertainty. In this paper, we present how to extend the model formulation of classical scheduling problems like the Job-Shop and Car-Sequencing problem by uncertain influences and give illustrating examples with solutions.
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