Bad-scenario-set robust optimization framework with two objectives for uncertain scheduling systems

This paper proposes a robust optimization framework generally for scheduling systems subject to uncertain input data, which is described by discrete scenarios. The goal of robust optimization is to hedge against the risk of system performance degradation on a set of bad scenarios while maintaining an excellent expected system performance. The robustness is evaluated by a penalty function on the bad-scenario set. The bad-scenario set is identified for current solution by a threshold, which is restricted on a reasonable-value interval. The robust optimization framework is formulated by an optimization problem with two conflicting objectives. One objective is to minimize the reasonable value of threshold, and another is to minimize the measured penalty on the bad-scenario set. An approximate solution framework with two dependent stages is developed to surrogate the biobjective robust optimization problem. The approximation degree of the surrogate framework is analyzed. Finally, the proposed bad-scenario-set robust optimization framework is applied to a scenario job-shop scheduling system. An extensive computational experiment was conducted to demonstrate the effectiveness and the approximation degree of the framework. The computational results testified that the robust optimization framework can provide multiple selections of robust solutions for the decision maker. The robust scheduling framework studied in this paper can provide a unique paradigm for formulating and solving robust discrete optimization problems.