# A comparison of four approaches from stochastic programming for large-scale unit-commitment

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## Abstract

In energy management, the unit-commitment problem deals with computing the most cost-efficient production schedule that meets customer load, while satisfying the operational constraints of the units. When the problem is large scale and/or much modelling detail is required, decomposition approaches are vital for solving this problem. The recent strong increase in intermittent, relative unforeseeable production has brought forth the need of examining methods from stochastic programming. In this paper we investigate and compare four such methods: probabilistically constrained programming, robust optimization and 2-stage stochastic and robust programming, on several large-scale instances from practice. The results show that the robust optimization approach is computationally the least costly but difficult to parameterize and has the highest recourse cost. The probabilistically constrained approach is second as computational cost is concerned and improves significantly the recourse cost functions with respect to the robust optimization approach. The 2-stage optimization approaches do poorly in terms of robustness, because the recourse decisions can compensate for this. Their total computational cost is highest. This leads to the insight that 2-stage flexibility and robustness can be (practically) orthogonal concepts.

### Keywords

Probabilistically constrained programming Robust optimization Stochastic programming Unit-commitment### Mathematics Subject Classification

49M37 65K05 90C15## Notes

### Acknowledgments

The author would like to thank three anonymous referees for their comments that helped improve this paper.

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