For optimal operation of power-intensive plants, production scheduling and electricity procurement have to be considered simultaneously. In addition, uncertainty needs to be taken into account. For this purpose, an integrated stochastic mixed-integer linear programming model is developed that considers the two most critical sources of uncertainty: spot electricity price, and product demand. Conditional value-at-risk is incorporated into the model as a measure of risk. Furthermore, scenario reduction and multicut Benders decomposition are implemented to solve large-scale real-world problems. The proposed model is applied to an illustrative example as well as an industrial air separation case. The results show the benefit from stochastic optimization and the effect of taking a risk-averse rather than a risk-neutral approach. An interesting insight from the analysis is that in risk-neutral optimization, accounting for electricity price uncertainty does not yield significant added value; however, in risk-averse optimization, modeling price uncertainty is crucial for obtaining good solutions.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the financial support from the National Science Foundation under Grant No. 1159443 and from Praxair .
- Conditional value-at-risk
- Demand response
- Electricity procurement
- Production scheduling
- Stochastic programming