# A biobjective chance constrained optimization model to evaluate the economic and environmental impacts of biopower supply chains

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## Abstract

Generating electricity by co-combusting biomass and coal, known as biomass cofiring, is shown to be an economically attractive option for coal-fired power plants to comply with emission regulations. However, the total carbon footprint of the associated supply chain still needs to be carefully investigated. In this study we propose a stochastic biobjective optimization model to analyze the economic and environmental impacts of biopower supply chains. We use a life cycle assessment approach to derive the emission factors used in the environmental objective function. We use chance constraints to capture the uncertain nature of energy content of biomass feedstocks. We propose a cutting plane algorithm which uses the sample average approximation method to model the chance constraints and finds high confidence feasible solutions. In order to find Pareto optimal solutions we propose a heuristic approach which integrates the \(\epsilon \)-constraint method with the cutting plane algorithm. We show that the developed approach provides a set of local Pareto optimal solutions with high confidence and reasonable computational time. We develop a case study using data about biomass and coal plants in North and South Carolina. The results indicate that, cofiring of biomass in these states can reduce emissions by up to 8%. Increasing the amount of biomass cofired will not result in lower emissions due to biomass delivery.

## Keywords

Stochastic multiobjective optimization Chance constraints Sample average approximation Biopower supply chain Biomass cofiring Life cycle assessment## Notes

### Acknowledgements

This work is supported by the National Science Foundation, Grant CMMI 1462420; this support is gratefully acknowledged. Clemson University is acknowledged for generous allotment of compute time on Palmetto cluster.

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