Abstract
This paper presents a heuristic method based on column generation for the EDF (Electricité De France) long-term electricity production planning problem proposed as subject of the ROADEF/EURO 2010 Challenge. This is to our knowledge the first-ranked method among those methods based on mathematical programming, and was ranked fourth overall. The problem consists in determining a production plan over the whole time horizon for each thermal power plant of the French electricity company, and for nuclear plants, a schedule of plant outages which are necessary for refueling and maintenance operations. The average cost of the overall outage and production planning, computed over a set of demand scenarios, is to be minimized. The method proceeds in two stages. In the first stage, dates for outages are fixed once for all for each nuclear plant. Data are aggregated with a single average scenario and reduced time steps, and a set-partitioning reformulation of this aggregated problem is solved for fixing outage dates with a heuristic based on column generation. The pricing problem associated with each nuclear plant is a shortest path problem in an appropriately constructed graph. In the second stage, the reload level is determined at each date of an outage, considering now all scenarios. Finally, the production quantities between two outages are optimized for each plant and each scenario by solving independent linear programming problems.
Similar content being viewed by others
References
Baldacci, R., Christophides, N., & Mingozzi, A. (2008). An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Mathematical Programming, 351–385.
Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1996). Branch-and-price: column generation for solving huge integer programs. Operations Research, 46, 316–329.
Desaulniers, G., Desrosiers, J., & Solomon, M. M. (2005). GERAD. Column generation. Berlin: Springer.
Dubost, L., Gonzalez, R., & Lemaréchal, C. (2005). A primal-proximal heuristic applied to the French unit-commitment problem. Mathematical Programming, 104(1), 129–151.
Finardi, E. C., da Silva, E. L., & Sagastizàbal, C. (2005). Solving the unit commitment problem of hydropower plants via Lagrangian relaxation and sequential quadratic programming. Computational and Applied Mathematics, 24, 317–342.
Frangioni, A., Gentile, C., & Lacalandra, F. (2008). Solving unit commitment problems with general ramp constraints. International Journal of Electrical Power & Energy Systems, 30(5), 316–326.
Kallrath, J., Pardalos, P. M., Rebennack, S., & Scheidt, M. (2009). Optimization in the energy industry.
Kazarlis, S. A., Bakirtzis, A. G., & Petridis, V. (1996). A genetic algorithm approach to solve the unit commitment problem. IEEE Transactions on Power Systems, 11, 83–92.
Khemmoudj, M. I., Porcheron, M., & Bennaceur, H. (2006). When constraints programming and local search solve the scheduling problem of edf nuclear power plant aoutages. In 12th international conference on principles and practice of constraint programming (pp. 271–283).
Lubbecke, M. E., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, November-December, 1007–1023.
Lusby, R., Muller, L. F., & Petersen, B. (2010). A solution approach to the roadef/euro 2010 challenge based on benders decomposition. Technical report.
Porcheron, M., Gorge, A., Juen, O., Simovic, T., & Dereu, G. (2010). EDF R&D, Challenge roadef/euro 2010: a large-scale energy management problem with varied constraints.
Wagelmans, A., van Hoesel, S., & Kolen, A. (1992). Economic lot sizing: an o(nlogn) algorithm that runs in linear time in the Wagner-Whitin case. Operations Research, 40, 145–156.
Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot size model. Management Science, 5, 89–96.
Wolsey, L. A. (1998). Integer programming.
Acknowledgements
We wish to thank anonymous reviewers for fruitful suggestions which helped improve a previous version of this paper. Moreover, we would like to thank Aristide Mingozzi and Guillaume Turri for their useful help and/or comments they gave at the beginning of this project.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rozenknop, A., Wolfler Calvo, R., Alfandari, L. et al. Solving the electricity production planning problem by a column generation based heuristic. J Sched 16, 585–604 (2013). https://doi.org/10.1007/s10951-012-0286-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-012-0286-9