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A New Mixed-Integer Programming Model for Harvest Scheduling Subject to Maximum Area Restrictions

Author

Listed:
  • Miguel Constantino

    (Universidade de Lisboa, Faculdade de Ciências, DEIO/Centro de Investigação Operacional, Bloco C6, piso 4, Cidade Universitária,1749-016 Lisboa, Portugal)

  • Isabel Martins

    (Universidade Técnica de Lisboa, Instituto Superior de Agronomia/Centro de Investigação Operacional, Tapada da Ajuda, 1349-017 Lisboa, Portugal)

  • José G. Borges

    (Universidade Técnica de Lisboa, Instituto Superior de Agronomia/Centro de Estudos Florestais, Tapada da Ajuda, 1349-017 Lisboa, Portugal)

Abstract

Forest ecosystem management often requires spatially explicit planning because the spatial arrangement of harvests has become a critical economic and environmental concern. Recent research on exact methods has addressed both the design and the solution of forest management problems with constraints on the clearcut size, but where simultaneously harvesting two adjacent stands in the same period does not necessarily exceed the maximum opening size. Two main integer programming approaches have been proposed for this area restriction model. However, both encompass an exponential number of variables or constraints. In this work, we present a new integer programming model with a polynomial number of variables and constraints. Branch and bound is used to solve it. The model was tested with both real and hypothetical forests ranging from 45 to 1,363 polygons. Results show that the proposed model's solutions were within or slightly above 1% of the optimal solution and were obtained in a short computation time.

Suggested Citation

  • Miguel Constantino & Isabel Martins & José G. Borges, 2008. "A New Mixed-Integer Programming Model for Harvest Scheduling Subject to Maximum Area Restrictions," Operations Research, INFORMS, vol. 56(3), pages 542-551, June.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:3:p:542-551
    DOI: 10.1287/opre.1070.0472
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    References listed on IDEAS

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    1. Martins, Isabel & Constantino, Miguel & Borges, Jose G., 2005. "A column generation approach for solving a non-temporal forest harvest model with spatial structure constraints," European Journal of Operational Research, Elsevier, vol. 161(2), pages 478-498, March.
    2. Marcos Goycoolea & Alan T. Murray & Francisco Barahona & Rafael Epstein & Andrés Weintraub, 2005. "Harvest Scheduling Subject to Maximum Area Restrictions: Exploring Exact Approaches," Operations Research, INFORMS, vol. 53(3), pages 490-500, June.
    3. Vielma, Juan Pablo & Murray, Alan T. & Ryan, David M. & Weintraub, Andres, 2007. "Improving computational capabilities for addressing volume constraints in forest harvest scheduling problems," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1246-1264, January.
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    Citations

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    Cited by:

    1. Marshalek, Elaina C. & Ramage, Benjamin S. & Potts, Matthew D., 2014. "Integrating harvest scheduling and reserve design to improve biodiversity conservation," Ecological Modelling, Elsevier, vol. 287(C), pages 27-35.
    2. Isabel Martins & Mujing Ye & Miguel Constantino & Maria Conceição Fonseca & Jorge Cadima, 2014. "Modeling target volume flows in forest harvest scheduling subject to maximum area restrictions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 343-362, April.
    3. Isabel Martins & Filipe Alvelos & Miguel Constantino, 2012. "A branch-and-price approach for harvest scheduling subject to maximum area restrictions," Computational Optimization and Applications, Springer, vol. 51(1), pages 363-385, January.
    4. Könnyű, Nóra & Tóth, Sándor F., 2013. "A cutting plane method for solving harvest scheduling models with area restrictions," European Journal of Operational Research, Elsevier, vol. 228(1), pages 236-248.
    5. Antonio Alonso-Ayuso & Laureano Escudero & Monique Guignard & Martín Quinteros & Andres Weintraub, 2011. "Forestry management under uncertainty," Annals of Operations Research, Springer, vol. 190(1), pages 17-39, October.
    6. Oğuzhan Ahmet Arık, 2021. "Long-term Plantation and Harvesting Planning for Industrial Plantation Forest Areas," SN Operations Research Forum, Springer, vol. 2(2), pages 1-23, June.
    7. Mafakheri, Fereshteh & Nasiri, Fuzhan, 2014. "Modeling of biomass-to-energy supply chain operations: Applications, challenges and research directions," Energy Policy, Elsevier, vol. 67(C), pages 116-126.
    8. Sinha, Ankur & Rämö, Janne & Malo, Pekka & Kallio, Markku & Tahvonen, Olli, 2017. "Optimal management of naturally regenerating uneven-aged forests," European Journal of Operational Research, Elsevier, vol. 256(3), pages 886-900.
    9. Rachel St. John & Sándor Tóth, 2015. "Spatially explicit forest harvest scheduling with difference equations," Annals of Operations Research, Springer, vol. 232(1), pages 235-257, September.
    10. Huizhen Zhang & Miguel Constantino & André Falcão, 2011. "Modeling forest core area with integer programming," Annals of Operations Research, Springer, vol. 190(1), pages 41-55, October.
    11. Ran Wei & Alan Murray, 2015. "Spatial uncertainty in harvest scheduling," Annals of Operations Research, Springer, vol. 232(1), pages 275-289, September.
    12. Fernando Veliz & Jean-Paul Watson & Andres Weintraub & Roger Wets & David Woodruff, 2015. "Stochastic optimization models in forest planning: a progressive hedging solution approach," Annals of Operations Research, Springer, vol. 232(1), pages 259-274, September.
    13. Augustynczik, Andrey Lessa Derci & Arce, Julio Eduardo & Yousefpour, Rasoul & da Silva, Arinei Carlos Lindbeck, 2016. "Promoting harvesting stands connectivity and its economic implications in Brazilian forest plantations applying integer linear programming and simulated annealing," Forest Policy and Economics, Elsevier, vol. 73(C), pages 120-129.
    14. Rodolfo Carvajal & Miguel Constantino & Marcos Goycoolea & Juan Pablo Vielma & Andrés Weintraub, 2013. "Imposing Connectivity Constraints in Forest Planning Models," Operations Research, INFORMS, vol. 61(4), pages 824-836, August.
    15. Belavenutti, Pedro & Ager, Alan A. & Day, Michelle A. & Chung, Woodam, 2022. "Designing forest restoration projects to optimize the application of broadcast burning," Ecological Economics, Elsevier, vol. 201(C).
    16. Teresa Neto & Miguel Constantino & Isabel Martins & João Pedro Pedroso, 2017. "Forest harvest scheduling with clearcut and core area constraints," Annals of Operations Research, Springer, vol. 258(2), pages 453-478, November.
    17. Constantino, Miguel & Martins, Isabel, 2018. "Branch-and-cut for the forest harvest scheduling subject to clearcut and core area constraints," European Journal of Operational Research, Elsevier, vol. 265(2), pages 723-734.
    18. Correa, Renata Naoko & Scarpin, Cassius Tadeu & Ferrari, Linamara Smaniotto & Arce, Julio Eduardo, 2020. "Application of relax-and-fix heuristic in the aggregation of stands for tactical forest scheduling," Forest Policy and Economics, Elsevier, vol. 119(C).

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