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A branch-price-and-cut method for the vegetable crop rotation scheduling problem with minimal plot sizes

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  • Santos, Lana M.R.
  • Munari, Pedro
  • Costa, Alysson M.
  • Santos, Ricardo H.S.

Abstract

Crop rotation plays an important role in agricultural production models with sustainability considerations. Commonly associated strategies include the alternation of botanical families in the plots, the use of fallow periods and the inclusion of green manure crops. In this article, we address the problem of scheduling vegetable production in this context. Vegetables crop farmers usually manage a large number of crop species with different planting periods and growing times. These crops present multiple and varied harvesting periods and productivities. The combination of such characteristics makes the generation of good vegetable crop rotation schedules a hard combinatorial task. We approach this problem while considering two additional important practical aspects: standard plot sizes (multiples of a base area) and total area minimisation. We propose an integer programming formulation for this problem and develop a branch-price-and-cut algorithm that includes several performance-enhancing characteristics, such as the inclusion of a family of subadditive valid inequalities, two primal heuristics and a strong branching rule. Extensive computational experiments over a set of instances based on real-life data validate the efficiency and robustness of the proposed method.

Suggested Citation

  • Santos, Lana M.R. & Munari, Pedro & Costa, Alysson M. & Santos, Ricardo H.S., 2015. "A branch-price-and-cut method for the vegetable crop rotation scheduling problem with minimal plot sizes," European Journal of Operational Research, Elsevier, vol. 245(2), pages 581-590.
  • Handle: RePEc:eee:ejores:v:245:y:2015:i:2:p:581-590
    DOI: 10.1016/j.ejor.2015.03.035
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    References listed on IDEAS

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    4. Lana dos Santos & Philippe Michelon & Marcos Arenales & Ricardo Santos, 2011. "Crop rotation scheduling with adjacency constraints," Annals of Operations Research, Springer, vol. 190(1), pages 165-180, October.
    5. Alfandari, Laurent & Plateau, Agnès & Schepler, Xavier, 2015. "A branch-and-price-and-cut approach for sustainable crop rotation planning," European Journal of Operational Research, Elsevier, vol. 241(3), pages 872-879.
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    7. Alysson Costa & Lana Santos & Douglas Alem & Ricardo Santos, 2014. "Sustainable vegetable crop supply problem with perishable stocks," Annals of Operations Research, Springer, vol. 219(1), pages 265-283, August.
    8. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    9. dos Santos, Lana Mara R. & Costa, Alysson M. & Arenales, Marcos N. & Santos, Ricardo Henrique S., 2010. "Sustainable vegetable crop supply problem," European Journal of Operational Research, Elsevier, vol. 204(3), pages 639-647, August.
    10. VANDERBECK, François & WOLSEY, Laurence A., 2010. "Reformulation and decomposition of integer programs," LIDAM Reprints CORE 2188, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Angelo Aliano Filho & Helenice Oliveira Florentino & Margarida Vaz Pato & Sônia Cristina Poltroniere & João Fernando Silva Costa, 2022. "Exact and heuristic methods to solve a bi-objective problem of sustainable cultivation," Annals of Operations Research, Springer, vol. 314(2), pages 347-376, July.
    3. Youzhu Li & Jinsi Liu & Hongyu Yang & Jianxin Chen & Jason Xiong, 2021. "A Bibliometric Analysis of Literature on Vegetable Prices at Domestic and International Markets—A Knowledge Graph Approach," Agriculture, MDPI, vol. 11(10), pages 1-17, September.
    4. Regis Mauri, Geraldo, 2019. "Improved mathematical model and bounds for the crop rotation scheduling problem with adjacency constraints," European Journal of Operational Research, Elsevier, vol. 278(1), pages 120-135.
    5. Víctor M. Albornoz & Marcelo I. Véliz & Rodrigo Ortega & Virna Ortíz-Araya, 2020. "Integrated versus hierarchical approach for zone delineation and crop planning under uncertainty," Annals of Operations Research, Springer, vol. 286(1), pages 617-634, March.
    6. Pedro Munari & Reinaldo Morabito, 2018. "A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 437-464, October.
    7. Víctor M. Albornoz & Gabriel E. Zamora, 2021. "Decomposition-based heuristic for the zoning and crop planning problem with adjacency constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 248-265, April.
    8. Castagna, Andrés & Matonte, Federico & Mauttone, Antonio & Rodríguez-Gallego, Lorena & Blumetto, Oscar, 2024. "Land use planning to minimize the export of phosphorus: An optimization model for dairy production at a catchment area scale," Land Use Policy, Elsevier, vol. 138(C).
    9. Ana Esteso & M. M. E. Alemany & Angel Ortiz & Shaofeng Liu, 2022. "Optimization model to support sustainable crop planning for reducing unfairness among farmers," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 1101-1127, September.
    10. Aliano Filho, Angelo & A. Oliveira, Washington & Melo, Teresa, 2023. "Multi-objective optimization for integrated sugarcane cultivation and harvesting planning," European Journal of Operational Research, Elsevier, vol. 309(1), pages 330-344.

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