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A branch-and-price-and-cut approach for sustainable crop rotation planning

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  • Alfandari, Laurent
  • Plateau, Agnès
  • Schepler, Xavier

Abstract

In this paper, we study a multi-periodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received considerable attention in the literature in recent years. Crop cultivation and fallow periods must be scheduled on land plots over a given time horizon so as to minimize the total surface area of land used, while satisfying crop demands every period. This problem is proven strongly NP-hard. We propose a 0-1 linear programming formulation based on crop-sequence graphs. An extended formulation is then provided with a polynomial-time pricing problem, and a Branch-and-Price-and-Cut (BPC) algorithm is presented with adapted branching rules and cutting planes. The numerical experiments on instances varying the number of crops, periods and plots show the effectiveness of the BPC for the extended formulation compared to solving the compact formulation, even though these two formulations have the same linear relaxation bound.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:872-879
    DOI: 10.1016/j.ejor.2014.09.066
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    3. Ernst-August Nuppenau, 2018. "Soil Fertility Management by Transition Matrices and Crop Rotation: On Spatial and Dynamic Aspects in Programming of Ecosystem Services," Sustainability, MDPI, vol. 10(7), pages 1-20, June.
    4. 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.
    5. Schepler, Xavier & Rossi, André & Gurevsky, Evgeny & Dolgui, Alexandre, 2022. "Solving robust bin-packing problems with a branch-and-price approach," European Journal of Operational Research, Elsevier, vol. 297(3), pages 831-843.
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    8. 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.
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