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Sustainable vegetable crop supply problem with perishable stocks

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Abstract

In this paper, we deal with a vegetable crop supply problem with two main particularities: (i) the production must respect certain ecologically-based constraints and (ii) harvested crops can be stocked but only for a limited period of time, given that they are perishable. To model these characteristics, we develop a linear formulation in which each variable is associated to a crop rotation plan. This model contains a very large number of variables and is therefore solved with the aid of a column generation approach. Moreover, we also propose a two-stage stochastic programming with recourse model which takes into consideration that information on the demands might be uncertain. We provide a discussion of the results obtained via computational tests run on instances adapted from real-world data.

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References

  • Ahumada, O., & Villalobos, J. R. (2009). Application of planning models in the agri-food supply chain: A review. European Journal of Operational Research, 196, 1–20.

    Article  Google Scholar 

  • Alem, D. J., Munari, P. A., Ferreira, P. A. V., & Arenales, M. N. (2010). On the cutting stock problem under stochastic demand. Annals of Operations Research, 179, 169–186.

    Article  Google Scholar 

  • Alfandari, L., Lemalade, J. L., Nagih, A., & Plateau, G. (2010). A MIP flow model for crop-rotation planning in a context of forest sustainable development. Annals of Operations Research. doi:10.1007/s10479-009-0553-0A (Forthcoming).

    Google Scholar 

  • Altieri, M. A. (1995). Agroecology: the science of sustainable agriculture. Boulder: Westview Press.

    Google Scholar 

  • Avriel, M., & Williams, A. C. (1970). The value of information and stochastic programming. Operations Research, 18, 947–954.

    Article  Google Scholar 

  • Bachinger, J., & Zander, P. (2006). ROTOR, a tool for generating and evaluating crop rotations for organic farming systems. European Journal Agronomy, 26, 130–143.

    Article  Google Scholar 

  • Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52, 35–53.

    Article  Google Scholar 

  • Birge, J. R. (1995). Models and model value in stochastic programming. Annals of Operations Research, 59, 1–18. Models for planning under uncertainty.

    Article  Google Scholar 

  • Birge, J. R., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.

    Google Scholar 

  • Costa, A. M., Cordeau, J.-F., & Laporte, G. (2009). Models and branch-and-cut algorithms for the Steiner tree problem with revenues, budget and hop constraints. Networks, 53, 141–159.

    Article  Google Scholar 

  • Dantzig, G. (1955). Linear programming under uncertainty. Management Science, 1, 197–206.

    Article  Google Scholar 

  • Detlefsen, N., & Jensen, A. L. (2007). Modelling optimal crop sequences using network flows. Agricultural Systems, 94, 566–572.

    Article  Google Scholar 

  • Du Merle, O., Villeneuve, D., Desrosiers, J., & Hansen, P. (1999). Stabilized column generation. Discrete Mathematics, 194, 229–237.

    Article  Google Scholar 

  • El-Nazer, T., & McCarl, B. A. (1986). The choice of crop rotation: A modeling approach and case study. American Journal of Agricultural Economics, 68, 127–136.

    Article  Google Scholar 

  • Escudero, L. F., Garín, A., Merino, M., & Pérez, G. (2007). The value of the stochastic solution in multistage problems. TOP, 15, 48–64.

    Article  Google Scholar 

  • Gliessman, S. R. (2000). Agroecology: ecological processes in sustainable agriculture. New York: Chelsea.

    Google Scholar 

  • Gouveia, L. (1999). Using hop-indexed models for constrained spanning and Steiner tree models. In B. Sansò & P. Soriano (Eds.), Telecommunications network planning (pp. 21–32). Dordrecht: Kluwer Academic.

    Chapter  Google Scholar 

  • Haneveld, W. K., & Stegeman, A. W. (2005). Crop succession requirements in agricultural production planning. European Journal of Operations Research, 166, 406–429.

    Article  Google Scholar 

  • Hildreth, C. G., & Reiter, S. (1951). On the choice of a crop rotation plan. In T. Koopmans (Ed.), Proceedings of the conference on linear programming held in Chicago in 1949 (pp. 177–188).

    Google Scholar 

  • ILOG (2006). ILOG CPLEX 10.1 Reference manual, ILOG.

  • Jones, J., Hoogenboom, G., Porter, C., Boote, K., Batchelor, W., Hunt, L., Wilkens, P., Singh, U., Gijsman, A., & Ritchie, J. (2003). The DSSAT cropping system model. European Journal of Agronomy, 18, 235–265.

    Article  Google Scholar 

  • Kall, P., & Wallace, S. (1994). Stochastic programming. New York: Wiley.

    Google Scholar 

  • Kantorovich, L. (1960). Mathematical methods of organizing and planning production. Management Science, 6, 366–422. (Translated from a report in Russian, dated 1939).

    Article  Google Scholar 

  • Liua, C., Fana, Y., & Ordònez, F. (2009). A two-stage stochastic programming model for transportation network protection. Computers & Operations Research, 36, 1582–1590.

    Article  Google Scholar 

  • Lübbecke, M. E., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, 53, 1007–1023.

    Article  Google Scholar 

  • Makatouni, A. (2002). What motivates consumers to buy organic food in the UK? Results from a qualitative study. British Food Journal, 104, 345–352.

    Article  Google Scholar 

  • Mulvey, J., Vanderbei, R., & Zenios, S. (1995). Robust optimization of large-scale systems. Operations Research, 43, 264–281.

    Article  Google Scholar 

  • Ong’wen, O., & Wright, S. (2007). Small farmers and the future of sustainable agriculture. Ecofair trade Dialogue, Discussion Paper n. 7.

  • Santos, L. M. R., Costa, A. M., Arenales, M. N., & Santos, R. H. S. (2010a). Sustainable vegetable crop supply problem. European Journal of Operational Research, 204, 639–647.

    Article  Google Scholar 

  • Santos, L. M. R., Michelon, P., Arenales, M. N., & Santos, R. H. S. (2010b). Crop rotation scheduling with adjacency constraints. Annals of Operations Research. doi:10.1007/s10479-008-0478-z (Forthcoming).

    Google Scholar 

  • Stöckle, C. O., Donatelli, M., & Nelson, R. (2003). CropSyst, a cropping systems simulation model. European Journal of Operations Research, 18, 289–307.

    Google Scholar 

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Correspondence to Alysson M. Costa.

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Costa, A.M., dos Santos, L.M.R., Alem, D.J. et al. Sustainable vegetable crop supply problem with perishable stocks. Ann Oper Res 219, 265–283 (2014). https://doi.org/10.1007/s10479-010-0830-y

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