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A two-stage stochastic programming model for scheduling replacements in sow farms

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Abstract

This paper presents a formulation and resolution of a two-stage stochastic linear programming model with recourse for sow farms producing piglets. The proposed model considers a medium-term planning horizon and specifically allows optimal replacement and schedule of purchases to be obtained for the first stage. This model takes into account sow herd dynamics, housing facilities, reproduction management, herd size with initial and final inventory of sows and uncertain parameters such as litter size, mortality and fertility rates. These last parameters are explicitly incorporated via a finite set of scenarios. The proposed model is solved by using the algebraic modelling software OPL Studio from ILOG, in combination with the solver CPLEX to solve the linear models resulting from different instances considered. The article also presents results obtained with previous deterministic models assessing the suitability of the stochastic approach. Finally, the conclusions drawn from the study including an outlook are presented.

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References

  • Albornoz VM, Canales C (2006) Total allowable catch for managing squat lobster fishery using stochastic nonlinear programming. Comput Oper Res 33:2113–2124

    Article  Google Scholar 

  • Albornoz VM, Contesse L (1999) Modelos de Optimización Robusta un Problema de Planificación Agregada de la Producción bajo Incertidumbre en las Demandas. Invest Oper 7(3):1–15

    Google Scholar 

  • Alonso-Ayuso A, Escudero L, Ortuño MT (2005) Modelling production planning and scheduling under uncertainty. In: Wallace SW, Ziemba WT (eds) Applications of stochastic programming. SIAM, Philadelphia

    Google Scholar 

  • Beale EML (1955) On minimizing a convex function subject to linear inequalities. J R Stat Soc, Ser B 17:173–184

    Google Scholar 

  • Birge JR, Louveaux FV (1997) Introduction to stochastic programming. Springer, New York

    Google Scholar 

  • Dantzig GB (1955) Linear programming under uncertainty. Manag Sci 1:197–206

    Article  Google Scholar 

  • Escudero L, Kamesan P, King A, Wets R (1993) Production planning via scenarios modelling. Ann Oper Res 43:311–335

    Google Scholar 

  • Gupta A, Maranas CD (2003) Managing demand uncertainty in supply chain planning. Comput Chem Eng 27:1219–1227

    Article  Google Scholar 

  • Huirne RB, Dijkhuizen AA, Van Beek P, Hendriks THB (1993) Stochastic dynamic programming to support sow replacement decisions. Eur J Oper Res 67:161–171

    Article  Google Scholar 

  • Jalvingh AW, Dijkhuizen AA, van Arendonk JAM (1992) Dynamic probabilistic modelling of reproduction and management in sow herds. General aspects and model description. Agric Syst 39:133–152

    Article  Google Scholar 

  • Kingwell R (1996) Programming models of farm supply response: the impact of specification errors. Agric Syst 50:307–324

    Article  Google Scholar 

  • Kristensen AR (1988) Hierarchic Markov processes and their applications in replacement models. Eur J Oper Res 35:207–215

    Article  Google Scholar 

  • Kristensen AR (1993) Markov decision techniques applied to the animal replacement problem. DrSc dissertation, Dina KVL Dep of Animal Science and Animal Helth, The Royal Veterinary and Agricultural University, Copenhagen, Denmark

  • Mula J, Poler R, García-Sabater JP, Lario FC (2006) Models for production planning under uncertainty: A review. Int J Prod Econ 103:271–285

    Article  Google Scholar 

  • Plà LM (2007) Review of mathematical models for sow herd management. Livest Sci 106:107–119

    Article  Google Scholar 

  • Plà LM, Faulin J, Rodríguez S (2008) A linear programming formulation of a semi-Markov model to design pig facilities. J Oper Res Soc Advance online publication 16 April 2008; doi:10.1057/palgrave.jors.2602599

  • Rodríguez SV, Albornoz VM, Plà LM (2008) A mixed-integer linear programming model for scheduling replacements and purchases in sow farms. Technical report, Mathematic Department, University of Lleida

  • Rowland WW, Langemeier MR, Schurle BW, Featherstone AM (1998) A nonparametric efficiency analysis for a sample of Kansas swine operations. J Agric Appl Econ 30:189–199

    Article  Google Scholar 

  • Ruszczynski A, Shapiro A (eds) (2003) Stochastic programming. Handbook in operations research and management science, vol 10. North-Holland, Amsterdam

    Google Scholar 

  • Wallace SW, Ziemba WT (eds) (2005) Applications of stochastic programming. SIAM, Philadelphia

    Google Scholar 

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Correspondence to Lluís M. Plà.

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Rodríguez, S.V., Albornoz, V.M. & Plà, L.M. A two-stage stochastic programming model for scheduling replacements in sow farms. TOP 17, 171–189 (2009). https://doi.org/10.1007/s11750-009-0087-2

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  • DOI: https://doi.org/10.1007/s11750-009-0087-2

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