Operational Research

, Volume 14, Issue 2, pp 253–260 | Cite as

Advantages of combining linear programming and weighted goal programming for agriculture application

  • Jernej Prišenk
  • Jernej Turk
  • Črtomir Rozman
  • Andreja Borec
  • Magdalena Zrakić
  • Karmen Pažek
Original Paper

Abstract

The aim of this paper is to present the basic characteristics of linear programing (LP) and weighted goal programming (WGP) to optimize processes on farms. Characteristics of both mathematical techniques are presented through the development of the crop planning model for solving some objective problems: maximizing financial results and minimizing different production costs on agricultural holdings. The model is structured from two sub-models, where the first based on linear programming and the second based on weighted goal programming are supported with penalty functions. The authors dispatch the weaknesses of LP with the application of WGP in the model and support this statement with results in this paper. The model was tested and validated on crop rotation with combinations of different field and vegetable crops in two different scenarios (WGPSC1 and WGPSC2) on a real agricultural holding in Slovenia. The results show that WGP combines more suitable crop rotation from an economic perspective than LP and provides a better solution for diversified and economically feasible crops that are included in the crop rotation. LP gives completely unacceptable results from the aspect of underachievement (for more than 100 %) of the maximum cropping area on a farm, while WGP completely satisfies all goals. From the obtained results in this paper, the authors identify several weaknesses of LP and present how it could be removed by applying the WGP technique.

Keywords

Crop planning model Linear programming Weighted goal programming Production costs 

References

  1. Babić Z, Perić T (2011) Optimization of livestock feed blend by use of goal programming. Int J Prod Econ 130:218–223CrossRefGoogle Scholar
  2. Ferguson EL, Darmon N, Fahmida U, Fitriyanti S, Harper TB, Premachandra IM (2006) Design of optimal food-based complementary feeding recommendations and identification of key “problem nutrients” using goal programming. J Nutr 136:2399–2404Google Scholar
  3. Gass S (1987) The setting of weights in linear goal-programming problems. Comput Oper Res 14(3):227–229CrossRefGoogle Scholar
  4. Harris P, Bishop REM (2007) Recent developments in equine nutrition and feeding. J R Agric Soc Engl 168:1–11Google Scholar
  5. Jafari H, Koshteli QR, Khabiri B (2008) An optimal model using goal programming for rice farm. Appl Math Sci 2(23):1131–1136Google Scholar
  6. Lara P, Romero C (1994) Relaxation of nutrient requirements on livestock rations through interactive multi-goal programming. Agric Syst 45:443–453CrossRefGoogle Scholar
  7. Lee H, Chambers RG (1986) Expenditure constraints and profit maximization in U.S. agriculture. Am J Agric Econ 68:857–865CrossRefGoogle Scholar
  8. Parsons JJ, Oja D, Ageloff R, Carey P (2008) New perspectives: Microsoft Office Excel 2007; comprehensive. Thomson Course Technology, USA, p 824Google Scholar
  9. Prišenk J, Pažek K, Rozman Č, Turk J, Janžekovič M, Borec A (2013) Application of weighted goal programming in optimization of rations for sport horses. J Anim Feed Sci 22:335–341Google Scholar
  10. Rehman T, Romero C (1984) Multiple-criteria decision-making techniques and their role in livestock ration formulation. Agric Syst 15:23–49CrossRefGoogle Scholar
  11. Sarker R, Ray T (2009) An improved evolutionary algorithm for solving multi-objective crop planning models. Comput Electron Agric 68(2):191–199CrossRefGoogle Scholar
  12. Sharma DK, Jana RK, Gaur A (2007) Fuzzy goal programming for agricultural land allocation problems. Yugosl J Oper Res 17(1):31–42CrossRefGoogle Scholar
  13. Taylor CR (1984) Stochastic dynamic duality: theory and empirical applicability. Amer. J. Agr. Econ. 66:351–357CrossRefGoogle Scholar
  14. Taylor CR (1989) Duality, optimization, and microeconomics theory: pitfalls for the applied researcher. West J Agric Econ 14(2):200–212Google Scholar
  15. Waugh FV (1951) The minimum-cost dairy feed. J Farm Econ 33:299–310CrossRefGoogle Scholar
  16. Žgajnar J, Erjavec E, Kavčič S (2010) Multi-step beef ration optimization: application of linear and weighted goal programming with a penalty function. Agric Food Sci 19:193–206CrossRefGoogle Scholar
  17. Zhang F, Roush WB (2002) Multiple-objective (goal) programming model for feed formulation: an example for reducing nutrient variation. Poult Sci 81:182–192CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jernej Prišenk
    • 1
  • Jernej Turk
    • 1
  • Črtomir Rozman
    • 1
  • Andreja Borec
    • 1
  • Magdalena Zrakić
    • 2
  • Karmen Pažek
    • 1
  1. 1.Faculty of Agriculture and Life SciencesUniversity of MariborHočeSlovenia
  2. 2.Faculty of AgricultureUniversity of ZagrebZagrebCroatia

Personalised recommendations