Environment Systems and Decisions

, Volume 33, Issue 3, pp 427–439 | Cite as

Simulation and mathematical programming decision-making support for smallholder farming

  • Andrew J. CollinsEmail author
  • Kasi Bharath Vegesana
  • Michael J. Seiler
  • Patrick O’Shea
  • Prasanna Hettiarachchi
  • Frederic McKenzie


Many mathematical programs have been developed over the past 50 years to aid agricultural experts and other farming decision-makers. The application of these mathematical programs has seen limited success because their development has focused on mathematical theory as opposed to the requirements needed for application. This paper describes the development of two mathematical programs that were designed to integrate with a visualization simulation that aids a nontraditional group of agricultural decision-makers: illiterate Sri Lankan subsistence farmers. The simulation was designed to help these illiterate farmers make business decisions about their crop selection choices which, in turn, will help them develop their business plans required for obtaining bank micro-loans. This paper’s focus is on the use of linear programming as a potential tool to demonstrate the benefits of crop diversification and rotation to the farmer based on various available crop types. It also highlights the issues using such an approach.


Agriculture Farming Mathematical programming Modeling and simulation Visualization 



We would also like to thank the Old Dominion University’s Office of Research for their generous support of this project through their Multidisciplinary Seed Funding Program (ODU# 523521).


  1. Bandyopadhyay R, Datta S (1990) Applications of OR in developing economies: some Indian experiences. Eur J Oper Res 49(2):188–199CrossRefGoogle Scholar
  2. Beckert B, Hahnle R (1996) Deduction by combining semantic tableaux and integer programming. Proceedings of the 9th international conference of computer science logic (CSL’95), September 22nd–29th, Paderborn, Germany, pp 52–63Google Scholar
  3. Bullock DG (1992) Crop rotation. Crit Rev Plant Sci 11(4):309–326Google Scholar
  4. Butterworth K (1985) Practical application of linear/integer programming in agriculture. J Oper Res Soc 36(2):99–107Google Scholar
  5. Dogliotti S, van Ittersum MK, Rossing WAH (2005) A method for exploring sustainable development options at farm scale: a case study for vegetable farms in South Uruguay. Agric Syst 86(1):29–51CrossRefGoogle Scholar
  6. Doole GJ, Pannell DJ (2008) Optimisation of a large, constrained simulation model using compressed annealing. J Agric Econ 59(1):188–206CrossRefGoogle Scholar
  7. Dury J, Schaller N, Garcia F, Reynaud A, Bergez JE (2012) Models to support cropping plan and crop rotation decisions. A Review. Agron Sustain Dev 32(2):567–580CrossRefGoogle Scholar
  8. Goudriaan J, van Laar HH (1994) Modeling potential crop growth processes. Kluwer Academic Publishers, Dordrecht, the NetherlandsCrossRefGoogle Scholar
  9. Hassan I, Raza MA, Khalil M, Rehmat I (2004) Determination of optimum cropping patterns in the Faisalabad division (Pakistan). Int J Agric Biol 6(5):901–903Google Scholar
  10. Hazell PBR (1971) A linear alternative to quadratic and semi variance programming for farm planning under uncertainty. Am J Agric Econ 53(1):53–62CrossRefGoogle Scholar
  11. Hildreth C, Knowles GJ (1982) Some estimates of farmers’ utility functions. Technical bulletins. University of Minnesota, Agricultural Experiment Station.
  12. Hooker JN (2002) Logic, optimization, and constraint programming. INFORMS J Comput 14(4):295–321CrossRefGoogle Scholar
  13. Index Mundi (2012) Diammonium phosphate (DAP) fertilizer price over last year. (Accessed on 24 Oct 2012)
  14. Jolayemi JK, Olaomi JO (1995) A mathematical programming procedure for selecting crops for mixed-cropping schemes. Ecol Modell 79(1–3):1–9CrossRefGoogle Scholar
  15. Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Plenum, New York, pp 85–103CrossRefGoogle Scholar
  16. Klein Haneveld WK, Stegeman AW (2005) Crop succession requirements in agricultural production planning. Eur J Oper Res 166(2):406–429CrossRefGoogle Scholar
  17. Malabuyoc JA, Real JG, De Datta SK (1993) Grain yield as a function of rainfall, soil moisture and solar radiation in upland rice (Oryza Sativa L.). Field Crops Res 34(1):37–45CrossRefGoogle Scholar
  18. Mayer C (2003) Crop rotation. Franklin county cooperative extension. Penn State. Mimeo.
  19. Pap Z (2008) Crop rotation constraints in agricultural production planning. In 6th international symposium on intelligent systems and informatics, SISY 2008, pp 1–5Google Scholar
  20. Plà LM, Sandars DL, Higgins AJ (2013) A perspective on operational research prospects for agriculture. J Oper Res Soc. doi: 10.1057/jors.2013.45
  21. Qu H, Zhu Q, Fu H, Lu Z (2010) Virtual EP: a simulator of multi-agents-based virtual plant growth in response to environmental heterogeneity. J Simul 4(3):181–195CrossRefGoogle Scholar
  22. Qualizza A, Belotti P, Margot F (2012) Linear programming relaxations of quadratically constrained quadratic programs, mixed integer nonlinear programming 154. Springer, New York, pp 407–426CrossRefGoogle Scholar
  23. Rossing WAH, Jansma JE, De Ruijter FJ, Schans J (1997) Operationalizing sustainability: exploring options for environmentally friendly flower bulb production systems. Eur J Plant Pathol 103:217–234CrossRefGoogle Scholar
  24. Sarker RA, Talukdar S, Haque AFM (1997) Determination of optimum crop mix for crop cultivation in Bangladesh. Appl Math Model 21(10):621–632CrossRefGoogle Scholar
  25. Stockle CO, Martin SA, Campbell GS (1994) CropSyst, a cropping systems simulation model: water/nitrogen budgets and crop yield. Agric Syst 46(3):335–359CrossRefGoogle Scholar
  26. Teh C (2006) Introduction to mathematical modeling of crop growth: how the equations are derived and assembled into a computer program. Brown Walker Press, Boca Raton, FLGoogle Scholar
  27. The World Bank (2012) Fertilizer consumption (kilograms per hectare of arable land). (Accessed on 24 Oct 2012)
  28. Vegesana KB, Mckenzie FD (2013) Analysis of generic crop growth model for use in decision support systems for farmers. In Proceedings of 3rd international conference on photonics and image in agriculture engineering. Sanya, China, January 27–28Google Scholar
  29. Wiens TB (1976) Peasant risk aversion and allocative behavior: a quadratic programming experiment. Am J Agric Econ 58(4): 629–635CrossRefGoogle Scholar
  30. Winston WL (2003) Operations research applications and algorithms, 4th edn. Cengage Learning, Stamford, CTGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Andrew J. Collins
    • 1
    Email author
  • Kasi Bharath Vegesana
    • 1
  • Michael J. Seiler
    • 2
  • Patrick O’Shea
    • 3
  • Prasanna Hettiarachchi
    • 4
  • Frederic McKenzie
    • 1
  1. 1.Old Dominion UniversityNorfolkUSA
  2. 2.The College of William & MaryWilliamsburgUSA
  3. 3.Appalachian State UniversityBooneUSA
  4. 4.SaarakethaColomboSri Lanka

Personalised recommendations