Journal of the Operational Research Society

, Volume 58, Issue 11, pp 1470–1479 | Cite as

Energy crop supply in France: a min-max regret approach

Case-Oriented Paper


This paper attempts to estimate energy crop supply using a linear programming (LP) model comprising hundreds of representative farms of the arable cropping sector in France. In order to enhance the predictive ability of such a model and to provide an analytical tool useful to policy makers, interval linear programming is used to formalize bounded rationality conditions. In the presence of uncertainty related to yields and prices, it is assumed that the farmer may adopt a min-max regret (MMR) criterion as an alternative to the classic profit maximization criterion. Recent advances in operational research are exploited, permitting an efficient implementation of the min-max criterion within an LP model. Model validation based on observed activity levels suggests that about 40% of the farms adopt the MMR criterion. Energy crop supply curves generated by the MMR model prove to be upward-sloped, like classic LP supply curves.


interval linear programming min-max regret energy crops France 


  1. Bitran G (1980). Linear multiple objective problems with interval coefficients. Mngt Sci 26: 694–705.CrossRefGoogle Scholar
  2. Brooke A, Kendrick D, Meeraus A and Raman R (1998). GAMS, A User's Guide. GAMS Development Corporation: Washington, DC.Google Scholar
  3. Chinneck JW and Ramadan K (2000). Linear programming with interval coefficients. J Opl Res Soc 51: 209–220.CrossRefGoogle Scholar
  4. Hardaker JB, Huirne RBM and Anderson JR (1997). Coping with Risk in Agriculture. CAB International: Wallingford, UK.Google Scholar
  5. Hazell P and Norton RD (1986). Mathematical Programming for Economic Analysis in Agriculture. Macmillan: New York.Google Scholar
  6. Inuiguchi M and Sakawa M (1995). Minmax regret solutions to linear programming problems with an interval objective function. Eur J Opl Res 86: 526–536.CrossRefGoogle Scholar
  7. Ishibuchi H and Tanaka H (1990). Multi-objective programming in the optimization of the interval objective function. Eur J Opl Res 48: 219–225.CrossRefGoogle Scholar
  8. Kazakçi OA and Vanderpooten D (2002). Modelling the uncertainty about crop prices and yields using intervals: The min-max regret approach. In: Rozakis S. and Sourie J-C (eds). Options Méditerannéenes, Special Issue ‘Comprehensive modeling of bio-energy systems', Serie A, Vol. 48, CIHEAM, MAI Chania, pp 9–22.Google Scholar
  9. Lehtonen H (2001). Principles, structure and application of dynamic regional sector model of Finnish agriculture. PhD thesis, Agrifood Research Finland Economic Research (MTTL), Publications 98.Google Scholar
  10. Loomes G and Sugden R (1982). Regret theory: An alternative theory of rational choice under uncertainty. Econom J 92: 805–824.Google Scholar
  11. Mausser HE and Laguna M (1998). A new mixed integer formulation for the maximum regret problem. Int Trans Opl Res 5: 389–403.CrossRefGoogle Scholar
  12. Mausser HE and Laguna M (1999a). A heuristic to mini-max absolute regret for linear programs with interval objective function coefficients. Eur J Opl Res 117: 157–174.CrossRefGoogle Scholar
  13. Mausser HE and Laguna M (1999b). Minimizing the maximum relative regret for linear programmes with interval objective function coefficients. J Opl Res Soc 50: 1063–1070.CrossRefGoogle Scholar
  14. Rommelfanger H (1989). Linear programming with fuzzy objectives. Fuzzy Sets and Systems 29: 31–48.CrossRefGoogle Scholar
  15. Shaocheng T (1994). Interval number and fuzzy number linear programming. Fuzzy Sets and Systems 66: 301–306.CrossRefGoogle Scholar
  16. Shimizu K and Aiyoshi E (1980). Necessary conditions for min max problems and algorithms by a relaxation procedure. IEEE Trans Automat Control 25: 62–66.CrossRefGoogle Scholar
  17. Simon H (1979). Rational decision making in business organisations. Amer Econom Rev 69: 493–513.Google Scholar
  18. Sourie J-C (2002). Agricultural raw materials cost and supply for biofuel production: Methods and concepts. In: Rozakis S. and Sourie J-C (eds). Options Méditerannéenes, Special Issue ‘Comprehensive modeling of bio-energy systems', Serie A, Vol. 48, CIHEAM, MAI Chania, pp 3–8.Google Scholar
  19. Sourie J-C, Millet G, Kervegant E and Bonnafous P (2000). Incidences de l'Agenda 2000 sur l'offre de ceréales, d'oléagineux et de protéagineux. Applications du modèle MAORIE. Etudes Economiques 38. INRA: Grignon.Google Scholar
  20. Sourie J-C and Rozakis S (2001). Bio-fuel production system in France: An economic analysis. Biomass and Bio-energy 20: 483–489.CrossRefGoogle Scholar
  21. Steuer R (1981). Algorithms for linear programming problems with interval objective function coefficients. Math Opns Res 6: 333–349.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.Université Paris DauphineFrance
  2. 2.Agricultural University of AthensGreece

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