Extended Goal Programming Approach with Interval Data Uncertainty for Resource Allocation in Farm Planning: A Case Study

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 248)


This paper presents an extended version of goal programming (GP) approach for modeling and solving farm planning problems having objectives with interval parameter sets by utilizing farming resources in the planning horizon. In the model formulation of the problem, the defined goals with interval parameters are converted into conventional goals by using interval arithmetic technique in interval programming and introducing under- and over-deviational variables to each of them. In the decision process, extended GP (EGP) approach, i.e. convex combination of both the modelling aspects, minsum GP and minmax GP are addressed in the achievement function for minimizing the possible regret towards goal achievement from the optimistic point of view in the inexact decision making environment. The potential use of the approach is demonstrated via a case example.


Farm Planning Goal Programming Interval arithmetic Interval Programming 


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  1. 1.
    Heady, E.O.: Simplified Presentation and Logical Aspects of Linear Programming Technique. J. Farm Econ. 36, 1035–1048 (1954)CrossRefGoogle Scholar
  2. 2.
    Nix, J.: Farm Management - the State of the Art (or Science). J. Agri. Eco. 30, 277–292 (1979)CrossRefGoogle Scholar
  3. 3.
    Ignizio, J.P.: Goal Programming and Extensions, Lexington, D.C. Health, Massachusetts (1976)Google Scholar
  4. 4.
    Simon, H.A.: Administrative Behavior. Free Press, New York (1957)Google Scholar
  5. 5.
    Wheeler, B.M., Russell, J.R.M.: Goal Programming and Agricultural Planning. Oper. Res. Quar. 28, 21–32 (1977)CrossRefGoogle Scholar
  6. 6.
    Pal, B.B., Basu, I.: Selection of appropriate priority structure for optimal land allocation in agricultural planning through goal programming. Indian Journal of Agricultural Economics 51, 342–354 (1996)Google Scholar
  7. 7.
    Zimmermann, H.-J.: Fuzzy Sets, Decision Making and Expert Systems. Kluwer-Nijhoff Publishing, Dordrecht (1987)Google Scholar
  8. 8.
    Pal, B.B., Moitra, B.N., Maulik, U.: A Goal Programming Procedure for Fuzzy Multiobjective Linear Fractional Programming Problem. Fuzzy Sets and Systs. 139, 395–405 (2003)Google Scholar
  9. 9.
    Biswas, A., Pal, B.B.: Application of Fuzzy Goal Programming Technique to Land use Planning in Agricultural System. Omega 33, 391–398 (2005)CrossRefGoogle Scholar
  10. 10.
    Pal, B.B., Kumar, M., Sen, S.: A Linear Fuzzy Goal Programming Approach for Solving Patrol Manpower Deployment Planning Problems -A Case Study, pp. 244–249. IEEE Xplore Digital Library (2009)Google Scholar
  11. 11.
    Pal, B.B., Kumar, M.: A Linear Fuzzy Goal Programming Method for Solving Optimal Power Generation and Dispatch Problem. Int. J. Adv. Comp. Res. 3, 56–64 (2013)Google Scholar
  12. 12.
    Bitran, G.R.: Linear Multiobjective Problems with Interval Coefficients. Manag. Sci. 26, 694–706 (1980)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Jiang, C., Han, X., Liu, G.R., Liu, G.P.: A Nonlinear Interval Number Programming Method for Uncertain Optimization Problems. Euro. J. Oper. Res. 188, 1–13 (2008)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Inuiguchi, M., Kume, Y.: Goal Programming Problems with Interval Coefficients and Target Intervals. Euro. J. Oper. Res. 52, 345–361 (1991)CrossRefMATHGoogle Scholar
  15. 15.
    Oliviera, C., Antunes, C.H.: Multiple Objective Linear Programming Models with Interval Coefficients - An Illustrated Overview. Euro. J. Oper. Res. 118, 1434–1463 (2007)CrossRefGoogle Scholar
  16. 16.
    Pal, B.B., Kumar, M., Sen, S.: A Priority - Based Goal Programming Method for Solving Academic Personnel Planning Problems with Interval - Valued Resource Goals in University Management System. Int. J. Appl. Manag. Sci. 4, 284–312 (2012)CrossRefGoogle Scholar
  17. 17.
    Moore, R.E.: Interval Analysis. Prentice-Hall, New Jersey (1966)Google Scholar
  18. 18.
    Romero, C.: A General Structure of Achievement Function for a Goal Programming Model. Euro. J. Oper. Res. 153, 675–686 (2004)CrossRefMATHGoogle Scholar
  19. 19.
    Romero, C.: Handbook of Critical Issues in Goal Programming. Pergamon Press, Oxford (1991)Google Scholar
  20. 20.
    District Statistical Hand Book, Burdwan. Department of Bureau of Applied Economics and Statistics. Govt. of West Bengal, India (2011)Google Scholar
  21. 21.
    Economic Review. Department of Bureau of Applied Economics and Statistics. Govt. of West Bengal, IndiaGoogle Scholar
  22. 22.
    Basak, R.K.: Soil testing and fertilizer recommendation. Kalyani Publishers, New Delhi (2000)Google Scholar
  23. 23.

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KalyaniKalyaniIndia
  2. 2.Department of MathematicsAlipurduar CollegeAlipurduar CourtIndia

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