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Integer Solutions via Goal Programming to Hierarchical Systems

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Abstract

Decision making to a hierarchical system is a difficult task in general, if several levels and large number of decision variables are involved in a system. The difficulty further increases if some or all the decision variables are restricted to discrete values. To this end Goal Programming provides a suitable answer. In this paper, we first establish goal programming model to the hierarchical systems. Then integer goal programming method is applied to find the solution. Finally, we demonstrate the solution procedure of the proposed method using numerical examples for different types of hierarchical systems. We are interested in purely integer solutions only.

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References

  1. Anandalingam G. “A Mathematical Programming Model of Decentralized Multi-Level Systems”. J Opl Res Soc, 39/11 (1988) 1021–1033.

    Article  Google Scholar 

  2. Anandlingam G and Apprey V. “Multi-level programming and conflict resolution”. European J Opl Res, 51 (1991) 233–247.

    Article  Google Scholar 

  3. Bard JF and Falk JE. “An explicit solution to the multi-level programming problem”. Computers Ope Res, 9 (1982) 77–100.

    Article  Google Scholar 

  4. Bialas WF and Karwan MH. “Two-level linear programming”. Mgmt Sc, 30 (1984) 1004–1020.

    Article  Google Scholar 

  5. Ben-ayed O et al. “Construction of a real-world bilevel linear programming model of the highway network design problem”. Annals Ope Res, 34 (1992) 219–254.

    Article  Google Scholar 

  6. Dakin RJ. “A Tree Search Algorithm for Mixed Integer Programming Problems”. (1966) 250–255.

  7. Gomory RE. “An Algorithm for Integer Solutions to Linear Programs”. In: Graves RL and Wolfe P (eds). Recent Advances in Mathematical Programming, McGraw Hill, New York (1963) 269–302.

    Google Scholar 

  8. Hilljer FS and Lieberman GJ. “Introduction to Operations Research”. McGraw Hill Inc (1995).

    Google Scholar 

  9. Hobbs BF and Nelson SK. “A nonlinear bilevel model for analysis of electricity utility demand-side planning issues”. Annals Ope Res, 34 (1992) 255–274.

    Article  Google Scholar 

  10. Homburg C. “Hierarchical multi-objective decision making”. European J Opl Res, 105 (1998) 155–161.

    Article  Google Scholar 

  11. Ignizio James P. “Goal Programming and Extensions”. Lexington Books, D.C. Heath & Co., Massachusetts (1976).

    Google Scholar 

  12. Karlof JK and Wang W. “Bilevel Programming applied to the flow shop scheduling problem”. Copmuters Ope Res, 23/5 (1996) 443–451.

    Article  Google Scholar 

  13. Land A and Doig A. “An Automatic Method for Solving Discrete Programming Problems”. Econometrica, 28 (1960) 497–520.

    Article  Google Scholar 

  14. Liu YH and Spencer T. “Solving a bilevel linear program when the inner decision maker controls a few Variables”. European J Opl Res, 81 (1995) 644–651.

    Article  Google Scholar 

  15. Onal H. “A modified simplex approach for solving bilevel linear programming problems”. European J Opl Res, 67 (1993) 126–135.

    Article  Google Scholar 

  16. Parker RG and Rardin RL. “Discrete Optimization”. Academic Press, San Diego (1988).

    Google Scholar 

  17. Saaty TL. “The Analytic Hierarchy Process: Planning, Priority Setting, and Resource Allocation”. RWS Publication, Pittsburgh (1990).

    Google Scholar 

  18. Sakawa M, Nishizaki I and Hitaka M. “Interactive fuzzy programming for multi-level 0-1 programming problems through genetic algorithms”. European J Opl Res, 114 (1999) 580–588.

    Article  Google Scholar 

  19. Sakawa M, I and Uemura Y “Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters”. Fuzzy Sets and Sys, 109/1 (2000) 3–19.

    Article  Google Scholar 

  20. Shih Hsu-Shih, Lai Young-Jou and Lee E Stanley. “Fuzzy Approach for Multi-Level Programming Problems”. Computers Ope.Res, 23/1 (1996) 73–91.

    Article  Google Scholar 

  21. Suh S and Kim T. “Solving Non-linear bilevel programming models of the highway network design problem: A comparative review”. Annals Ope Res, 34 (1992) 203–218.

    Article  Google Scholar 

  22. Taha Hamdy A. “Operations Research An Introduction”. Prentice-Hall Inc. New Delhi (1997).

    Google Scholar 

  23. Unlu G. “A linear bilevel programming algorithm based on bicriteria programming”. Computers Ope Res, 14 (1987) 173–179.

    Article  Google Scholar 

  24. White DJ. “Multilevel Programming, Rational Reaction Sets, and Efficient Solutions”. J Opt Theory and Appl, 87/3 (1995) 727–746.

    Article  Google Scholar 

  25. White DJ. “Solving bi-level linear programmes”. J of Mathematical Anal and Appl, 200/1 (1996) 254–258.

    Article  Google Scholar 

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Authors and Affiliations

  1. Dept of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India

    Surabhi Sinha & M. P. Biswal

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  1. Surabhi Sinha
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  2. M. P. Biswal
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Sinha, S., Biswal, M.P. Integer Solutions via Goal Programming to Hierarchical Systems. OPSEARCH 37, 204–220 (2000). https://doi.org/10.1007/BF03398613

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