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The Optimization of a Revenue Function in a Fuzzy Linear Programming Model Used for Industrial Production Planning

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, the S-curve membership function methodology is used in a reallife industrial problem in which there are various products, each of which requires a certain mix of raw materials selected from a set of available raw materials. This problem occurs in the chocolate manufacturing industry where decision makers and implementers play important roles that enable successful manufacturing of the products in an uncertain environment. The analysis in this paper tries to find a solution that helps a decision maker when deciding on what to implement. This problem is considered because it can be modeled with the help of fuzzy parameters (for example, the availability of raw materials is not always certain, and so can be treated as a fuzzy parameter). With 29 constraints and 8 variables the problem here is sufficiently large for the S-curve methodology employed because this methodology is applicable to problems with as few as 1 constraint and 1 variable. A decision maker can specify which vagueness parameter  is suitable for achieving a revenue which through the analysis results in an initial solution that can be implemented. From the results of this implementation the decision maker can then suggest some possible and practicable changes in fuzzy intervals for improving the revenue. Within the framework of the analysis this interactive process has to go on between the decision maker and the implementer until an optimum solution is achieved and implemented.
Rocznik
Strony
65--83
Opis fizyczny
Bibliogr. 31 poz., rys., tab.
Twórcy
autor
  • Universiti Teknologi Petronas, Electrical & Electronic Engineering Program, 31750 Tronoh, BSI, Perak DR, Malaysia
autor
  • School of Electrical and Computer Engineering, Curtin University of Technology, Miri, Sarawak, Malaysia
autor
  • Swinburne University of Technology, Sarawak Campus, Kuching, Sarawak, Malaysia
Bibliografia
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  • 3. H.K. Chen, H.W. Chou, Solving multi objective linear programming problems – A Generic Approach. Fuzzy Sets and Systems 82 (1996) 35-38
  • 4. A.N.S Freeling, Fuzzy sets and decision analysis. IEEE Transaction on Systems, Man and Cybernetics 10 (1980) 341-354
  • 5. J.A. Goguen, The logic of inexact concepts. Syntheses 19 (1969) 325-373.
  • 6. E.L. Hannan, Linear programming with multiple fuzzy goals. Fuzzy Sets and Systems 6 (1981) 235-248.
  • 7. C.F. Hu, S.C. Fang, Solving fuzzy inequalities with piecewise linear membership functions. IEEE Transactions On Fuzzy Systems 7 (1999) 230-235.
  • 8. A. Jeffery. Mathematics for Engineers And Scientists. Fifth Edition Chapman and Hall, London, 1996.
  • 9. Kuz’min,V. B. A Parametric Approach to Description of Linguistic Values of Variables and Hedges. Fuzzy Sets and Systems 6 (1981) 27-41.
  • 10. T.Y. Lai, C.L. Hwang, possibilistic linear programming for managing interest rate risk. Fuzzy Sets and Systems 54 (1993) 135-146.
  • 11. T.Y. Lai, C.L. Hwang, Fuzzy Multi Objective Decision Making: Methods and Applications, Spinger-Verlag, Berlin, 1994.
  • 12. H. Leberling, On finding compromise solutions in multicriteria problems using the fuzzy min-operator . Fuzzy Sets and Systems 6 (1981) 105-118.
  • 13. F.A. Lootsma, Fuzzy Logic For Planning And Decision Making, Kluwer Academic Publishers, Dordrecht/Boston/London, 1997.
  • 14. H.R. Maleki, M. Tata, M. Mashinchi, Linear programming with fuzzy variables. Fuzzy Sets and Systems 109 (2000) 21-33.
  • 15. N. Nowakowska, Methodological problems of measurement of fuzzy concepts in the social sciences. Behavioral Science 22 (1977) 107-115.
  • 16. P. Vasant, Solving fuzzy linear programming problems with modified scurve membership function. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13 (2005) 97-109.
  • 17. P. Vasant, Application of fuzzy linear programming in production planning. Fuzzy Optimization and Decision Making 3 (2003) 229-241.
  • 18. M.A. Parra, A.B. Terol, M.V. Rodrfguez Una, Theory and methodology solving the multi- objective possiblistic linear programming problem. European Journal of Operational Research 117 (1999) 175-182.
  • 19. H. Rommelfanger, Fuzzy linear programming and applications. European Journal of Operational Research 92 (1996) 512-527.
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  • 21. A. Sengupta, T.K. Pal, D. Chakraborty, Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets And Systems 119 (2001) 29-138.
  • 22. M.T. Tabucanon, Multi objective programming for industrial engineers. In Mathematical Programming for Industrial Engineers. eds. M. Avriel, B. Golany: Marcel Dekker, Inc, New York, 1996, pp. 487-542.
  • 23. J. Watada, Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematics Publication 13 (1997) 219-248.
  • 24. Y.K. Wu, S.M. Guu, Two phase approach for solving the fuzzy linear programming problems. Fuzzy Sets and Systems 107 (1999) 191-195.
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  • 26. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, II, III. Information Sciences 8 (1975) 199-251, 301-357 ; 9(1975)43-80.
  • 27. H. J. Zimmermann, Description and optimization of fuzzy system. International Journal of General Systems 2,(1976)209-215.
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  • 31. H. J. Zimmermann, Fuzzy Set Theory-and Its Applications. (2nd rev. ed.). Kluwer, Boston, 1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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