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Q-Taylor method for multiobjective fractional programming problem

Year 2019, Issue: 16, 26 - 31, 31.08.2019
https://doi.org/10.31590/ejosat.540089

Abstract

In this work, we have
proposed a solution to Multi Objective Lineer Fractional Programming Problem
(MOLFPP) by using the first-order q-Taylor expansion of these objective
functions at optimal points of each fractional objective functions in feasible
region. In q-calculus, q-Taylor series is a q-series expansion of a function
with respect to q-derivatives. MOFPP reduces to an equivalent Multi Objective
Linear Programming Problem (MOLPP). The resulting MOLPP is solved assuming that
weights of these objective functions are equal and considering the sum of the
these objective functions. Thus, the problem is reduced to a single objective.
The proposed solution to MOFPP always yields efficient solution. Therefore, the
complexity in solving MOFPP has reduced and to show the efficiency of the
q-Taylor series method, we applied the method to a problem
.

References

  • Bitran G.R., Novaes A.G. (1973). Linear programming with a fractional objective function, Operation Research (21) 22–29.
  • Craven B.D. (1988). Fractional Programming, Heldermann Verlag, Berlin,
  • Charnes A., Cooper W. (1962). Programming with linear fractional functions, Naval Research Logistics Quarterly (9) 181-186.
  • Kac V., Cheung P. (2002). Quantum Calculus, Springer, New York,
  • Kornbluth J.S.H., Steuer R.E. (1981). Multiple objective linear fractional programming, Management Science (27) 1024–1039.
  • Nykowski I., Zolkiski Z. (1985). A compromise procedure for the multiple objective linear fractional programming problem, European Journal of Operational Research (19) 91–97.
  • Rajkovic P.M., Stankovic M.S., Marinkovic S.D. (2003). On q-iterative methods for solving equations and systems. Novi Sad J.Math (33) 127-137.
  • Saad O. (2007). On stability of proper efficient solutions in multiobjective fractional programming problems under fuzziness, Mathematical and Computer Modelling (45) 221–231.
  • M. Sakawa, K. Kato, Interactive decision-making for multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers, Fuzzy Sets and Systems 97 (1988) 19--31.

Çokamaçlı Kesirli Programlama Problemleri için Q- Taylor Metodu

Year 2019, Issue: 16, 26 - 31, 31.08.2019
https://doi.org/10.31590/ejosat.540089

Abstract

Bu çalışmada, çok amaçlı
lineer kesirli programlama problemlerinin (ÇALKPP) çözümleri için uygun
bölgedeki herbir kesirli amaç fonksiyonunun optimal noktalarında amaç
fonksiyonlarının birinci dereceden -Taylor seri açılımları
sunulmuştur. Q-Analizde, -Taylor serisi -Türevlerine göre
bir fonksiyonun -Serisine
genişlemesidir. ÇALKPP problemi, kendisine denk olan çok amaçlı lineer programlama
problemlerini (ÇALPP) problemine indirgendi. Amaç fonksiyonlarının
ağırlıklarının eşit olduğu kabulü altında ÇALPP çözüldü. Böylece problem tek
amaca indirgenmiş oldu. Sunulan metot ile elde edilen çözümler etkin
çözümlerdir. Bu sayede ÇALPP problemlerinin çözümündeki karmaşıklık giderilmiş
olundu ve sunulan metodun etkinliğini göstermek için bir problem üzerinde
uygulanması yapıldı.

References

  • Bitran G.R., Novaes A.G. (1973). Linear programming with a fractional objective function, Operation Research (21) 22–29.
  • Craven B.D. (1988). Fractional Programming, Heldermann Verlag, Berlin,
  • Charnes A., Cooper W. (1962). Programming with linear fractional functions, Naval Research Logistics Quarterly (9) 181-186.
  • Kac V., Cheung P. (2002). Quantum Calculus, Springer, New York,
  • Kornbluth J.S.H., Steuer R.E. (1981). Multiple objective linear fractional programming, Management Science (27) 1024–1039.
  • Nykowski I., Zolkiski Z. (1985). A compromise procedure for the multiple objective linear fractional programming problem, European Journal of Operational Research (19) 91–97.
  • Rajkovic P.M., Stankovic M.S., Marinkovic S.D. (2003). On q-iterative methods for solving equations and systems. Novi Sad J.Math (33) 127-137.
  • Saad O. (2007). On stability of proper efficient solutions in multiobjective fractional programming problems under fuzziness, Mathematical and Computer Modelling (45) 221–231.
  • M. Sakawa, K. Kato, Interactive decision-making for multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers, Fuzzy Sets and Systems 97 (1988) 19--31.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Adem Çevikel 0000-0002-7359-3156

Muttalip Özavşar This is me

Publication Date August 31, 2019
Published in Issue Year 2019 Issue: 16

Cite

APA Çevikel, A., & Özavşar, M. (2019). Q-Taylor method for multiobjective fractional programming problem. Avrupa Bilim Ve Teknoloji Dergisi(16), 26-31. https://doi.org/10.31590/ejosat.540089