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Ulaştırma Modellerinde Can'ın Yaklaşım Metodunda Uygun Ortalama Seçimi İçin Simülasyon

Year 2023, Volume: 21 Issue: 1, 189 - 200, 28.03.2023
https://doi.org/10.18026/cbayarsos.1117589

Abstract

Klasik ulaştırma modelleri birim taşıma maliyetlerini göz önüne alarak homojen malların arz noktalarından talep noktalarına taşınma maliyeti toplamını minimize etmeyi amaçlamaktadır. Ulaştırma problemi, ağ modellerinin özel bir halidir ve doğrusal programlama temelli bir tekniktir. Başlangıç dağıtım yöntemlerinden Tuncay Can yaklaşım metodu 2015 yılında geliştirilmiş bir metottur. Yöntem, birim taşıma maliyetlerinin geometrik ortalamalarının alınması esasına dayanmakla birlikte teoremde yöntem uygulanırken geometrik ortalamalar yerine farklı ortalamaların da kullanılabileceği belirtilmiştir. Bu çalışmanın amacı, Tuncay Can Yaklaşım Metodunu (TCYM) temel alarak, yöntemin belirttiği şekilde birim maliyetlerin geometrik ortalamalarının alınması ve ayrıca aritmetik, kareli ve harmonik ortalama kullanılarak da yöntemin uygulanması ile elde edilen toplam maliyetleri minimize eden başlangıç dağıtım planı incelenerek hangi ortalamada optimal sonuç verdiğini ortaya koymaktır. Bu amaca yönelik olarak kurulan ulaştırma modelinin katsayıları simülasyon yardımıyla rassal olarak değiştirilmiş ve yöntem farklı ortalamalara göre problem üzerinde tekrarlanarak, optimal toplam maliyet değerleri karşılaştırılmış ve uygun ortalama tespit edilmiştir.

References

  • Barthelemy, J.-F. M. & Haftka, R. T. (1993). Approximation Concepts for Optimum Structural Design - A Review, Structural Optimization, 5, 129-144.
  • Box, G. E. P. & Draper, N. R. (1969). Evolutionary Operation: A Statistical Method for Process Management, New York, John Wiley & Sons.
  • Can, T. (2015). Yöneylem Araştırması: Nedensellik Üzerine Diyaloglar 1. Istanbul: Beta Yayınları.
  • Can, T. & Koçak, H. (2016). Tuncay Can’s Approximation Method to obtain initial basic feasible solution to transport problem, Applied and Computational Mathematics, 5(2), 78-82.
  • Dantzig, G.B. & Thapa, M.N. (1997). Linear Programming 1: Introduction. New York: Springer-Verlag.
  • Dantzig, G.B. & Thapa, M.N. (2003). Linear Programming 2: Theory and Extensions. New York: Springer.
  • Karagül, K. & Şahin, Y. (2019). A Novel Approximation Method to Obtain Initial Basic Feasible Solution of Transportation Problem, Journal of King Saud University-Engineering Sciences, https://doi.org/10.1016/j.jksues.2019.03.003.
  • Koch, P. N., Simpson, T. W., Allen, J. K. & Mistree, F. (1999). Statistical Approximations for Multidisciplinary Optimization: The Problem of Size, Special Multidisciplinary Design Optimization Issue of Journal of Aircraft, 36( 1), 275-286.
  • Korukoğlu, S. & Ballı, S. (2011). An Improved Vogel’s Approximation Method for the Transportation Problem, Mathematical and Computational Applications, 16 (2), 370-381.
  • Luenberger, D.G. & Ye, Y. (2008). Linear and Nonlinear Programming (3rd ed.). New York: Springer-Verlag.
  • Mathirajan, M. & Meenakshi, B. (2004). Experimental Analysis of Some Variants of Vogel's Approximation Method, Asia-Pacific Journal of Operational Research, 21(4), 447-462.
  • Plackett, R. L. & Burman, J. P. (1946). The Design of Optimum Multifactorial Experiments, Biometrika, 33(4), 305-325.
  • Simpson, T. W., Peplinski, J., Koch, P. N. & Allen, J. K. (2001). Metamodels for Computer-based Engineering Design: Survey and Recommendations, Engineering with Computers, 17(2), 129-150.
  • Somenath, S. (2016). TransP: Implementation of Transportation Problem Algorithms. R package version 0.1.

Simulation for Appropriate Mean Selection for Can's Approximation Method in Transportation Models

Year 2023, Volume: 21 Issue: 1, 189 - 200, 28.03.2023
https://doi.org/10.18026/cbayarsos.1117589

Abstract

Classical transportation models aim to minimize the total costs of homogeneous goods transport from supply points to demand points, taking into account unit transportation costs. They constitute a special case of network models and employ a technique based on linear programming. Suggested in 2015 and one of the early distribution methods, Tuncay Can’s Approximation Method (TCAM) is based on the geometric averages of unit transportation costs, although it is stated in the theorem that other means than geometric can be used. The aim of this study is to compare the total costs of a transportation model by solving a problem using geometric, arithmetic, square, and harmonic means based on TCAM. The coefficients of the transportation model were obtained randomly by simulation, and the method was repeated on the problem according to the different means and the appropriate means determined.

References

  • Barthelemy, J.-F. M. & Haftka, R. T. (1993). Approximation Concepts for Optimum Structural Design - A Review, Structural Optimization, 5, 129-144.
  • Box, G. E. P. & Draper, N. R. (1969). Evolutionary Operation: A Statistical Method for Process Management, New York, John Wiley & Sons.
  • Can, T. (2015). Yöneylem Araştırması: Nedensellik Üzerine Diyaloglar 1. Istanbul: Beta Yayınları.
  • Can, T. & Koçak, H. (2016). Tuncay Can’s Approximation Method to obtain initial basic feasible solution to transport problem, Applied and Computational Mathematics, 5(2), 78-82.
  • Dantzig, G.B. & Thapa, M.N. (1997). Linear Programming 1: Introduction. New York: Springer-Verlag.
  • Dantzig, G.B. & Thapa, M.N. (2003). Linear Programming 2: Theory and Extensions. New York: Springer.
  • Karagül, K. & Şahin, Y. (2019). A Novel Approximation Method to Obtain Initial Basic Feasible Solution of Transportation Problem, Journal of King Saud University-Engineering Sciences, https://doi.org/10.1016/j.jksues.2019.03.003.
  • Koch, P. N., Simpson, T. W., Allen, J. K. & Mistree, F. (1999). Statistical Approximations for Multidisciplinary Optimization: The Problem of Size, Special Multidisciplinary Design Optimization Issue of Journal of Aircraft, 36( 1), 275-286.
  • Korukoğlu, S. & Ballı, S. (2011). An Improved Vogel’s Approximation Method for the Transportation Problem, Mathematical and Computational Applications, 16 (2), 370-381.
  • Luenberger, D.G. & Ye, Y. (2008). Linear and Nonlinear Programming (3rd ed.). New York: Springer-Verlag.
  • Mathirajan, M. & Meenakshi, B. (2004). Experimental Analysis of Some Variants of Vogel's Approximation Method, Asia-Pacific Journal of Operational Research, 21(4), 447-462.
  • Plackett, R. L. & Burman, J. P. (1946). The Design of Optimum Multifactorial Experiments, Biometrika, 33(4), 305-325.
  • Simpson, T. W., Peplinski, J., Koch, P. N. & Allen, J. K. (2001). Metamodels for Computer-based Engineering Design: Survey and Recommendations, Engineering with Computers, 17(2), 129-150.
  • Somenath, S. (2016). TransP: Implementation of Transportation Problem Algorithms. R package version 0.1.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Naciye Tuba Yılmaz Soydan 0000-0002-4009-9047

Ahmet Çilingirtürk 0000-0001-8677-7969

Tuncay Can 0000-0002-4169-2563

Publication Date March 28, 2023
Published in Issue Year 2023 Volume: 21 Issue: 1

Cite

APA Yılmaz Soydan, N. T., Çilingirtürk, A., & Can, T. (2023). Simulation for Appropriate Mean Selection for Can’s Approximation Method in Transportation Models. Manisa Celal Bayar Üniversitesi Sosyal Bilimler Dergisi, 21(1), 189-200. https://doi.org/10.18026/cbayarsos.1117589