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HEDEF PROGRAMLAMA İLE BELİRLENMEYEN ORTAM KAPSAMINDA SAĞLAM TAŞIMA SORUNLARINI ÇÖZMEK

Yıl 2022, Cilt: 33 Sayı: 1, 130 - 144, 30.04.2022

Öz

Bir nakliye sorunu, birden çok hedefi, birden çok ürünü ve birden çok nakliyeyi içerebilir. Bu tür ulaşım sorunları, çok amaçlı çok öz nitelikli katı taşımacılık sorunları (MMSTP) olarak adlandırılır. Bu çalışmada arz ve talebin belirsiz olduğu MMSTP için hedef programlamaya dayalı bir çözüm önerilmiştir. Ayrıca belirsizliği ele almak için 0,6 ile 0,9 arasında değişen farklı belirsizlik parametreleri kullanılmıştır. Daha sonra elde edilen bu parametrelerle elde edilen sonuçlar maliyet fonksiyonu değerleri kullanılarak karşılaştırılmıştır. Sonuçlar, belirsizlik parametresi azaldığında maliyetin arttığını göstermektedir. Son olarak, bir örnek aracılığıyla bu model kullanılarak optimal bir çözüm bulunabileceği gösterilmiştir.

Kaynakça

  • Baidya, A, and U. K. Bera. 2014. “An Interval Valued Solid Transportation Problem with Budget Constraint in Different Interval Approaches.” Journal of Transportation Security 7(2): 147–55.
  • Baidya, Abhijit, Uttam Kumar Bera, and Manoranjan Maiti. 2013. “A Solid Transportation Problem with Safety Factor under Different Uncertainty Environments.” Journal of Uncertainty Analysis and Applications 1(1): 18.
  • Baidya, A., Bera, U. K., & Maiti, M.. 2015. “Interval Oriented Entropy Based Multi-Item Solid Transportation Problem with Budget and Breakability.” International Journal of Applied and Computational Mathematics 1(2): 279–92.
  • Bit, AK, MP Biswal, and SS Alam. 1993. “Fuzzy Programming Approach to Multiobjective Solid Transportation Problem.” Fuzzy sets and systems 57(2): 183–94.
  • Chakraborty, Dipankar, Dipak Kumar Jana, and Tapan Kumar Roy. 2014. “Multi-Objective Multi-Item Solid Transportation Problem with Fuzzy Inequality Constraints.” Journal of Inequalities and Applications 2014(1): 338.
  • Charnes, A, and WW Cooper. 1961. Management Models and Industrial Applications of Linear Programming. New York: John Wiley and Sons Inc.
  • Charnes, Abraham, and WW135619 Cooper. 1962. “Chance Constraints and Normal Deviates.” Journal of the American statistical association 57(297): 134–48.
  • Chen, Lin, Jin Peng, and Bo Zhang. 2017. “Uncertain Goal Programming Models for Bicriteria Solid Transportation Problem.” Applied Soft Computing 51: 49–59.
  • Chen, Yueh-Li, Long-Hui Chen, and Chien-Yu Huang. 2009. “Fuzzy Goal Programming Approach to Solve the Equipment-Purchasing Problem of an FMC.” International journal of industrial engineering: theory, applications and practice 164.
  • Cui, Qing, and Yuhong Sheng. 2012. “Uncertain Programming Model for Solid Transportation Problem.” Information 15(12): 342–48. Dalman, Hasan. 2019. “Entropy-Based Multi-Item Solid Transportation Problems with Uncertain Variables.” Soft Computing 23(14): 5931–43.
  • Dalman, Hasan, Nuran Güzel, and Mustafa Sivri. 2016. “A Fuzzy Set-Based Approach to Multi-Objective Multi-Item Solid Transportation Problem under Uncertainty.” International Journal of Fuzzy Systems 18(4): 716–29.
  • Das, Amrit, and Uttam Kumar Bera. 2015. “A Bi-Objective Solid Transportation Model under Uncertain Environment.” Facets of uncertainties and applications. Springer, New Delhi: 261–75.
  • Das, Amrit, Uttam Kumar Bera, and Manoranjan Maiti. 2018. “Defuzzification and Application of Trapezoidal Type-2 Fuzzy Variables to Green Solid Transportation Problem.” Soft Computing 22(7): 2275–97.
  • Das, A., Bera, U. K., & Maiti, M. . 2019. “A Solid Transportation Problem in Uncertain Environment Involving Type-2 Fuzzy Variable.” Neural Computing and Applications 31(9): 4903–27.
  • Gakhar, D. 2012. “Total Time Minimization Solid Trasportation Problem.” Thapar University, India.
  • Gen, M, K Ida, Y Li, and E Kubota. 1995. “Solving Bicriteria Solid Transportation Problem with Fuzzy Numbers by a Genetic Algorithm.” Computers & Industrial Engineering 29(1): 537–41.
  • Haley, K. B. 1962. “New Methods in Mathematical Programming—The Solid Transportation Problem.” Operations Research 10(4): 448–63.
  • Jalil, Syed Aqib, Shakeel Javaid, and Syed Mohd Muneeb. 2018. “A Decentralized Multi-Level Decision Making Model for Solid Transportation Problem with Uncertainty.” International Journal of System Assurance Engineering and Management 9(5): 1022–33.
  • Jayaraman, R, C Colapinto, D La Torre, and T Malik. 2017. “A Weighted Goal Programming Model for Planning Sustainable Development Applied to Gulf Cooperation Council Countries.” Applied Energy 185: 1931–39.
  • Jiménez, Fernando, and José L. Verdegay. 1998. “Uncertain Solid Transportation Problems.” Fuzzy sets and systems 100(1): 45–57.
  • Jiménez, F., & Verdegay, J. L.. 1999a. “An Evolutionary Algorithm for Interval Solid Transportation Problems.” Evolutionary Computation 7(1): 103–7.
  • Jiménez, F., & Verdegay, J. L.. 1999b. “Solving Fuzzy Solid Transportation Problems by an Evolutionary Algorithm Based Parametric Approach.” European Journal of Operational Research 117(3): 485–510.
  • Kocken, Hale Gonce, and Mustafa Sivri. 2016. “A Simple Parametric Method to Generate All Optimal Solutions of Fuzzy Solid Transportation Problem.” Applied Mathematical Modelling 40: 4612–24.
  • Kuiri, Anjana, and Barun Das. “An Application of FISM and TOPSIS to a Multi-Objective Multi-Item Solid Transportation Problem.” OPSEARCH: 1–20.
  • Kundu, Pradip, Samarjit Kar, and Manoranjan Maiti. 2014a. “A Fuzzy MCDM Method and an Application to Solid Transportation Problem with Mode Preference.” Soft Computing 18(9): 1853–64.
  • Kundu, P., Kar, S., & Maiti, M.. 2014b. “Multi-Objective Solid Transportation Problems with Budget Constraint in Uncertain Environment.” International Journal of Systems Science 45(8): 1668–82.
  • Li, Y, K Ida, M Gen, and R Kobuchi. 1997. “Neural Network Approach for Multicriteria Solid Transportation Problem.” Computers & industrial engineering 33(3): 465–68.
  • Li, Yinzhen, Kenichi Ida, and Mitsuo Gen. 1997. “Improved Genetic Algorithm for Solving Multiobjective Solid Transportation Problem with Fuzzy Numbers.” Computers & Industrial Engineering 33(3): 589–92.
  • Liu, Baoding. 2007. Uncertainty Theory. 2nd ed. Heidelberg, Berlin: Springer.
  • Liu, B. 2011. “Uncertain Logic for Modeling Human Language.” Journal of Uncertain Systems 5(1): 3–20.
  • Narayanamoorthy, S, and P. Anukokila. 2015. “Optimal Solution of Fractional Programming Problem Based on Solid Fuzzy Transportation Problem.” International Journal of Operational Research 22(1): 91–105.
  • Ojha, A, B Das, S. K Mondal, and M Maiti. 2013. “A Multi-Item Transportation Problem with Fuzzy Tolerance.” Applied Soft Computing 13(8): 3703–12.
  • Ojha, A, B Das, S Mondal, and M Maiti. 2009. “An Entropy Based Solid Transportation Problem for General Fuzzy Costs and Time with Fuzzy Equality.” Mathematical and Computer Modelling 50(1–2): 166–78.
  • Ojha, A., Das, B., Mondal, S., & Maiti, M.. 2010 A Stochastic Discounted Multi-Objective Solid Transportation Problem for Breakable Items Using Analytical Hierarchy Process. “.” Applied Mathematical Modelling 34(8): 2256–71.
  • Ozmutlu, S., and M. Jeya Chandra. 2001. “Computation of Optimal Mean for a Larger-the-Better Type Quality Characteristic Using Goal Programming.” International Journal of Industrial Engineering: Theory Applications and Practice 8(1): 62–71.
  • Pandian, P, and D. Anuradha. 2010. “A New Approach for Solving Solid Transportation Problems.” Applied Mathematical Sciences 4(72): 3603–10.
  • Pramanik, Sutapa, Dipak Kumar Jana, and M. Maiti. 2013. “Multi-Objective Solid Transportation Problem in Imprecise Environments.” Journal of Transportation Security 6(2): 131–50.
  • Radhakrishnan, B, and P. Anukokila. 2014. “Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost.” Fuzzy Information and Engineering 6(3): 359–77.
  • Sarma, Deepshikha, Amrit Das, and Uttam Kumar Bera. 2020. “An Optimal Redistribution Plan Considering Aftermath Disruption in Disaster Management.” Soft Computing 24(1): 65–82.
  • Sengupta, Dipanjana, Amrit Das, and Uttam Kumar Bera. 2018. “A Gamma Type-2 Defuzzification Method for Solving a Solid Transportation Problem Considering Carbon Emission.” Applied Intelligence 48(11): 3995–4022.
  • Shell, E. 1955. “Distribution of a Product by Several Properties, Directorate of Management Analysis.” In Proceedings of the Second Symposium in Linear Programming, , 615–42.
  • Tao, Zhimiao, and Jiuping Xu. 2012. “A Class of Rough Multiple Objective Programming and Its Application to Solid Transportation Problem.” Information Sciences 188: 215–35.
  • Yang, L et al. 2015. “Reduction Methods of Type-2 Uncertain Variables and Their Applications to Solid Transportation Problem.” Information Sciences 291: 204–37.

SOLVING SOLID TRANSPORTATION PROBLEMS UNDER UNCERTAIN ENVIRONMENT USING GOAL PROGRAMMING

Yıl 2022, Cilt: 33 Sayı: 1, 130 - 144, 30.04.2022

Öz

A transportation problem can be involving multiple objectives, multiple products, and multiple conveyances. These kinds of transportation problems are named multi-objective multi-attributes solid transportation problems (MMSTP). In this study, a solution based on goal programming has been proposed for MMSTP, in which the supply and demand are uncertain. Moreover, to handle uncertainty, different uncertainty parameters, which are between 0.6 and 0.9, have been used. Then, the results with obtained these parameters are compared by using cost function values. The results indicate that when the uncertainty parameter decreases, the cost increases. Finally, it is shown that an optimal solution can be found using this model through an example.

Kaynakça

  • Baidya, A, and U. K. Bera. 2014. “An Interval Valued Solid Transportation Problem with Budget Constraint in Different Interval Approaches.” Journal of Transportation Security 7(2): 147–55.
  • Baidya, Abhijit, Uttam Kumar Bera, and Manoranjan Maiti. 2013. “A Solid Transportation Problem with Safety Factor under Different Uncertainty Environments.” Journal of Uncertainty Analysis and Applications 1(1): 18.
  • Baidya, A., Bera, U. K., & Maiti, M.. 2015. “Interval Oriented Entropy Based Multi-Item Solid Transportation Problem with Budget and Breakability.” International Journal of Applied and Computational Mathematics 1(2): 279–92.
  • Bit, AK, MP Biswal, and SS Alam. 1993. “Fuzzy Programming Approach to Multiobjective Solid Transportation Problem.” Fuzzy sets and systems 57(2): 183–94.
  • Chakraborty, Dipankar, Dipak Kumar Jana, and Tapan Kumar Roy. 2014. “Multi-Objective Multi-Item Solid Transportation Problem with Fuzzy Inequality Constraints.” Journal of Inequalities and Applications 2014(1): 338.
  • Charnes, A, and WW Cooper. 1961. Management Models and Industrial Applications of Linear Programming. New York: John Wiley and Sons Inc.
  • Charnes, Abraham, and WW135619 Cooper. 1962. “Chance Constraints and Normal Deviates.” Journal of the American statistical association 57(297): 134–48.
  • Chen, Lin, Jin Peng, and Bo Zhang. 2017. “Uncertain Goal Programming Models for Bicriteria Solid Transportation Problem.” Applied Soft Computing 51: 49–59.
  • Chen, Yueh-Li, Long-Hui Chen, and Chien-Yu Huang. 2009. “Fuzzy Goal Programming Approach to Solve the Equipment-Purchasing Problem of an FMC.” International journal of industrial engineering: theory, applications and practice 164.
  • Cui, Qing, and Yuhong Sheng. 2012. “Uncertain Programming Model for Solid Transportation Problem.” Information 15(12): 342–48. Dalman, Hasan. 2019. “Entropy-Based Multi-Item Solid Transportation Problems with Uncertain Variables.” Soft Computing 23(14): 5931–43.
  • Dalman, Hasan, Nuran Güzel, and Mustafa Sivri. 2016. “A Fuzzy Set-Based Approach to Multi-Objective Multi-Item Solid Transportation Problem under Uncertainty.” International Journal of Fuzzy Systems 18(4): 716–29.
  • Das, Amrit, and Uttam Kumar Bera. 2015. “A Bi-Objective Solid Transportation Model under Uncertain Environment.” Facets of uncertainties and applications. Springer, New Delhi: 261–75.
  • Das, Amrit, Uttam Kumar Bera, and Manoranjan Maiti. 2018. “Defuzzification and Application of Trapezoidal Type-2 Fuzzy Variables to Green Solid Transportation Problem.” Soft Computing 22(7): 2275–97.
  • Das, A., Bera, U. K., & Maiti, M. . 2019. “A Solid Transportation Problem in Uncertain Environment Involving Type-2 Fuzzy Variable.” Neural Computing and Applications 31(9): 4903–27.
  • Gakhar, D. 2012. “Total Time Minimization Solid Trasportation Problem.” Thapar University, India.
  • Gen, M, K Ida, Y Li, and E Kubota. 1995. “Solving Bicriteria Solid Transportation Problem with Fuzzy Numbers by a Genetic Algorithm.” Computers & Industrial Engineering 29(1): 537–41.
  • Haley, K. B. 1962. “New Methods in Mathematical Programming—The Solid Transportation Problem.” Operations Research 10(4): 448–63.
  • Jalil, Syed Aqib, Shakeel Javaid, and Syed Mohd Muneeb. 2018. “A Decentralized Multi-Level Decision Making Model for Solid Transportation Problem with Uncertainty.” International Journal of System Assurance Engineering and Management 9(5): 1022–33.
  • Jayaraman, R, C Colapinto, D La Torre, and T Malik. 2017. “A Weighted Goal Programming Model for Planning Sustainable Development Applied to Gulf Cooperation Council Countries.” Applied Energy 185: 1931–39.
  • Jiménez, Fernando, and José L. Verdegay. 1998. “Uncertain Solid Transportation Problems.” Fuzzy sets and systems 100(1): 45–57.
  • Jiménez, F., & Verdegay, J. L.. 1999a. “An Evolutionary Algorithm for Interval Solid Transportation Problems.” Evolutionary Computation 7(1): 103–7.
  • Jiménez, F., & Verdegay, J. L.. 1999b. “Solving Fuzzy Solid Transportation Problems by an Evolutionary Algorithm Based Parametric Approach.” European Journal of Operational Research 117(3): 485–510.
  • Kocken, Hale Gonce, and Mustafa Sivri. 2016. “A Simple Parametric Method to Generate All Optimal Solutions of Fuzzy Solid Transportation Problem.” Applied Mathematical Modelling 40: 4612–24.
  • Kuiri, Anjana, and Barun Das. “An Application of FISM and TOPSIS to a Multi-Objective Multi-Item Solid Transportation Problem.” OPSEARCH: 1–20.
  • Kundu, Pradip, Samarjit Kar, and Manoranjan Maiti. 2014a. “A Fuzzy MCDM Method and an Application to Solid Transportation Problem with Mode Preference.” Soft Computing 18(9): 1853–64.
  • Kundu, P., Kar, S., & Maiti, M.. 2014b. “Multi-Objective Solid Transportation Problems with Budget Constraint in Uncertain Environment.” International Journal of Systems Science 45(8): 1668–82.
  • Li, Y, K Ida, M Gen, and R Kobuchi. 1997. “Neural Network Approach for Multicriteria Solid Transportation Problem.” Computers & industrial engineering 33(3): 465–68.
  • Li, Yinzhen, Kenichi Ida, and Mitsuo Gen. 1997. “Improved Genetic Algorithm for Solving Multiobjective Solid Transportation Problem with Fuzzy Numbers.” Computers & Industrial Engineering 33(3): 589–92.
  • Liu, Baoding. 2007. Uncertainty Theory. 2nd ed. Heidelberg, Berlin: Springer.
  • Liu, B. 2011. “Uncertain Logic for Modeling Human Language.” Journal of Uncertain Systems 5(1): 3–20.
  • Narayanamoorthy, S, and P. Anukokila. 2015. “Optimal Solution of Fractional Programming Problem Based on Solid Fuzzy Transportation Problem.” International Journal of Operational Research 22(1): 91–105.
  • Ojha, A, B Das, S. K Mondal, and M Maiti. 2013. “A Multi-Item Transportation Problem with Fuzzy Tolerance.” Applied Soft Computing 13(8): 3703–12.
  • Ojha, A, B Das, S Mondal, and M Maiti. 2009. “An Entropy Based Solid Transportation Problem for General Fuzzy Costs and Time with Fuzzy Equality.” Mathematical and Computer Modelling 50(1–2): 166–78.
  • Ojha, A., Das, B., Mondal, S., & Maiti, M.. 2010 A Stochastic Discounted Multi-Objective Solid Transportation Problem for Breakable Items Using Analytical Hierarchy Process. “.” Applied Mathematical Modelling 34(8): 2256–71.
  • Ozmutlu, S., and M. Jeya Chandra. 2001. “Computation of Optimal Mean for a Larger-the-Better Type Quality Characteristic Using Goal Programming.” International Journal of Industrial Engineering: Theory Applications and Practice 8(1): 62–71.
  • Pandian, P, and D. Anuradha. 2010. “A New Approach for Solving Solid Transportation Problems.” Applied Mathematical Sciences 4(72): 3603–10.
  • Pramanik, Sutapa, Dipak Kumar Jana, and M. Maiti. 2013. “Multi-Objective Solid Transportation Problem in Imprecise Environments.” Journal of Transportation Security 6(2): 131–50.
  • Radhakrishnan, B, and P. Anukokila. 2014. “Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost.” Fuzzy Information and Engineering 6(3): 359–77.
  • Sarma, Deepshikha, Amrit Das, and Uttam Kumar Bera. 2020. “An Optimal Redistribution Plan Considering Aftermath Disruption in Disaster Management.” Soft Computing 24(1): 65–82.
  • Sengupta, Dipanjana, Amrit Das, and Uttam Kumar Bera. 2018. “A Gamma Type-2 Defuzzification Method for Solving a Solid Transportation Problem Considering Carbon Emission.” Applied Intelligence 48(11): 3995–4022.
  • Shell, E. 1955. “Distribution of a Product by Several Properties, Directorate of Management Analysis.” In Proceedings of the Second Symposium in Linear Programming, , 615–42.
  • Tao, Zhimiao, and Jiuping Xu. 2012. “A Class of Rough Multiple Objective Programming and Its Application to Solid Transportation Problem.” Information Sciences 188: 215–35.
  • Yang, L et al. 2015. “Reduction Methods of Type-2 Uncertain Variables and Their Applications to Solid Transportation Problem.” Information Sciences 291: 204–37.
Toplam 43 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Endüstri Mühendisliği
Bölüm Araştırma Makaleleri
Yazarlar

Nuran Güzel 0000-0002-6585-7326

Selçuk Alp 0000-0002-6545-4287

Ebru Geçici 0000-0002-7954-9578

Erken Görünüm Tarihi 22 Nisan 2022
Yayımlanma Tarihi 30 Nisan 2022
Kabul Tarihi 18 Şubat 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 33 Sayı: 1

Kaynak Göster

APA Güzel, N., Alp, S., & Geçici, E. (2022). SOLVING SOLID TRANSPORTATION PROBLEMS UNDER UNCERTAIN ENVIRONMENT USING GOAL PROGRAMMING. Endüstri Mühendisliği, 33(1), 130-144.

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