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A new mathematical model for distribution network expansion problem with distributed generation

Year 2022, Volume: 6 Issue: 1, 1134 - 1152, 30.06.2022

Abstract

Due to rapidly developing technology, growth in world population and electrification studies, demand for electrical energy is increasing. Ensuring the energy needs of the new residential and industrial zones is one of the main challenges that institutions that are responsible for electricity distribution face. To deal with this challenge, the grid needs to be regularly expanded and its capacity increased, with a proper investment plan. In this case, finding the most appropriate investment plan emerges as a strategic design issue. In addition to meeting the increasing demand, the designed distribution networks are expected to be reliable, cost-effective and use clean energy. To achieve these goals, in recent years the planning of networks in distributed generation structure has come to the fore. Distribution network expansion problem with distributed generation (DNEP_DG) involves reinforcement existing grid or installing new grid components such as line, substation, and distributed generation source. The most used network structure in distribution systems is tree-structured radial network. Providing the radial structure requires additional constraints when the distribution networks are expanded considering the distributed generation and complicates the problem. In this study, a new formulation was developed based on spanning tree subtour elimination to provide radiality in the DNEP_DG. A mixed-integer mathematical model has been developed to find the multi-stage expansion plan that minimizes investment, maintenance, production, and emission costs. In this study, it has been shown that obtain the same result in a shorter time when the proposed radiality constraints are compared to the structure in the literature.

References

  • Ackermann T., Andersson G. ve Söder L. (2001). Distributed generations: a definition. Electric Power Systems Research, 57, 195-204. doi: 10.1016/S0378-7796(01)00101-8
  • Alotaibi, M. A. ve Salama, M. M. (2018). An Incentive-Based Multistage Expansion Planning Model for Smart Distribution Systems. IEEE Transactions on Power Systems, 33(5), 5469-5485. doi: 10.1109/TPWRS.2018.2805322
  • Asensio, M., de Quevedo, P. M., Muñoz-Delgado, G. ve Contreras, J. (2018). Joint distribution network and renewable energy expansion planning considering demand response and energy storage—Part I: Stochastic programming model. IEEE Transactions on Smart Grid, 9(2), 655-666. doi: 10.1109/TSG.2016.2560339
  • Bagheri, A., Monsef, H. ve Lesani, H. (2015a). An approach for distribution network expansion planning considering reliability issues. In 2015 30th International Power System Conference, 309-317. doi: 10.1109/IPSC.2015.7827765 Bagheri, A., Monsef, H. ve Lesani, H. (2015b). Comprehensive distribution network expansion plannig: A dynamic approach. 20th Conference on Electrical Power Distribution Networks Conference, 156-165. doi: 10.1109/EPDC.2015.7330489
  • Bagheri, A., Monsef, H., & Lesani, H. (2015c). Renewable power generation employed in an integrated dynamic distribution network expansion planning. Electric Power Systems Research, 127, 280-296. doi: 10.1016/j.epsr.2015.06.004
  • Ball, M. O., Magnanti, T. L., Monma, C. L., and Nemhauser, G. L. (1995). Network Models, Handbooks in OR and MS, Vol. 7, North-Holland, Amsterdam. Erişim adresi: https://www.sciencedirect.com/handbook/handbooks-in-operations-research-and-management-science/vol/7/suppl/C
  • Çevik, O., Karaca, S. S., & Özkan, M. (2011). En küçük yayılma modeli ile İç Anadolu Bölgesinde bir kargo firmasının dağıtım güzergâhının belirlenmesi. Karamanoğlu Mehmetbey Üniversitesi Sosyal ve Ekonomik Araştırmalar Dergisi, 2011(2), 1-9. Erişim adresi: https://dergipark.org.tr/tr/pub/kmusekad/issue/10215/125548
  • Enerdata. (2021). World Energy & Climate Statistics – Yearbook 2021. Erişim adresi: https://yearbook.enerdata.net/electricity/electricity-domestic-consumption-data.html.
  • Gholizadeh-Roshanagh, R., Najafi-Ravadanegh, S. ve Hosseinian, S. H. (2016). A framework for optimal coordinated primary-secondary planning of distribution systems considering MV distributed generation. IEEE Transactions on Smart Grid, 9(2), 1408-1415. doi: 10.1109/TSG.2016.2590425
  • Haffner, S., Pereira, L. F. A., Pereira, L. A. ve Barreto, L. S. (2008). Multistage model for distribution expansion planning with distributed generation—Part I: Problem formulation. IEEE Transactions on Power Delivery, 23(2), 915-923. doi: 10.1109/TPWRD.2008.917916
  • Hemmati, R., Hooshmand, R. A. ve Taheri, N. (2015). Distribution network expansion planning and DG placement in the presence of uncertainties. International Journal of Electrical Power & Energy Systems, 73, 665-673.doi: 10.1016/j.ijepes.2015.05.024
  • Huang, Y., Alvehag, K. ve Söder, L. (2014). Distribution network expansion planning considering distributed generation using probabilistic voltage constraints. In 2014 International Conference on Probabilistic Methods Applied to Power Systems, 1-6. doi: 10.1109/PMAPS.2014.6960581
  • Jahromi, M. E., Ehsan, M. ve Meyabadi, A. F. (2012). A dynamic fuzzy interactive approach for DG expansion planning. International Journal of Electrical Power & Energy Systems, 43(1), 1094-1105. doi: 10.1016/j.ijepes.2012.06.017
  • Kabirifar, M., Fotuhi-Firuzabad, M., Moeini-Aghtaie, M. ve Pourghaderia, N. (2019). Joint Distributed Generation and Active Distribution Network Expansion Planning Considering Active Management of Network. 27th Iranian Conference on Electrical Engineering, 702-708. doi: 10.1109/IranianCEE.2019.8786665
  • Kanwar, N., Gupta, N., Niazi, K. R., Swarnkar, A. ve Bansal, R. C. (2017). Simultaneous allocation of distributed energy resource using improved particle swarm optimization. Applied energy, 185, 1684-1693. doi: 10.1016/j.apenergy.2016.01.093
  • Karimi-Arpanahi, S., Jooshaki, M., Moeini-Aghtaei, M., Abbaspour, A. ve Fotuhi-Firuzabad, M. (2019). A Flexibility-Oriented Model for Distribution System Expansion Planning Studies. In 2019 27th Iranian Conference on Electrical Engineering, 737-741. doi: 10.1109/IranianCEE.2019.8786398
  • Kersting, W. H. (1991). Radial distribution test feeders. IEEE Transactions on Power Systems, 6(3), 975-985. doi: 10.1109/59.119237.
  • Koutsoukis, N. C., Georgilakis, P. S. ve Hatziargyriou, N. D. (2017). Multistage coordinated planning of active distribution networks. IEEE Transactions on Power Systems, 33(1), 32-44. doi: 10.1109/TPWRS.2017.2699696
  • Malee, R. K., Jain, P., Gupta, P. P., ve Dharampal, S. S. (2016). Distribution system expansion planning incorporating distributed generation. In 2016 IEEE 7th Power India International Conference, 1-6. doi: 10.1109/POWERI.2016.8077273
  • Muñoz-Delgado, G., Contreras, J. ve Arroyo, J. M. (2015). Joint expansion planning of distributed generation and distribution networks. IEEE Transactions on Power Systems, 30(5), 2579-2590. doi: 10.1109/TPWRS.2014.2364960
  • Prakash, K., Lallu, A., Islam, F. R., ve Mamun, K. A. (2016). Review of power system distribution network architecture. In 2016 3rd Asia-Pacific World Congress on Computer Science and Engineering, 124-130. doi: 10.1109/APWC-on-CSE.2016.030
  • Santos, S. F., Fitiwi, D. Z., Shafie-khah, M., Bizuayehu, A. W. ve Catalão, J. P. S. (2017). Optimal sizing and placement of smart-grid-enabling technologies for maximizing renewable integration. In Smart Energy Grid Engineering, 47-81. doi: 10.1016/B978-0-12-805343-0.00003-6
  • Seta, F. D. S., de Oliveira, L. W. ve de Oliveira, E. J. (2020). Distribution System Planning with Representation of Uncertainties Based on Interval Analysis. Journal of Control, Automation and Electrical Systems, 31(2), 494-510. doi: 10.1007/s40313-020-00573-0
  • SHURA (2020). 2030 Yılına Doğru Türkiye’nin Optimum Elektrik Üretim Kapasitesi. Erişim adresi: 2030-yılına-doğru-Türkiye’nin-optimum-elektrik-üretim-kapasitesi.pdf .
  • Siahi, M., Porkar, S., Abbaspour-Tehrani-fard, A., Poure, P. ve Saadate, S. (2010). Competitive distribution system planning model integration of DG, interruptible load and voltage regulator devices. Iranian Journal of Science and Technology, 34(B6), 619. doi: 10.22099/IJSTE.2010.829
  • Soroudi, A., Ehsan, M. ve Zareipour, H. (2011). A practical eco-environmental distribution network planning model including fuel cells and non-renewable distributed energy resources. Renewable energy, 36(1), 179-188. doi: 10.1016/j.renene.2010.06.019
  • Sun, K., Liu, Y., He, D., Wang, H., Wang, L. ve Sun, Z. (2018). Coordinated Planning of Distributed Generation and Distribution Networking Considering Network Reconfiguration. In 2018 International Conference on Power System Technology, 2227-2232. doi: 10.1109/POWERCON.2018.8601935
  • TAŞ (2018). Türkiye Akıllı Şebekeler 2023 Vizyon ve Strateji Belirleme Projesi Raporu. Erişim adresi: http://www.elder.org.tr/Content/yayinlar/TAS%20TR.pdf .
  • Theo, W. L., Lim, J. S., Ho, W. S., Hashim, H. ve Lee, C. T. (2017). Review of distributed generation (DG) system planning and optimisation techniques: Comparison of numerical and mathematical modelling methods. Renewable and Sustainable Energy Reviews, 67, 531-573. doi: 10.1016/j.rser.2016.09.063
  • Ugranlı, F. (2019). Analysis of renewable generation’s integration using multi-objective fashion for multistage distribution network expansion planning. International Journal of Electrical Power & Energy Systems, 106, 301-310. doi: 10.1016/j.ijepes.2018.10.002
  • Wu, Z., Liu, Y., Gu, W., Zhou, J., Li, J. ve Liu, P. (2018). Decomposition method for coordinated planning of distributed generation and distribution network. IET Generation, Transmission & Distribution, 12(20), 4482-4491. doi: 10.1049/iet-gtd.2017.2050
  • Xing, H., Cheng, H., Zhang, L., Zhang, S. ve Zhang, Y. (2015). Second-order cone model for active distribution network expansion planning. In 2015 IEEE Power & Energy Society General Meeting, 1-5. doi: 10.1109/PESGM.2015.7286204

Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model

Year 2022, Volume: 6 Issue: 1, 1134 - 1152, 30.06.2022

Abstract

Hızlı gelişen teknolojiye, dünya nüfusunun artmasına ve elektrifikasyon çalışmalarına bağlı olarak elektrik enerjisine olan talep artış göstermektedir. Mevcut elektrik şebekesi ile yeni açılan yerleşim ve sanayi bölgelerinin ihtiyacı olan enerji gereksiniminin sağlanması, elektrik dağıtımından sorumlu kurumların karşılaştığı temel zorluklardan biridir. Bu zorlukla başa çıkabilmek için uygun yatırım planıyla şebekenin düzenli olarak genişletilmesi ve kapasitesinin arttırılması gerekir. Burada en uygun yatırım planının bulunması stratejik bir tasarım problemi olarak karşımıza çıkmaktadır. Tasarlanan dağıtım şebekelerinin artan talebi karşılamasının yanı sıra güvenilir, maliyet etkin ve temiz enerji kullanan şebekeler olması da beklenmektedir. Bu amaçlara ulaşabilmek için şebekelerin dağıtık üretim yapısında planlanması son yıllarda ön plana çıkmaktadır. Dağıtık üretim içeren dağıtım şebekesi genişleme problemi (DNEP_DG), mevcut şebekenin güçlendirilmesini ya da hat, trafo merkezi, dağıtık üretim kaynağı gibi yeni şebeke bileşenlerinin eklenmesini içerir. Dağıtım sistemlerinde en sık kullanılan şebeke yapısı, ağaç yapısındaki radyal şebekelerdir. Dağıtım şebekeleri dağıtık üretim kaynağı dikkate alınarak genişletildiğinde radyal yapının sağlanması ek kısıtlar gerektirmekte olup problemi zorlaştırmaktadır. Bu çalışmada, DNEP_DG’de radyal yapının sağlanması için yayılan ağaç alt tur eleme kısıtlarına dayalı yeni bir formülasyon önerilmiştir. Yatırım, bakım, üretim ve emisyon maliyetlerini en küçükleyen çok dönemli genişleme planının bulunması için karma-tamsayılı matematiksel bir model geliştirilmiştir. Bu çalışmada önerilen radyallik kısıtlarını içeren model ile literatürdeki kısıt yapısını içeren modelden daha kısa sürede sonuca ulaşıldığı gösterilmiştir.

References

  • Ackermann T., Andersson G. ve Söder L. (2001). Distributed generations: a definition. Electric Power Systems Research, 57, 195-204. doi: 10.1016/S0378-7796(01)00101-8
  • Alotaibi, M. A. ve Salama, M. M. (2018). An Incentive-Based Multistage Expansion Planning Model for Smart Distribution Systems. IEEE Transactions on Power Systems, 33(5), 5469-5485. doi: 10.1109/TPWRS.2018.2805322
  • Asensio, M., de Quevedo, P. M., Muñoz-Delgado, G. ve Contreras, J. (2018). Joint distribution network and renewable energy expansion planning considering demand response and energy storage—Part I: Stochastic programming model. IEEE Transactions on Smart Grid, 9(2), 655-666. doi: 10.1109/TSG.2016.2560339
  • Bagheri, A., Monsef, H. ve Lesani, H. (2015a). An approach for distribution network expansion planning considering reliability issues. In 2015 30th International Power System Conference, 309-317. doi: 10.1109/IPSC.2015.7827765 Bagheri, A., Monsef, H. ve Lesani, H. (2015b). Comprehensive distribution network expansion plannig: A dynamic approach. 20th Conference on Electrical Power Distribution Networks Conference, 156-165. doi: 10.1109/EPDC.2015.7330489
  • Bagheri, A., Monsef, H., & Lesani, H. (2015c). Renewable power generation employed in an integrated dynamic distribution network expansion planning. Electric Power Systems Research, 127, 280-296. doi: 10.1016/j.epsr.2015.06.004
  • Ball, M. O., Magnanti, T. L., Monma, C. L., and Nemhauser, G. L. (1995). Network Models, Handbooks in OR and MS, Vol. 7, North-Holland, Amsterdam. Erişim adresi: https://www.sciencedirect.com/handbook/handbooks-in-operations-research-and-management-science/vol/7/suppl/C
  • Çevik, O., Karaca, S. S., & Özkan, M. (2011). En küçük yayılma modeli ile İç Anadolu Bölgesinde bir kargo firmasının dağıtım güzergâhının belirlenmesi. Karamanoğlu Mehmetbey Üniversitesi Sosyal ve Ekonomik Araştırmalar Dergisi, 2011(2), 1-9. Erişim adresi: https://dergipark.org.tr/tr/pub/kmusekad/issue/10215/125548
  • Enerdata. (2021). World Energy & Climate Statistics – Yearbook 2021. Erişim adresi: https://yearbook.enerdata.net/electricity/electricity-domestic-consumption-data.html.
  • Gholizadeh-Roshanagh, R., Najafi-Ravadanegh, S. ve Hosseinian, S. H. (2016). A framework for optimal coordinated primary-secondary planning of distribution systems considering MV distributed generation. IEEE Transactions on Smart Grid, 9(2), 1408-1415. doi: 10.1109/TSG.2016.2590425
  • Haffner, S., Pereira, L. F. A., Pereira, L. A. ve Barreto, L. S. (2008). Multistage model for distribution expansion planning with distributed generation—Part I: Problem formulation. IEEE Transactions on Power Delivery, 23(2), 915-923. doi: 10.1109/TPWRD.2008.917916
  • Hemmati, R., Hooshmand, R. A. ve Taheri, N. (2015). Distribution network expansion planning and DG placement in the presence of uncertainties. International Journal of Electrical Power & Energy Systems, 73, 665-673.doi: 10.1016/j.ijepes.2015.05.024
  • Huang, Y., Alvehag, K. ve Söder, L. (2014). Distribution network expansion planning considering distributed generation using probabilistic voltage constraints. In 2014 International Conference on Probabilistic Methods Applied to Power Systems, 1-6. doi: 10.1109/PMAPS.2014.6960581
  • Jahromi, M. E., Ehsan, M. ve Meyabadi, A. F. (2012). A dynamic fuzzy interactive approach for DG expansion planning. International Journal of Electrical Power & Energy Systems, 43(1), 1094-1105. doi: 10.1016/j.ijepes.2012.06.017
  • Kabirifar, M., Fotuhi-Firuzabad, M., Moeini-Aghtaie, M. ve Pourghaderia, N. (2019). Joint Distributed Generation and Active Distribution Network Expansion Planning Considering Active Management of Network. 27th Iranian Conference on Electrical Engineering, 702-708. doi: 10.1109/IranianCEE.2019.8786665
  • Kanwar, N., Gupta, N., Niazi, K. R., Swarnkar, A. ve Bansal, R. C. (2017). Simultaneous allocation of distributed energy resource using improved particle swarm optimization. Applied energy, 185, 1684-1693. doi: 10.1016/j.apenergy.2016.01.093
  • Karimi-Arpanahi, S., Jooshaki, M., Moeini-Aghtaei, M., Abbaspour, A. ve Fotuhi-Firuzabad, M. (2019). A Flexibility-Oriented Model for Distribution System Expansion Planning Studies. In 2019 27th Iranian Conference on Electrical Engineering, 737-741. doi: 10.1109/IranianCEE.2019.8786398
  • Kersting, W. H. (1991). Radial distribution test feeders. IEEE Transactions on Power Systems, 6(3), 975-985. doi: 10.1109/59.119237.
  • Koutsoukis, N. C., Georgilakis, P. S. ve Hatziargyriou, N. D. (2017). Multistage coordinated planning of active distribution networks. IEEE Transactions on Power Systems, 33(1), 32-44. doi: 10.1109/TPWRS.2017.2699696
  • Malee, R. K., Jain, P., Gupta, P. P., ve Dharampal, S. S. (2016). Distribution system expansion planning incorporating distributed generation. In 2016 IEEE 7th Power India International Conference, 1-6. doi: 10.1109/POWERI.2016.8077273
  • Muñoz-Delgado, G., Contreras, J. ve Arroyo, J. M. (2015). Joint expansion planning of distributed generation and distribution networks. IEEE Transactions on Power Systems, 30(5), 2579-2590. doi: 10.1109/TPWRS.2014.2364960
  • Prakash, K., Lallu, A., Islam, F. R., ve Mamun, K. A. (2016). Review of power system distribution network architecture. In 2016 3rd Asia-Pacific World Congress on Computer Science and Engineering, 124-130. doi: 10.1109/APWC-on-CSE.2016.030
  • Santos, S. F., Fitiwi, D. Z., Shafie-khah, M., Bizuayehu, A. W. ve Catalão, J. P. S. (2017). Optimal sizing and placement of smart-grid-enabling technologies for maximizing renewable integration. In Smart Energy Grid Engineering, 47-81. doi: 10.1016/B978-0-12-805343-0.00003-6
  • Seta, F. D. S., de Oliveira, L. W. ve de Oliveira, E. J. (2020). Distribution System Planning with Representation of Uncertainties Based on Interval Analysis. Journal of Control, Automation and Electrical Systems, 31(2), 494-510. doi: 10.1007/s40313-020-00573-0
  • SHURA (2020). 2030 Yılına Doğru Türkiye’nin Optimum Elektrik Üretim Kapasitesi. Erişim adresi: 2030-yılına-doğru-Türkiye’nin-optimum-elektrik-üretim-kapasitesi.pdf .
  • Siahi, M., Porkar, S., Abbaspour-Tehrani-fard, A., Poure, P. ve Saadate, S. (2010). Competitive distribution system planning model integration of DG, interruptible load and voltage regulator devices. Iranian Journal of Science and Technology, 34(B6), 619. doi: 10.22099/IJSTE.2010.829
  • Soroudi, A., Ehsan, M. ve Zareipour, H. (2011). A practical eco-environmental distribution network planning model including fuel cells and non-renewable distributed energy resources. Renewable energy, 36(1), 179-188. doi: 10.1016/j.renene.2010.06.019
  • Sun, K., Liu, Y., He, D., Wang, H., Wang, L. ve Sun, Z. (2018). Coordinated Planning of Distributed Generation and Distribution Networking Considering Network Reconfiguration. In 2018 International Conference on Power System Technology, 2227-2232. doi: 10.1109/POWERCON.2018.8601935
  • TAŞ (2018). Türkiye Akıllı Şebekeler 2023 Vizyon ve Strateji Belirleme Projesi Raporu. Erişim adresi: http://www.elder.org.tr/Content/yayinlar/TAS%20TR.pdf .
  • Theo, W. L., Lim, J. S., Ho, W. S., Hashim, H. ve Lee, C. T. (2017). Review of distributed generation (DG) system planning and optimisation techniques: Comparison of numerical and mathematical modelling methods. Renewable and Sustainable Energy Reviews, 67, 531-573. doi: 10.1016/j.rser.2016.09.063
  • Ugranlı, F. (2019). Analysis of renewable generation’s integration using multi-objective fashion for multistage distribution network expansion planning. International Journal of Electrical Power & Energy Systems, 106, 301-310. doi: 10.1016/j.ijepes.2018.10.002
  • Wu, Z., Liu, Y., Gu, W., Zhou, J., Li, J. ve Liu, P. (2018). Decomposition method for coordinated planning of distributed generation and distribution network. IET Generation, Transmission & Distribution, 12(20), 4482-4491. doi: 10.1049/iet-gtd.2017.2050
  • Xing, H., Cheng, H., Zhang, L., Zhang, S. ve Zhang, Y. (2015). Second-order cone model for active distribution network expansion planning. In 2015 IEEE Power & Energy Society General Meeting, 1-5. doi: 10.1109/PESGM.2015.7286204
There are 32 citations in total.

Details

Primary Language Turkish
Subjects Industrial Engineering
Journal Section Research Article
Authors

Ayşenur Yurtsever 0000-0002-5010-1956

Berna Dengiz 0000-0002-2806-3308

Burçin Çakır 0000-0002-3158-4518

İsmail Karaoğlan 0000-0002-6023-6918

Publication Date June 30, 2022
Submission Date April 20, 2022
Acceptance Date May 25, 2022
Published in Issue Year 2022 Volume: 6 Issue: 1

Cite

APA Yurtsever, A., Dengiz, B., Çakır, B., Karaoğlan, İ. (2022). Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model. Journal of Turkish Operations Management, 6(1), 1134-1152.
AMA Yurtsever A, Dengiz B, Çakır B, Karaoğlan İ. Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model. JTOM. June 2022;6(1):1134-1152.
Chicago Yurtsever, Ayşenur, Berna Dengiz, Burçin Çakır, and İsmail Karaoğlan. “Dağıtık üretim içeren dağıtım şebekesi genişleme Problemi için Yeni Bir Matematiksel Model”. Journal of Turkish Operations Management 6, no. 1 (June 2022): 1134-52.
EndNote Yurtsever A, Dengiz B, Çakır B, Karaoğlan İ (June 1, 2022) Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model. Journal of Turkish Operations Management 6 1 1134–1152.
IEEE A. Yurtsever, B. Dengiz, B. Çakır, and İ. Karaoğlan, “Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model”, JTOM, vol. 6, no. 1, pp. 1134–1152, 2022.
ISNAD Yurtsever, Ayşenur et al. “Dağıtık üretim içeren dağıtım şebekesi genişleme Problemi için Yeni Bir Matematiksel Model”. Journal of Turkish Operations Management 6/1 (June 2022), 1134-1152.
JAMA Yurtsever A, Dengiz B, Çakır B, Karaoğlan İ. Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model. JTOM. 2022;6:1134–1152.
MLA Yurtsever, Ayşenur et al. “Dağıtık üretim içeren dağıtım şebekesi genişleme Problemi için Yeni Bir Matematiksel Model”. Journal of Turkish Operations Management, vol. 6, no. 1, 2022, pp. 1134-52.
Vancouver Yurtsever A, Dengiz B, Çakır B, Karaoğlan İ. Dağıtık üretim içeren dağıtım şebekesi genişleme problemi için yeni bir matematiksel model. JTOM. 2022;6(1):1134-52.

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