Goal programming model for bi-objective inverse multiple criteria sorting problem

Öz

A type of multi-criteria decision-making problems is about the assignment of objects to predetermined classes by considering multiple criteria. Such problems are defined as multi-criteria sorting or classification problem based on whether the classes are ordered or not. Inverse multi-criteria sorting problem deals with the improvement of assigned classes of objects by determining the possible actions that can change the state of objects. In this study, a goal programming model of inverse multi-criteria ranking problem is proposed to find a compromise solution between the improvement at least cost and the number of objects assigned to a particular class. The proposed model is tested on an application of building energy class improvement and obtained solution results are evaluated.

Anahtar Kelimeler

• Inverse multiple criteria sorting problem
• goal programming
• linear sorting model

İki amaçlı ters çok kriterli sıralama problemi için hedef programlama modeli

Öz

Çok kriterli karar verme problemlerinin çözümlerinin bir kısmında, nesnelerin birden fazla kriter temelinde değerlendirilerek önceden belirlenmiş sınıflara atanması gerçekleştirilir. Bu tip problemler sınıfların sıralı olup olmamasına bağlı olarak çok kriterli sıralama veya sınıflandırma problemi olarak tanımlanırlar. Ters çok kriterli sıralama problemi ise, nesnelerin durumlarını değiştirebilecek olası eylemler arasında seçimler yapılması yoluyla nesnelerin atandığı sınıfların iyileştirilmesiyle ilgilenir. Bu çalışmada ters çok kriterli sıralama problemi için en düşük maliyetli iyileştirme ve belirli bir sınıfa atanan nesne sayısı hedefi arasında uzlaşık çözümü bulmayı amaçlayan bir hedef programlama modeli geliştirilmiştir. Geliştirilen model bina enerji sınıflarını iyileştirmeye yönelik bir uygulama çalışması üzerinde test edilerek elde edilen çözüm sonuçları değerlendirilmiştir.

Anahtar Kelimeler

• Ters çok kriterli sıralama problemi
• hedef programlama
• doğrusal sıralama modeli

Kaynakça

1. Aires, R.F.d.F, Ferreira, L., Araujo, A.G.d., Borenstein, D., Student selection in a Brazilian university: Using a multi-criteria method, Journal of the Operational Research Society, 69(4), 528-540, 2018.
2. Arikan, F., Citak, S., Multiple Criteria Inventory Classification in an Electronics Firm, International Journal of Information Technology & Decision Making, 16(2), 315–331, 2017.
3. Parreiras, R.O., Kokshenev, I., Carvalho, M.O.M., Willer, A.C.M., Dellezzopolles Jr., C.F., Nacif Jr., D.B., Santana, J.A., A flexible multicriteria decision-making methodology to support the strategic management of Science, Technology and Innovation research funding programs, European Journal of Operational Research, 272, 725–739, 2019.
4. Hasan, M., Buyuktahtakın, I.E., Elamin, E., A multi-criteria ranking algorithm (MCRA) for determining breast cancer therapy, OMEGA, 82, 83-101, 2019.
5. Chen, Y. D., Kilgour, M., Hipel, K. W., Multiple criteria classification with an application in water resources planning, Computers and Operations Research, 33(11), 3301–3323, 2006.
6. Zopounidis, C., Doumpos, M. Multi criteria classification and sorting methods: a literature review, European Journal of Operations Research, 138(2), 229–246, 2002.
7. Mousseau, V., Ozpeynirci, O., Ozpeynirci, S. Inverse multiple criteria sorting problem, Annals of Operations Research, 267, 379-412, 2018.
8. Karsu, O., Approaches for inequity-averse sorting. Computers and Operations Research, 66, 67-80, 2016.

9. Safdar, S., Zafar, S., Zafar, N., Khan, N. F., Machine learning based decision support systems (DSS) for heart disease diagnosis: a review, Artificial Intelligence Review 50, 597-623, 2018.
10. López-Soto, D., Yacout, S., Angel-Bello, F. Root cause analysis of familiarity biases in classification of inventory items based on logical patterns recognition. Computers & Industrial Engineering, 93, 121–130, 2016.
11. Katz, D. B., Makhmutova, D. I., Opokina, N. A. The Logistic Regression as an Instrument of the Personnel Policy in an Organization. Helix, 8(1), 2231- 2235, 2018.
12. Illias, H. A., Chai, X. R., Abu Bakar A. H. Hybrid modified evolutionary particle swarm optimisation-time varying acceleration coefficient-artificial neural network for power transformer fault diagnosis. Measurement, 90, 94-102, 2016.
13. Gholami, A., Sheikh, R., Mizani, N., Sana, S. S. ABC analysis of the customers using axiomatic design and incomplete rough set. RAIRO -- Operations Research, 52, 1219-1232, 2018, 2018.
14. Atici, K. B., Ulucan, A. A Multiple Criteria Energy Decision Support System. Technological and Economic Development of Economy, 17(2), 219-245, 2011.
15. Zhao, H., Jiang, P., Yu, Q., Zhang, Y., Ma, W. A comprehensive enterprise classification approach based on three indicators of emissions, efficiency and location. Journal of Cleaner Production, 175, 489-500, 2018.
16. Chen, H. L., Yang, B., Wang, G., Liu, J., Xu, X., Wang, S. J., Liu, D. Y., A novel bankruptcy prediction model based on an adaptive fuzzy k-nearest neighbor method, Knowledge Based Systems, 24, 1348-1359, 2011.
17. Çelik, B., Karasakal, E., İyigün, C. A probabilistic multiple criteria sorting approach based on distance functions, Expert Systems with Applications, 42, 3610–3618, 2015.
18. Berk, E., Cercioglu, H. The productive efficiency of the Turkish health care sector based on provincial panel data, Journal of the Faculty of Engineering and Architecture of Gazi University, 2018, https://doi.or./10.17341/gazimmfd.460491.
19. Mousseau, V., Ozpeynirci, O., Ozpeynirci, S. Inverse multiple criteria sorting problem, 23rd International Conference On Multiple Criteria Decision Making, Hamburg-Almanya, 2-7 Ağustos, 2015.
20. Charnes A., Cooper W. W., Ferguson R. Optimal Estimation of Executive Compensation by Linear Programming, Management Science, 1, 138- 151, 1955.
21. Dağdeviren, M., Eren, T. Analytical hierarchy process and use of 0-1 goal programming methods in selecting supplier firm, Journal of the Faculty of Engineering and Architecture of Gazi University, 16, 41-52, 2001.
22. Karaman, B., Cercioglu, H. 0-1 Goal Programming Aided AHP – VIKOR Integrated Method: An Application of Hospital Investment Project Selection, Journal of the Faculty of Engineering and Architecture of Gazi University, 30, 567-576, 2015.
23. Aksakal, E., Dagdeviren, M. Talent Management Based Personnel Assignment Model And Solution Proposal, Journal of the Faculty of Engineering and Architecture of Gazi University, 30, 249-262, 2015.
24. Durmaz, E. D., Sahin, R. NSGA-II and goal programming approach for the multi-objective single row facility layout problem, Journal of the Faculty of Engineering and Architecture of Gazi University, 32, 941-955, 2017.
25. Colapinto, C., Jayaraman, R., Marsiglio, S. Multi-criteria decision analysis with goal programming in engineering, management and social sciences: a state-of-the art review, Annals of Operations Research, 251, 7-40, 2017.
26. Garcia-Martinez, G., Guijarro, F., Poyatos, J.A. Measuring the social responsibility of European companies: a goal programming approach, International Transactions in Operational Research, 26, 1074-1095, 2019.
27. Yigit, K., Acarkan, B. Assessment of energy performance certificate systems: a case study for residential buildings in Turkey, Turkish Journal of Electrical Engineering & Computer Sciences, 24, 4839–4848, 2016.
28. Hui, S.C., Lee, R. Development of energy labels for residential buildings in Hong Kong. Proceedings of the 10th Asia Pacific Conference on the Built Environment: Green Energy for Environment, Kaohsiung, Taiwan, 2009.
29. Resmi Gazete (2008), Binalarda Enerji Performansı Yönetmeliği, Tarih: 05.12.2008, Sayı: 27075.
30. Kabak, M., Köse, E., Kırılmaz, O., Burmaoğlu, S. A fuzzy multi-criteria decision making approach to assess building energy performance, Energy and Buildings, 72, 382–389, 2014.