A New Fuzzy Inventory Model for the Recycling Process

Öz

Making products that have reached the end of their lifespan reusable after several processes provide many benefits to human beings in environmental, economic, and social areas. The importance of the recycling industry is increasing worldwide due to its benefits such as environmental protection, reduction of raw material needs, economical use of resources, and reduction of pollution. In this study, a fuzzy inventory model including the recycling process is proposed. Firstly, an expanded production/recycling model with fixed demand and return rates developed by Dobos and Richter (2003) is rearranged in terms of the waste disposal process and the level of stock to be created. Then, the model is fuzzified by taking the demand, marginal recovery, and marginal utilization rate parameters as trapezoidal fuzzy numbers. The graded mean integration representation method was used for the defuzzification process. Thus, the total cost per unit time and the optimal cycle time are expressed as deterministic values. When the results of the solved problem are evaluated, it is observed that the proposed fuzzy stock model gives better results for cycle times compared to the deterministic stock model based on.

Anahtar Kelimeler

• Inventory Model
• Recycling
• Fuzzy Logic
• GMIR Model

Geri Dönüşüm Süreci İçin Yeni Bir Bulanık Envanter Modeli

Öz

Kullanım ömrü sona eren ürünlerin çeşitli işlemlerden sonra yeniden kullanılabilir hale getirilmesi çevresel, ekonomik ve sosyal alanlarda insanoğluna birçok fayda sağlar. Çevrenin korunması, hammadde ihtiyacının azalması, kaynakların ekonomik kullanımı ve kirliliğin azaltılması gibi faydaları nedeniyle de geri dönüşüm sektörünün önemi dünya çapında giderek artmaktadır. Bu çalışmada, geri dönüşüm sürecini içeren bulanık bir stok modeli önerilmiştir. İlk olarak, Dobos ve Richter (2003) tarafından geliştirilen sabit talep ve geri dönüş oranlarına sahip genişletilmiş bir üretim/geri dönüşüm modeli atıkların yok edilme süreci ve oluşacak stok düzeyi bakımından yeniden düzenlenmiştir. Ardından talep, marjinal geri alma ve marjinal kullanım oranı parametreleri yamuk bulanık sayı olarak kabul edilip model bulanıklaştırılmıştır. Durulaştırma işlemi için kademeli ortalama entegrasyon temsil yöntemi kullanılmıştır. Böylece birim zamandaki toplam maliyet ve optimal çevrim süresi deterministik değerler olarak ifade edilmiştir. Çözülen problemin sonuçları değerlendirildiğinde, önerilen bulanık stok modelinin temel alınan deterministik stok modeline kıyasla çevrim süresi bakımından daha iyi sonuçlar verdiği gözlemlenmiştir.

Anahtar Kelimeler

• Stok modeli
• Geri Dönüşüm
• Bulanık Mantık
• GMIR Modeli
• Inventory Model
• Recycling
• Fuzzy Logic
• GMIR Model

Kaynakça

1. [1] Waters, D. 2003. Inventory Control of Management, 2nd, WILEY, England, 407s.
2. [2] Chandrasiri, A. M. P. 2016, Fuzzy Inventory Model without Shortages Using Triangular Fuzzy Numbers and Signed Distance Method, International Journal of Science and Research (IJSR), Cilt. 5, s. 187-190. DOI:10.21275/v5i7.ART2016144
3. [3] TÜDAM 2016, Geri Dönüşüm Sektörü Teşvik Raporu, http://www.tudam.org.tr/geri-donusum-sektoru-tesvik-raporu.pdf (Erişim Tarihi: 01.11.2021).
4. [4] Eroğlu, R., Aydemir, E. 2021, Geri Dönüşüm Sürecinde Kusurlu Yeniden Üretim Durumu için Yeni Bir Envanter Modeli, Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, Cilt. 23, s. 381- 397. DOI:10.21205/deufmd.2021236804
5. [5] Aydemir, E. ed. 2015, An EPQ Model With Imperfect Items Using Interval Grey Numbers, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt 5(1), s. 21-32. DOI: 10.11121/ijocta.01.2015.00204
6. [6] Sulak, H. ed. 2019, Ekonomik Sipariş Miktarı Modellerinde Talebin Kısmen Ertelenmesi ve Bir Uygulama, Yönetim ve Ekonomi Dergisi, Cilt. 26, s. 11-32. DOI:10.18657/yonveek.508931
7. [7] Aydemir, E., Bedir, F., Ozdemir, G., 2015, Degree of Greyness Approach for an EPQ Model with Imperfect Items in Copper Wire Industry, Journal of Grey System, 27(2), 13-26.
8. [8] Tiwari, S., Daryanto, Y., Wee, H. M. 2018, Sustainable Inventory Management with Deteriorating and Imperfect Quality Items Considering Carbon Emission, Journal of Cleaner Production, Cilt 192, 281-292. DOI: 10.1016/j.jclepro.2018.04.261

9. [9] Battini, D., Persona, A., Sgarbossa, F. 2014, A Sustainable EOQ Model: Theoretical Formulation and Applications, International Journal of Production Economics, Cilt 149, 145-153. DOI:10.1016/j.ijpe.2013.06.026
10. [10] Aydemir, E. 2015, Envanter Yönetimi Ve Uzantıları: Ekonomik Üretim Miktarı Modelleri Üzerine Bir Bilimsel Yazın Araştırması, Anadolu Üniversitesi Sosyal Bilimler Dergisi, Cilt 15(3), 97-112. DOI:10.18037/ausbd.95553
11. [11] Koh, S. G. ed. 2002, An Optimal Ordering and Recovery Policy for Reusable Items, Computers and IndustrialEngineering, Cilt. 43, s. 59-73. DOI:10.1016/S0360-8352(02)00062-1
12. [12] Teunter, R. 2003, Lot-Sizing for Inventory Systems with Product Recovery, Computers & Industrial Engineering, Cilt. 46, s. 431-441. DOI:10.1016/j.cie.2004.01.006
13. [13] Dobos, I, Richter, K. 2004, An Extended Production/ Recycling Model with Stationary Demand and Return Rates, International Journal of Production Economics, Cilt. 90, s. 311–323. DOI: 10.1016/j.ijpe.2003.09.007
14. [14] Dobos, I, Richter, K. 2006, A Production/Recycling Model with Quality Consideration, International Journal of Production Economics, Cilt. 104, s. 571–579. DOI: 10.1016/j.ijpe.2005.09.006
15. [15] Choi, D. W. Ed. 2007, A Generalized Ordering and Recovery Policy for Reusable Items, European Journal of Operational Research, Cilt. 182, s. 764–774. DOI: 10.1016/j.ejor.2006.08.048
16. [16] Konstantaras, I, Skouri, K. 2010, Lot Sizing for a Single Product Recovery System with Variable Setup Numbers, European Journal of Operational Research, Cilt. 203, s. 326–335. DOI: 10.1016/j.ejor.2009.07.018
17. [17] Hishamuddin, H. ed. 2012, A Disruption Recovery Model for a Single Stage Production-Inventory System, European Journal of Operational Research, Cilt. 222, s. 464-473. DOI: 10.1016/j.ejor.2012.05.033
18. [18] Schulz, T., Voigt, G. 2014, A Flexibly Structured Lot Sizing Heuristic for a Static Remanufacturing System, Omega, Cilt. 44, s. 21-31. DOI: 10.1016/j.omega.2013.09.003.
19. [19] Kozlovskaya, N. ed. 2016, A General Production And Recovery EOQ Model With Stationary Demand And Return Rates, Sayı. 378.
20. [20] Marshall, R. S., Vierstra, R. D. 2018, Autophagy: The Master of Bulk and Selective Recycling, Annual Review of Plant Biology, Cilt. 69, s. 173-208. DOI: 10.1146/annurev-arplant-042817-040606
21. [21] Rani, S. ed. 2020, Inventory Model for Deteriorating Items in Green Supply Chain with Credit Period Dependent Demand. International Journal of Applied Engineering Research, Cilt. 15, s. 157-172.
22. [22] Eroğlu, R., Aydemir, E. 2020, Tamir Sürecini İçeren Geri Dönüşüm Süreci İçin Yeni bir Envanter Modeli Geliştirilmesi, Mühendislik Bilimleri ve Tasarım Dergisi, 8(4), 1086-1098. DOI:10.21923/jesd.776390
23. [23] Mohapatra, S. ed. 2021, A Deterministic Inventory Model of Aluminium Refreshment Cans in Reverse Supply Chain, International Journal of Services and Operations Management, Cilt. 39, s. 151-180.
24. [24] Liao, H., Li, L. 2021, Environmental Sustainability EOQ Model for Closed-Loop Supply Chain Under Market Uncertainty: A Case Study of Printer Remanufacturing, Computers & Industrial Engineering, Cilt 151. DOI:10.1016/j.cie.2020.106525.
25. [25] Zadeh, L. A. 1965, Fuzzy Sets, Information and Control, Cilt. 8, s.338-353.
26. [26] Kacprzyk, J., Stanieski, P. 1982, Long-term Inventory Policy-Making Through Fuzzy Decision-Making Models. Fuzzy Sets and Systems, Cilt 8, s. 117-132. DOI: 10.1016/0165-0114(82)90002-1
27. [27] Petrovic, D., Sweeney, E. 1994, Fuzzy Knowledge-Based Approach to Treating Uncertainty in Inventory Control, Computer Integrated Manufacturing Systems, Cilt. 7, s. 147-152. DOI: 10.1016/0951-5240(94)90033-7
28. [28] Chen, S. H. ed. 1996, Backorder Fuzzy Inventory Model Under Function Principle. Information Sciences, Cilt. 95, s. 71-79. DOI: 10.1016/S0020-0255(96)00085-0
29. [29] Chang, S. C. ed. 1998, Economic Reorder Point for Fuzzy Backorder Quantity, European Journal of Operational Research, Cilt. 109, s. 183-202. DOI: 10.1016/S0377-2217(97)00069-6
30. [30] Yao, J. S. 2000, Fuzzy Inventory without Backorder for Fuzzy Order Quantity and Fuzzy Total Demand Quantity, Computers & Operations Research, Cilt. 27, s. 935-962. DOI: 10.1016/S0305-0548(99)00068-4
31. [31] Kao, C., Hsu, W. K. 2002, Lot Size-Reorder Point Inventory Model with Fuzzy Demands, Computers & Mathematics with Applications, Cilt. 43, s. 1291-1302. DOI: 10.1016/S0898-1221(02)00101-3
32. [32] Chang, H. C. 2004, An Application of Fuzzy Sets Theory to the EOQ Model with Imperfect Quality Items. Computers & Operations Research, Cilt. 31, s. 2079-2092. DOI: 10.1016/S0305-0548(03)00166-7
33. [33] Björk, K. M. 2008, The Economic Production Quantity Problem with a Finite Production Rate and Fuzzy Cycle Time, In Proceedings of the 41st Annual Hawaii International Conference on System Sciences, January, 68-68. IEEE. DOI: 10.1109/HICSS.2008.433
34. [34] Kazemi, N. ed. (2010), An Inventory Model with Backorders with Fuzzy Parameters and Decision Variables, International Journal Of Approximate Reasoning, Cilt. 51, s. 964-972. DOI: 10.1016/j.ijar.2010.07.001
35. [35] Jaggi, C. K. ed. 2012, Fuzzy Inventory Model for Deteriorating Items with Time-Varying Demand and Shortages, American Journal of Operational Research, Cilt. 2, s. 81-92. DOI: 10.5923/j.ajor.20120206.01
36. [36] Jana, D. K. ed. 2014, A Multiobjective Multi-Item Inventory Control Problem in Fuzzy-Rough Environment using Soft Computing Techniques, Advances in Decision Sciences. DOI: 10.1155/2014/617989
37. [37] Sahoo, N. K. ed. 2016, Fuzzy Inventory Model with Exponential Demand and Time-Varying Deterioration, Global Journal of Pure and Applied Mathematics, Cilt. 12, s. 2573-2589.
38. [38] Samanta, P. N. ed. 2017, Fuzzy Inventory Model For Two Parameter Weibull Deteriorating Items, Transactions on Mathematics, Cilt. 3, s. 27-36.
39. [39] Rani, S. ed. 2019, Fuzzy Inventory Model for Deteriorating Items in a Green Supply Chain with Carbon Concerned Demand. Opsearch, Cilt. 56, s. 91-122. DOI: 10.1007/s12597-019-00361-8.
40. [40] Khatua, D. ed. 2021, A Fuzzy Production Inventory Control Model Using Granular Differentiability Approach. Soft Computing, Cilt. 25, s. 2687-2701. DOI: 10.1007/s00500-020-05329-1
41. [41] Jeyakumari, S. R. ed. 2021, Optımızatıon of Fuzzy Inventory Model without Shortages, European Journal of Molecular & Clinical Medicine, Cilt. 7, s. 3116-3124.
42. [42] Muller, M. 2003, Essentıals of Inventory Management, 1. Inventory control. I. Title, American Management Association, USA. 255s.
43. [43] Alfares, H. K., Ghaithan, A. M. 2019, EOQ and EPQ Production-Inventory Models with Variable Holding Cost: State-of-the-Art Review, Arabian Journal for Science and Engineering, Cilt. 44, s. 1737-1755. DOI: 10.1007/s13369-018-3593-4
44. [44] S. N. Sivanandam, S. Sumathi and S. N. Deepa, 2007, Introduction to Fuzzy Logic Using MATLAB, Cill. 1, Berlin: Springer, 430s.
45. [45] Paksoy, T. ed. 2013, Bulanık Küme Teorisi, 1. Basım, Nobel Yayın: Ankara.
46. [46] Bolayır, B. 2016, Bulanık Doğrusal Programlamanın Gıda ve Tarım Ürünleri Atıklarının Geri Dönüşümünde Faaliyet Gösteren Bir İşletmede Uygulaması, Cumhuriyet Üniversitesi, Sosyal Bilimler Enstitüsü, Doktora Tezi, 274s, Sivas.
47. [47] Timothy J. R. 2010, Fuzzy Logıc wıth Engıneerıng Applıcatıons, Third Edition, John Wiley & Sons, USA, 577s.
48. [48] Zhao, J., Bose, B. K. 2002, Evaluation of Membership Functions for Fuzzy Logic Controlled Induction Motor Drive, In IEEE 2002 28th Annual Conference of the Industrial Electronics Society. IECON, 229-234, IEEE. DOI: 10.1109/IECON.2002.1187512
49. [49] İsen, E. 2017, Anfıs ve Bulanık C-Ortalamalar Yöntemleri Tabanlı Çok Kriterli Envanter Sınıflandırma Modeli , Sakarya Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 70s, Sakarya.
50. [50] . Mahata, G. C., Goswami, A. 2013, Fuzzy Inventory Models for Items with Imperfect Quality and Shortage Backordering Under Crisp and Fuzzy Decision Variables, Computers & Industrial Engineering, Cilt. 64, s. 190-199. DOI: 10.1016/j.cie.2012.09.003
51. [51] Deb, M., De, P. K. 2015, Optimal Solution of a Fully Fuzzy Linear Fractional Programming Problem By Using Graded Mean Integration Representation Method, Applications and Applied Mathematics, Cilt. 10, s. 571-587.
52. [52] Dobos, I., Richter, K. 2003, A Production/ Recycling Model with Stationary Demand and Return Rate, Central European Journal of Operations Research, Cilt. 11, s. 35- 46.