KAPASİTELİ BİR KEÇE ÜRETİM SİSTEMİNDE MAKİNE HIZI EN İYİLEME PROBLEMİ

Yıl 2025, Cilt: 33 Sayı: 2, 1780 - 1795, 22.08.2025

Banu Kabakulak

https://doi.org/10.31796/ogummf.1475020

Öz

Bu çalışmada, kimyasal reaksiyonların başarılı bir şekilde gerçekleşmesini sağlamak için makine hızlarının belirli sınırlar içinde tutulması gibi kendine özgü gereksinimlere sahip bir keçe üretim sistemi ele alınmıştır. Makine hızı kısıtları ve hem yarı mamul (YM) hem de nihai ürün stok sınırlamaları dikkate alınarak, her keçe türü için en iyi üretim miktarlarının ve ilgili makine hızlarının belirlenmesi amaçlanmaktadır. Amaç, makine kurulum ve üretim maliyetleri ile YM ve nihai ürün stok tutma maliyetlerini en küçüklemektir. Bu doğrultuda, Makine Hızı En İyileme (MHE) problemi tanımlanmış ve İstanbul, Türkiye'de faaliyet gösteren bir keçe üretim firmasının gereksinimlerine uyarlanmıştır. MHE problemi, en iyi üretim kararlarının bulunmasının NP-zor olduğu karma-tamsayılı doğrusal programlama modeli olarak ifade edilmiştir. Önerilen MHE modelinin üretim planlaması ve makine hız kararlarının otomasyonu konusunda etkinliği keçe üretim firmasının beş dönemlik verileri üzerinde doğrulanmıştır. 5 günlük planlama ufku için yapılan simülasyonlar, firmanın mevcut uygulamasına kıyasla toplam maliyette 3853 TL azalma, YM stoklarında %24 düşüş ve makine kullanım oranında %15’e varan iyileşme sağlandığını göstermektedir. Ayrıca, MHE modeli ile en iyilenen makine hızları, sistemin üretim kapasitesini %11 arttırmıştır. MHE modelinin karmaşıklığına dair deneysel analizler, modelin makine hızlarını içeren 6 aylık bir üretim planını bir saatten daha kısa sürede en iyileyebildiğini ortaya koymuştur.

Anahtar Kelimeler

Keçe Üretimi , Parti Büyüklüğü , Makine Hızı , Karma-Tamsayılı Programlama

A MACHINE SPEED OPTIMIZATION PROBLEM IN A CAPACITATED FELT PRODUCTION SYSTEM

Öz

In this study, we analyze a felt production system with unique requirements, such as maintaining machine speeds within specific limits to facilitate successful chemical reactions. By incorporating machine speed constraints and restrictions on both work-in-process (WIP) and end-product inventories, we aim to determine the optimal production quantities for each felt type and the corresponding machine speeds over a defined planning horizon. The objective is to minimize total costs, including machine setup and production costs as well as WIP and end-product inventory holding costs. To achieve this, we introduce the Machine Speed Optimization (MSO) problem and adapt it to the specific requirements of a felt manufacturing company operating in Istanbul, Türkiye. The MSO problem is formulated as a mixed-integer linear programming (MILP) model, which is NP-hard to solve for optimal production decisions. We validate the MSO model using the felt manufacturing company's case over five periods, demonstrating its effectiveness in automating production planning and machine speed decisions. The simulations for a 5-day planning horizon demonstrate a cost reduction of 3853 TL, a 24% decrease in WIP inventory, and up to a 15% improvement in machine utilization compared to the current practices of the felt manufacturing company. Additionally, the optimized machine speeds achieved through the MSO model enable the system to increase throughput by 11%. Experimental analysis of computational complexity reveals that the MSO model can generate an optimal 6-month production plan, including machine speeds, in under one hour.

Anahtar Kelimeler

Felt Production , Lot Sizing , Machine Speed , Mixed-Integer Programming

Kaynakça

• Akbalik, A., Penz, B., & Rapine, C. (2015). Capacitated lot sizing problems with inventory bounds. Annals of Operations Research, 229, 1–18. doi: https://doi.org/10.1007/s10479-015-1816-6
• Absi, N., Detienne B., & Dauzere-Peres, S. (2013). Heuristics for the multi-item capacitated lot-sizing problem with lost sales. Computers & Operations Research, 40(1), 264–272. doi: https://doi.org/10.1016/j.cor.2012.06.010
• Ben Ammar, H., Ayadi O., & Masmoudi, F. (2020). An effective multi-objective particle swarm optimization for the multi-item capacitated lot-sizing problem with set-up times and backlogging. Engineering Optimization, 52(7), 1198-1224. doi: https://doi.org/10.1080/0305215X.2019.1636978
• Brahimi, N., Dauzere-Peres, S., & Najid, N.M. (2005). Capacitated multi-item lot-sizing problems with time windows. Operations Research, 54, 951–967. doi: https://doi.org/10.1287/opre.1060.0325
• Chung-Yee, L., Çetinkaya, S., & Wagelmans, A.P.M. (2000). A dynamic lot-sizing model with demand time windows. Management Science, 47(10), 1384-1395. doi: https://doi.org/10.1287/mnsc.47.10.1384
• Florian, M., Lenstra, J.K., & Kan, A.H.G.R. (1980). Deterministic production planning: Algorithms and complexity. Management Science, 26(7), 669–679. doi: https://doi.org/10.1287/mnsc.26.7.669
• Ganesh, K. (2019). Capacitated lot sizing problems in process industries. Cham, Switzerland: Springer. doi: https://doi.org/10.1007/978-3-030-01222-9
• Geng, Z., & Yuan, J. (2023). Single-machine scheduling of multiple projects with controllable processing times. European Journal of Operational Research, 308(3), 1074-1090. doi: https://doi.org/10.1016/j.ejor.2023.01.026
• Gramani, M., França, P., & Arenales, M. (2009). A lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem. International Journal of Production Economics, 119(2), 219–227. doi: https://doi.org/10.1016/j.ijpe.2009.02.011
• Jans, R., & Degraeve, Z. (2008). Modeling industrial lot sizing problems: A review. International Journal of Production Research, 46, 1619–1643. doi: https://doi.org/10.1080/00207540600902262
• Karimi, B., Ghomi, S.M.T.F., & Wilson, J.M. (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega, 31, 365-378. doi: https://doi.org/10.1016/S0305-0483(03)00059-8
• Kimms, A. (2012). Multi-level lot sizing and scheduling: methods for capacitated, dynamic, and deterministic models. Springer Science & Business Media. doi: https://doi.org/10.1007/978-3-642-50162-3
• Koca, E., Yaman, H., & Aktürk, A.S. (2015). Stochastic lot sizing problem with controllable processing times. Omega, 53, 1-10. doi: https://doi.org/10.1016/j.omega.2014.11.003
• Levin, A., & Shusterman, T. (2023). Weighted throughput in a single machine preemptive scheduling with continuous controllable processing times. Acta Informatica, 60(2), 101-122. doi: https://doi.org/10.1007/s00236-022-00430-4
• Martinez, K.Y., Toso, E.A., & Morabito, R. (2016). Production planning in the molded pulp packaging industry. Computers & Industrial Engineering, 98, 554–566. doi: https://doi.org/10.1016/j.cie.2016.05.024
• Masmoudi, O., Yalaoui, A., Ouazene, Y., & Chehade, H. (2016). Multi-item capacitated lot- sizing problem in a flow-shop system with energy consideration. 8th IFAC Conference on Manufacturing Modelling, Management and Control, 49(12), 301–306. doi: https://doi.org/10.1016/j.ifacol.2016.07.621
• Naeem, M., Dias, D., Tibrewal, R., Chang, P.C., & Tiwari, M. (2012). Production planning optimization for manufacturing and remanufacturing system in stochastic environment. Journal of Intelligent Manufacturing, 24. doi: https://doi.org/10.1007/s10845-011-0619-0
• Özdamar, L., & Bozyel, M.A. (2000). The capacitated lot sizing problem with overtime decisions and setup times. IIE Transactions, 32(11), 1043-1057. doi: https://doi.org/10.1023/A:1013733024060
• Özyörük, D.A. ve Erol, P. (2000). Parti Büyüklüğü Problemleri ile İlgili Literatür Araştırması. Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 5(2), 105-119. Retrieved from https://dergipark.org.tr/tr/download/article-file/195154
• Quadt, D. (2004). Lot-sizing and scheduling for flexible flow lines. Springer Science & Business Media. doi: https://doi.org/10.1007/978-3-642-17101-7
• Ramya, R., Rajendran, C., Ziegler, H., Mohapatra, S., & Ganesh, K. (2019). Capacitated lot sizing problems in process industries. Cham, Switzerland: Springer.
• Renna, P. (2023) Controllable processing times with limited resources and energy consumption in flow shops: an assessment by simulation, International Journal of Management Science and Engineering Management, doi: https://doi.org/10.1080/17509653.2023.2285774
• Shabtay, D., & Steiner, G. (2007). A survey of scheduling with controllable processing times. Discrete Applied Mathematics. 155(3), 1643-1666. doi: https://doi.org/10.1016/j.dam.2007.02.003
• Wang, S., Wu, R., Chu, F., & Yu, J. (2022). Unrelated parallel machine scheduling problem with special controllable processing times and setups. Computers & Operations Research, 148, 105990. doi: https://doi.org/10.1016/j.cor.2022.105990
• Wagner, H.M., & Whitin, T.M. (1958). A dynamic version of the economic lot size model. Management Science, 5(1), 89–96. doi: https://doi.org/10.1287/mnsc.5.1.89
• Wu, T., Shi, L., & Duffie, N.A. (2010). An hnp-mp approach for the capacitated multi-item lot sizing problem with setup times. IEEE Transactions on Automation Science and Engineering, 7, 500–511. doi: https://doi.org/10.1109/TASE.2009.2039134
• Yanzhi, L., Yi, T., & Wang, F. (2012). An effective approach to multi-item capacitated dynamic lot-sizing problems. International Journal of Production Research, 50, 5348–5362. doi: https://doi.org/10.1080/00207543.2011.626459