ÜÇ BOYUTLU MERMER KESME PROBLEMİ İÇİN BİR TAM SAYILI DOĞRUSAL PROGRAMLAMA MODELİ

Mermer ocaklarından bloklar halinde çıkarılan mermerler fabrikalarda birtakım kesim işleminden geçmektedir. Bloklar ilk önce plakalar halinde kesilmektedir. Daha sonra bu plakalardan nihai ürün olan fayanslar elde edilmektedir. Hem plaka hem de fayans üretimi esnasında müşterilerin talep ettiği ürün boyutları dikkate alınmaktadır. Bu durum her talep için farklı kesim planlarının oluşturulmasına neden olmaktadır. Kesim planları oluşturulurken dikkat edilen en önemli husus atık miktarının en aza indirilmesidir. Atık miktarının minimize edilebilmesi için kesilecek her blok ve sipariş için yeniden kesim planının belirlenmesi gerekmektedir. Bu çalışmada atık mermer miktarını en aza indirecek kesim planını oluşturmaya odaklanılmıştır. Bunun için tam sayılı doğrusal programlama modeli geliştirilmiştir. Geliştirilen model hem plaka üretim sürecinde hem de fayans üretim sürecinde ortaya çıkacak atık miktarını en aza indirmeyi amaçlamıştır. Model bir mermer fabrikasının verileri kullanılarak çözülmüştür.

Anahtar Kelimeler:

Mermer kesme problemi, Tam sayılı doğrusal programlama, Atık minimizasyonu.

AN INTEGER LINEAR PROGRAMMING MODEL FOR THE THREE-DIMENSIONAL MARBLE CUTTING PROBLEM

Marbles extracted in blocks from marble quarries go through a number of cutting processes in factories. The blocks are first cut into plates. Then, the final product, tiles, is obtained from these plates. During the production of both slabs and tiles, the product dimensions requested by the customers are taken into account. This situation causes the creation of different cutting plans for each demand. The most important point that is taken into consideration while creating cutting plans is minimizing the amount of waste. In order to minimize the amount of waste, a re-cutting plan must be determined for each block and order to be cut. In this study, the focus is on creating a cutting plan that will minimize the amount of waste marble. For this, integer linear programming model has been developed. The developed model aims to minimize the amount of waste that will arise in both the plate production process and the tile production process. The model is solved using data from a marble factory.

Keywords:

Mermer kesme problemi, Tam sayılı doğrusal programlama, Atık minimizasyonu.,

PDF

___

Akbulut, H., ve Gürer, C. (2007). Use of aggregates produced from marble quarry waste in asphalt pavements. Building and environment, 42(5), 1921-1930.
Aksu, D. T., Durak B. (2016). A dynamic programming algorithm for the online cutting problem with defects and quality grades. IFAC-PapersOnLine 49(12), 17-22.
Alves, C., Bras, P., Valerio de Carvalho, J. M., ve Pinto, T. (2012). A variable neighborhood search algorithm for the leather nesting problem. Mathematical Problems in Engineering, 2012.
Baykasoğlu, A., ve Özbel, B. K. (2021). Modeling and solving a real-world cutting stock problem in the marble industry via mathematical programming and stochastic diffusion search approaches. Computers ve Operations Research, 128, 105173.
Bilgin, N., Yeprem, H. A., Arslan, S., Bilgin, A., Günay, E., ve Marşoglu, M. (2012). Use of waste marble powder in brick industry. Construction and Building Materials, 29, 449-457.
Brás, P., Alves, C., de Carvalho, J. V., ve Pinto, T. (2010). Exploring new constructive algorithms for the leather nesting problem in the automotive industry. IFAC Proceedings Volumes, 43(17), 225-230.
Diyaley, S., ve Chakraborty, S. (2022). Metaheuristics-based nesting of parts in sheet metal cutting operation. Operational Research in Engineering Sciences: Theory and Applications, 5(2), 1-16.
Durak, B., Aksu, D. T. (2017). Dynamic programming and mixed integer programming based algorithms for the online glass cutting problem with defects and production targets. International Journal of Production Research, 55(24), 7398-741.
Eroğlu, D. Y., Orbak, A. Y. (2020). Simulated Annealing Algorithm and Implementation Software for Fabric Cutting Problem. Textile and Apparel, 30(1), 10-19.
Ersoy, M., ve Yeşilkaya, L. (2013). Choice of marble block cutting machine by using Analytic Hierarchy Process (AHP) method. International Journal of Information Technology and Business Management, 19(1), 67-80.
Gazi, A., Skevis, G., ve Founti, M. A. (2012). Energy efficiency and environmental assessment of a typical marble quarry and processing plant. Journal of cleaner production, 32, 10-21.
Hebhoub, H., Aoun, H., Belachia, M., Houari, H., ve Ghorbel, E. (2011). Use of waste marble aggregates in concrete. Construction and Building Materials, 25(3), 1167-1171.
Kahraman, B. (2011). Three dimensional cutting problem: an integer programming approach. Mathematical and Computational Applications, 16(1), 105-112.
Maden Tetkik ve Arama Müdürlüğü (2022). Erişim adresi: https://www.mta.gov.tr/v3.0/bilgi-merkezi/maden-dis-ticaret
Marvila, M. T., Alexandre, J., de Azevedo, A. R., ve Zanelato, E. B. (2019). Evaluation of the use of marble waste in hydrated lime cement mortar based. Journal of Material Cycles and Waste Management, 21(5), 1250-1261.
Menningen, J., Siegesmund, S., Lopes, L., Martins, R., ve Sousa, L. (2018). The Estremoz marbles: an updated summary on the geological, mineralogical and rock physical characteristics. Environmental earth sciences, 77(5), 1-31.
MKS Makina (2022 a). Erişim adresi: https://www.mks.com.tr/tr/urun/blok-kesme-este-st-makinesi-.html#
MKS Makina (2022 b). Erişim adresi: https://www.mks.com.tr/tr/urun/kafa-kesme-boy-ebatlama-makinesi-.html
Orhan, H., ve Arık, F. (2019). Doğal taşların işletme mevzuatı ve çevre dostu uygulama örnekleri. Mavi Gezegen Popüler Yerbilim Dergisi, 26, 14-25.
Özfirat, P. M. (2012). An integer programming approach for the three-dimensional cutting planning problem of marble processing industry. The International Journal of Advanced Manufacturing Technology, 59(9), 1057-1064.
Petunin, A. A., ve Stylios, C. (2016). Optimization models of tool path problem for CNC sheet metal cutting machines. IFAC-PapersOnLine, 49(12), 23-28.
Plankovskyy, S., Tsegelnyk, Y., Shypul, O., Pankratov, A., ve Romanova, T. (2020). Cutting irregular objects from the rectangular metal sheet. In Integrated Computer Technologies in Mechanical Engineering (pp. 150-157). Springer, Cham.
Rodrigues, C. D., Cherri, A. C., ve de Araujo, S. A. (2023). Strip based compact formulation for two-dimensional guillotine cutting problems. Computers & Operations Research, 149, 106044.
Siegesmund, S., ve Török, Á. (2011). Building stones. In Stone in Architecture (pp. 11-95). Springer, Berlin, Heidelberg.
Ticaret Bakanlığı (2021). Erişim adresi: https://ticaret.gov.tr/data/5b87000813b8761450e18d7b/Do%C4%9Fal%20Ta%C5%9Flar%20Sekt%C3%B6r%20Raporu%202021.pdf
Traverso, M., Rizzo, G., ve Finkbeiner, M. (2010). Environmental performance of building materials: life cycle assessment of a typical Sicilian marble. The international journal of life cycle assessment, 15(1), 104-114.
Tsao, Y. C., Delicia, M., ve Vu, T. L. (2022). Marker planning problem in the apparel industry: Hybrid PSO-based heuristics. Applied Soft Computing, 123, 108928.