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

Year 2023, Volume: 10 Issue: 1, 658 - 669, 29.03.2023

Gokhan Yilmaz , Yusuf Şahin

https://doi.org/10.30798/makuiibf.1220059

Abstract

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.

Keywords

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

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

Abstract

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.

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