Linear Mixed Integer Modeling of Two-Objective Unrelated Parallel Production Line Scheduling Problem Based on Divisibility of Orders in Garment Industry

Filiz Işık; Mustafa Yılmaz; Özden Üstün

Makale detayları

Linear Mixed Integer Modeling of Two-Objective Unrelated Parallel Production Line Scheduling Problem Based on Divisibility of Orders in Garment Industry

Yazarlar:

Filiz Işık | Mustafa Yılmaz | Özden Üstün

Yayıncı:

Süleyman Demirel University

Ana Başlıklar:

Üretimde Optimizasyon

Dergi:

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.29 Issue 1, pp.134-148

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

Türkçe

Document ID (Org No.):

2001345526

pISSN:

1308-6529

Anahtar kelimeler:

Özet:

 Based on studies addressing parallel machine scheduling problems, this study addresses the parallel production line scheduling problem in the garment sewing area of the textile sector. In general, scheduling problems assume that tasks are indivisible. However, dividing tasks can offer opportunities to prevent delays, increase customer satisfaction, and maximize machine capacity utilization. In this study, two mathematical models are developed for unrelated parallel machine scheduling problems, where tasks are either indivisible or divisible. The first model addresses the case where orders cannot be divided, while the second model allows for task division. In the second model, in addition to determining the production lines and sequences to which the orders are assigned, the model also determines how many parts each task will be divided into and the proportions at which they will be processed. The objectives of both models are to minimize the completion Abstract: Based on studies addressing parallel machine scheduling problems, this study addresses the parallel production line scheduling problem in the garment sewing area of the textile sector. In general, scheduling problems assume that tasks are indivisible. However, dividing tasks can offer opportunities to prevent delays, increase customer satisfaction, and maximize machine capacity utilization. In this study, two mathematical models are developed for unrelated parallel machine scheduling problems, where tasks are either indivisible or divisible. The first model addresses the case where orders cannot be divided, while the second model allows for task division. In the second model, in addition to determining the production lines and sequences to which the orders are assigned, the model also determines how many parts each task will be divided into and the proportions at which they will be processed. The objectives of both models are to minimize the completion time of the last task and the number of machines used. The bi-objective models are transformed into single-objective structures using the Weighted Sum method and the epsilon constraint method. Randomly generated test problems were solved with the proposed models using the GAMSCplex solver, and the results were compared. In the tests, considering the problems where the optimal solution was obtained, it was observed that the second model provided better results than the first model. It was also found that the epsilon constraint method in multi-objective programming yielded better appropriate points on the Pareto front. Additionally, it is suggested that heuristic methods may be applied in future studies for solving large-scale problems that the divisible task mathematical model cannot solve.

 Based on studies addressing parallel machine scheduling problems, this study addresses the parallel production line scheduling problem in the garment sewing area of the textile sector. In general, scheduling problems assume that tasks are indivisible. However, dividing tasks can offer opportunities to prevent delays, increase customer satisfaction, and maximize machine capacity utilization. In this study, two mathematical models are developed for unrelated parallel machine scheduling problems, where tasks are either indivisible or divisible. The first model addresses the case where orders cannot be divided, while the second model allows for task division. In the second model, in addition to determining the production lines and sequences to which the orders are assigned, the model also determines how many parts each task will be divided into and the proportions at which they will be processed. The objectives of both models are to minimize the completion Abstract: Based on studies addressing parallel machine scheduling problems, this study addresses the parallel production line scheduling problem in the garment sewing area of the textile sector. In general, scheduling problems assume that tasks are indivisible. However, dividing tasks can offer opportunities to prevent delays, increase customer satisfaction, and maximize machine capacity utilization. In this study, two mathematical models are developed for unrelated parallel machine scheduling problems, where tasks are either indivisible or divisible. The first model addresses the case where orders cannot be divided, while the second model allows for task division. In the second model, in addition to determining the production lines and sequences to which the orders are assigned, the model also determines how many parts each task will be divided into and the proportions at which they will be processed. The objectives of both models are to minimize the completion time of the last task and the number of machines used. The bi-objective models are transformed into single-objective structures using the Weighted Sum method and the epsilon constraint method. Randomly generated test problems were solved with the proposed models using the GAMSCplex solver, and the results were compared. In the tests, considering the problems where the optimal solution was obtained, it was observed that the second model provided better results than the first model. It was also found that the epsilon constraint method in multi-objective programming yielded better appropriate points on the Pareto front. Additionally, it is suggested that heuristic methods may be applied in future studies for solving large-scale problems that the divisible task mathematical model cannot solve.

 Based on studies addressing parallel machine scheduling problems, this study addresses the parallel production line scheduling problem in the garment sewing area of the textile sector. In general, scheduling problems assume that tasks are indivisible. However, dividing tasks can offer opportunities to prevent delays, increase customer satisfaction, and maximize machine capacity utilization. In this study, two mathematical models are developed for unrelated parallel machine scheduling problems, where tasks are either indivisible or divisible. The first model addresses the case where orders cannot be divided, while the second model allows for task division. In the second model, in addition to determining the production lines and sequences to which the orders are assigned, the model also determines how many parts each task will be divided into and the proportions at which they will be processed. The objectives of both models are to minimize the completion Abstract: Based on studies addressing parallel machine scheduling problems, this study addresses the parallel production line scheduling problem in the garment sewing area of the textile sector. In general, scheduling problems assume that tasks are indivisible. However, dividing tasks can offer opportunities to prevent delays, increase customer satisfaction, and maximize machine capacity utilization. In this study, two mathematical models are developed for unrelated parallel machine scheduling problems, where tasks are either indivisible or divisible. The first model addresses the case where orders cannot be divided, while the second model allows for task division. In the second model, in addition to determining the production lines and sequences to which the orders are assigned, the model also determines how many parts each task will be divided into and the proportions at which they will be processed. The objectives of both models are to minimize the completion time of the last task and the number of machines used. The bi-objective models are transformed into single-objective structures using the Weighted Sum method and the epsilon constraint method. Randomly generated test problems were solved with the proposed models using the GAMSCplex solver, and the results were compared. In the tests, considering the problems where the optimal solution was obtained, it was observed that the second model provided better results than the first model. It was also found that the epsilon constraint method in multi-objective programming yielded better appropriate points on the Pareto front. Additionally, it is suggested that heuristic methods may be applied in future studies for solving large-scale problems that the divisible task mathematical model cannot solve.

 Özet: Paralel makina çizelgeleme problemlerini ele alan çalışmalardan yola çıkarak tekstil sektöründe konfeksiyon dikim alanında paralel üretim hattı çizelgeleme problemi ele alınmıştır. Çizelgeleme problemlerine baktığımızda genellikle işlerin bölünemediği varsayılmaktadır. Oysaki işlerin bölünmesi, gecikmelerin önlenmesini, müşteri tatminini arttırmayı veya işlerin makinalardaki kapasite doluluklarını da arttırmayı gibi fırsatlar sunabilmektedir. Bu çalışmada, işlerin bölünemediği ve bölünebildiği ilişkisiz paralel makina çizelgeleme problemi için iki farklı çok amaçlı matematiksel model önerilmiştir. Birinci modelde siparişlerin bölünemediği durum ikinci modelde ise bölünebildiği durum gösterilmiştir. İkinci modelde siparişlerin hangi üretim hatlarına atanacağının ve sıralarının yanı sıra işlerin kaça bölüneceği ve hangi oranlarda işleneceği de belirlenmektedir. Her iki modellin amaçları, son işin tamamlanma zamanının ve kullanılacak makine sayısının enküçüklenmesidir. Çok amaçlı modeller Ağırlıklı Toplam yöntemi ve epsilon kısıt yöntemiyle tek amaçlı yapıya dönüştürülmüştür. Rassal türetilen test problemleri, GAMSCplex çözücüsü kullanılarak önerilen modeller ile çözülmüş, elde edilen sonuçlar karşılaştırılmıştır. Yapılan testlerde eniyi çözümü elde edilen problemler dikkate alındığında, ikinci modelin birinci modele göre daha iyi sonuçlar verdiği gözlemlenmiştir. Çok amaçlı programlama yöntemlerinin de epsilon kısıt yönteminde daha pareto yüzeyde daha iyi uygun noktalar verildiği görülmüştür. Ayrıca işlerin bölünmesine izin verilen matematiksel modelin çözemediği büyük boyutlu problemlerin çözümü için de ilerleyen çalışmalar da sezgisel yöntemlerin uygulanabileceği de önerilmiştir.

Makale detayları

Linear Mixed Integer Modeling of Two-Objective Unrelated Parallel Production Line Scheduling Problem Based on Divisibility of Orders in Garment Industry

Yazarlar:

Filiz Işık | Mustafa Yılmaz | Özden Üstün

Yayıncı:

Süleyman Demirel University

Ana Başlıklar:

Üretimde Optimizasyon

Dergi:

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.29 Issue 1, pp.134-148

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

Türkçe

Document ID (Org No.):

2001345526

pISSN:

1308-6529

Parallel production line scheduling

Multi-objective programming

Gams/Cplex

Splitting ordersParalel üretim hattı çizelgeleme

Çok amaçlı programlama

Gams/Cplex

Siparişlerin bölünmesi

Sayı

Makale detayları

Yazarlar: Filiz Işık | Mustafa Yılmaz | Özden Üstün

Yayıncı: Süleyman Demirel University

Ana Başlıklar: Üretimde Optimizasyon

Dergi: Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.29 Issue 1, pp.134-148

Belge Tipi: Makale

Yayın Tarihi: 4/2025

Belge Dili: Türkçe

Document ID (Org No.): 2001345526

pISSN: 1308-6529

Sayı

Yazarlar:

Filiz Işık | Mustafa Yılmaz | Özden Üstün

Yayıncı:

Süleyman Demirel University

Ana Başlıklar:

Üretimde Optimizasyon

Dergi:

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.29 Issue 1, pp.134-148

Belge Tipi:

Makale

Yayın Tarihi:

4/2025

Belge Dili:

Türkçe

Document ID (Org No.):

2001345526

pISSN:

1308-6529