Solving the Unrelated Parallel Batch Machine Scheduling Problem with Mixed-Integer Programming

Yıl 2023, Cilt: 26 Sayı: 2, 653 - 663, 05.07.2023

Merve Bakır , Aslı Sebatlı Sağlam , Fatih Çavdur

https://doi.org/10.2339/politeknik.996529

Cited By: 1

Öz

In this study, the problem of scheduling jobs with arbitrary sizes and non-zero release times on a set of unrelated parallel batch processing machines with different capacities is discussed. Three mixed-integer programming models with different objective functions are developed to solve the problem. Corresponding models aim at minimizing (i) the total flow time, (ii) the makespan and (iii) the total tardiness, respectively, which are considered to be among the most important objectives in scheduling problems. In order to test the validity and applicability of the proposed solution approach, different datasets are generated using some rules in the literature. The results obtained by solving the mathematical programming models with these data sets are analyzed in terms of some performance parameters.

Anahtar Kelimeler

Unrelated parallel batch processing, machine scheduling, total flow time, makespan, total tardiness, mixed-integer programming

Bağlantısız Paralel Parti Üretimi Yapan Makine Çizelgeleme Probleminin Karışık-Tamsayılı Programlama ile Çözümü

Öz

Bu çalışmada, keyfi boyutlara ve sıfır olmayan hazır olma zamanlarına sahip işlerin farklı kapasitelere sahip bir dizi bağlantısız paralel parti üretimi yapan makinelerde çizelgelenmesi problemi ele alınmıştır. Problemin çözümü için farklı amaç fonksiyonlarına sahip üç karışık-tamsayılı programlama modeli geliştirilmiştir. Bu modeller, sırasıyla, çizelgeleme problemlerinde en önemli amaçlar arasında bulunan (i) toplam akış süresini, (ii) son işin tamamlanma zamanını ve (iii) toplam gecikmeyi minimize etmeyi amaçlamaktadır. Sunulan çözüm yaklaşımının doğruluğunun ve uygulanabilirliğinin test edilmesi amacıyla, literatürdeki birtakım kurallar doğrultusunda farklı veri setleri üretilmiştir. Matematiksel programlama modellerinin bu veri setleri ile çözülmesiyle birlikte elde edilen sonuçlar çeşitli performans parametreleri açısından analiz edilmiştir.

Anahtar Kelimeler

Bağlantısız paralel parti üretimi, makine çizelgeleme, toplam akış süresi, son işin tamamlanma zamanı, toplam gecikme, karışık-tamsayılı programlama

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