DEĞİŞKEN MAKİNE HIZLARINA SAHİP KAPASİTELİ İLİŞKİSİZ PARALEL MAKİNE ÇİZELGELEME PROBLEMİ İÇİN ÇÖZÜM YAKLAŞIMLARI

Öz

Bu çalışmada, değişken makine hızlarına sahip kapasiteli ilişkisiz paralel makine çizelgeleme problemi ele alınmıştır. Paralel makine çizelgeleme problemini ele alan çalışmaların çoğunda makinelerin sabit hızlarda çalıştığı varsayılmaktadır. Ancak pek çok üretim ortamında, makineler farklı hız seviyelerinde çalışabilmekte ve kapasite kısıtlarına tabi olabilmektedir. Bu nedenle bu çalışmada, makine hızlarının iş bazında değişebildiği ve kapasite kısıtlarının dikkate alındığı bir matematiksel model önerilmiştir. Önerilen model, işlerin hangi makinalara atanacağının yanı sıra hangi hızlarda üretileceklerine de karar vermektedir. Amaç enerji tüketimi ve fazla mesai maliyetlerinin toplamının enküçüklenmesidir. Modelin performansı, farklı ölçeklerdeki rassal türetilen test problemleri kullanılarak değerlendirilmiş ve değişken hızların toplam maliyet üzerindeki etkisi analiz edilmiştir. Elde edilen sonuçlar, iş bazında makine hızlarının değişebilmesine izin vermenin toplam maliyeti önemli ölçüde iyileştirebildiğini göstermiştir. Ayrıca daha büyük boyutlu problemlerin çözümü için iki aşamalı bir çözüm yaklaşımı önerilmiştir. Önerilen çözüm yaklaşımı ile matematiksel modelle süre limiti içinde çözülemeyen 100 iş 12 makineye kadar büyük boyutlu problemlere çözüm bulunmuştur.

Anahtar Kelimeler

• İlişkisiz paralel makine çizelgeleme
• Değişken makine hızları
• Kapasite kısıtı
• Matematiksel modelleme.

SOLUTION APPROACHES FOR CAPACITATED UNRELATED PARALLEL MACHINE SCHEDULING PROBLEM WITH VARIABLE MACHINE SPEEDS

Öz

In this study, the unrelated parallel machine scheduling problem with variable machine speeds is considered. In most studies addressing the parallel machine scheduling problem, machines are assumed to operate at fixed speeds. However, in most of the production environments, machines can usually operate at different speed levels and may be subject to capacity constraints. Therefore, in this study, a mathematical model is proposed in which machine speeds can vary on a job basis and capacity constraints are taken into account. The proposed model decides which machines to assign jobs to as well as at which speeds, they will be produced. The objective is to minimize the sum of energy consumption and overtime costs. The performance of the model is evaluated using randomly generated test problems at different sizes and the effect of variable speeds on total cost is analyzed. The results show that allowing machine speeds to vary for each individual job can significantly improve total cost. Additionally, a two-stage solution approach is proposed for large sized problems. The proposed approach addresses large sized problems with up to 100 jobs and 12 machines that cannot be solved by the proposed mathematical model.

Anahtar Kelimeler

• Unrelated parallel machine scheduling
• Variable machine speeds
• Capacity constraint
• Mathematical modeling.

Kaynakça

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