Atama kısıtlı tip-1 montaj hattı dengeleme problemi: Bir kısıt programlama modeli yaklaşımı

Montaj hattı dengeleme problemi (MHDP) çevrim zamanı/istasyon sayısı ve görevler arasındaki öncelik ilişkileri gibi bazı kısıtlar içerir. Ancak, teknolojik ve organizasyonel kısıtlamalardan dolayı, uyumlu görevler, uyumsuz görevler, istasyon ve kaynak kısıtları gibi bazı diğer kısıtlar ile gerçek hayat üretim sistemlerinde karşılaşılabilmektedir. Bu çalışmada, bu kısıtların MHDP üzerindeki etkileri araştırılacaktır. Bu amaçla, bir kısıt programlama (KP) modeli önerilmiştir. Modelin amacı verilen bir çevrim zamanı değeri için istasyon sayısının en küçüklenmesidir (Tip-1 problemi). Önerilen KP modelinin karışık tamsayılı programlama (KTP) ve ABSALOM yaklaşımına göre kesinleştirilmiş optimal çözüm sayısı, optimal çözüm sayısı, iyi çözüm sayısı, optimal çözüm ile ulaşılan çözüm arasındaki görece fark ve ortalama toplam çözüm zamanı gibi performans ölçütleri açısından çözüm kalitesi araştırılmıştır. Ayrıca, önerilen yaklaşım literatürde yer alan problem örnekleri ile test edilmiştir ve modeller arasındaki karşılaştırmalı sonuçlar rapor edilmiştir. Sayısal deneyler, atama kısıtlarının problemin karmaşıklığını artırmasına rağmen, KP'nin MHDP'nin çözümünde etkin ve kaliteli bir çözüm yöntemi olduğunu göstermiştir.

Anahtar Kelimeler:

Montaj hattı dengeleme, Tip-1 problemi, Atama kısıtları, Kısıt programlama, Karışık tamsayılı programlama

Assembly line balancing type-1 problem with assignment restrictions: A constraint programming modeling approach

The assembly line balancing problem (ALBP) contains some constraints which are cycle time/number of stations and precedence relations between tasks. However, due to the technological and organizational limitations, several other restrictions, such as linked tasks, incompatible tasks, station, and resource constraints, can be encountered in real production systems. In this study, we evaluate the effect of these restrictions on ALBP. For this purpose, a Constraint Programming (CP) model is proposed. The objective of the model is to minimize the number of stations for given cycle time (Type-1 problem). We investigate the solution quality of the proposed CP model according to the mixed-integer programming (MIP) and ABSALOM in terms of the several performance measurements such as the number of proofing optimal solution, number of the optimal solution, number of the best solution, relative gap between the solution with the optimal solution and average total solution time. Furthermore, the proposed approach is tested on the literature test instances, and the comparison results between models are reported. Although assignment restrictions increase the complexity of the problem, numerical experiments demonstrate that CP is an effective and high-quality solution method in solving ALBP.

Keywords:

Assembly line balancing, Type-1 problem, Assignment restrictions, Constraint programming, Mixed-integer programming,

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