MONTAJ HATLARINDA YENİDEN İŞLEME İSTASYON POZİSYONUNUN OPTİMİZASYONU İÇİN BİR KARIŞIK-TAMSAYILI PROGRAMLAMA MODELİ

Montaj hatlarında, ürünün önceden belirlenen birtakım özelliklere uygun olmaması (hatalı olması) durumunda, ürün, hata giderme çalışmalarının gerçekleştirilmesi için yeniden işleme istasyonuna gönderilmektedir. Yeniden işleme istasyonuna gönderilen hatalı ürün sayısı ise montaj hattının hata oranına bağlıdır. Yeniden işleme istasyonunun kullanım oranının düşük olması durumunda, bu istasyon hata giderme işlemlerine ek olarak standart görevlerin gerçekleştirilmesi için de kullanılabilir. Yeniden işleme istasyonunun bu amaçla kullanılması ile hattın çevrim süresi azaltılabilir. Yeniden işleme istasyonu genellikle montaj hattının sonunda konumlandırılmakla birlikte, standart görevlerin gerçekleştirilmesi için de kullanılması durumunda pozisyonunun değiştirilmesi avantajlı olabilir. Bu çalışmada, hata giderme işlemlerine ek olarak standart görevlerin gerçekleştirilmesi için de kullanılan bir yeniden işleme istasyonunun dinamik olarak pozisyonunun belirlenmesi ile çevrim süresini minimize eden bir doğrusal olmayan-karışık-tamsayılı programlama modeli önerilmektedir. Önerilen modelin doğrusal olmayan yapısı değişken dönüşümleri ile doğrusal hale dönüştürülmüştür. Yeniden işleme istasyon pozisyonunun seçimi, görevler arasındaki öncelik ilişkilerine bağlı olarak bu istasyona atanabilecek olan potansiyel görev sayısını etkilemektedir. Bu çalışmada, önerilen model kullanılarak yeniden işleme istasyon pozisyonu optimize edilmektedir. Yeniden işleme istasyonuna atanabilecek olan potansiyel görev sayısını etkileyen diğer bir faktör de montaj hattı hata oranıdır. Çalışma kapsamında önerilen model literatürde yer alan farklı örneklemler kullanılarak test edilmiştir. Problemlerin optimal çözümleri elde edilerek, sonuçlar analiz edilmiştir.

Anahtar Kelimeler:

Montaj hattı dengeleme, Yeniden işleme istasyonu, İstasyon pozisyonu belirlenmesi, Çevrim süresi minimizasyonu, Karışık-tamsayılı programlama

A Mixed-Integer Programming Model for Assembly Line Balancing: Using Rework Station for Standard Tasks and Optimizing Station Position

In an assembly line, if a product does not meet some pre-defined specifications (i.e., if it is defective), it is generally sent to a rework station where necessary correction (rework) operations are performed. On the other hand, the number of products sent to the rework station for rework operations depends on the rework (defect) rate of the assembly line. If the defect rate is relatively low, the rework station can be used to perform standard tasks in addition to rework operations. Using the rework station for this purpose might decrease the cycle time of the assembly line. Although rework stations are generally positioned at the end of an assembly line, it might be advantageous to change its position if it is also used for performing standard tasks. In this study, a nonlinear-mixed-integer programming model is proposed to minimize the cycle time of an assembly line by dynamically positioning the rework station which is also used to perform standard tasks in addition to rework operations. The nonlinear structure of the proposed model is linearized using some variable transformations. The position of the rework station affects the number of potential tasks assigned to this station depending on the precedence relationships of the tasks. In this study, the position of the rework station is optimized using the proposed model. Another factor that affects the number of potential tasks assigned to the rework station is defect rate of the assembly line. The proposed model is tested for different defect rates using some sample problems from the literature. The problems are solved to optimality and the results are analyzed.

Keywords:

Assembly line balancing, Rework station, Determination of station position, Cycle time minimization, Mixed-integer programming,

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