Bulanık Bozulma ve Öğrenme Etkileri Altında Tek Makine Erken/Geç Tamamlanma Probleminin Bulanık Şans Kısıtlı Programlama Tekniği ile İncelenmesi

Abstract

 Bu çalışmada tek makine ortamında bulanık bozulma ve öğrenme etkileri altında ağırlıklı erken/geç tamamlanma maliyetlerinin en aza indirilmesi amaçlanmaktadır. Probleme konu olan teslim tarihleri, işlem süreleri, öğrenme etkisi katsayıları ve bozulma etkisi katsayıları belirsizlik altındadır ve belirsizliği modelleyebilmek için üçgen bulanık sayılardan faydalanılmıştır. Belirsizlik parametrelere ait değerlerin rassal olarak ifade edilmesi değildir; iyi bilinmeyen, kesin olarak ifade edilemeyen değerlerin kapalı bir aralık içerisinde tanımlanmasıdır. Öyle ki, daha önce yapılmamış bir işe ait işlem süresinin ne kadar olacağının belirlenmesi bulanık sayılardan faydalanılarak, gerçekleşmesi beklenen işlem süresinin karar verici için uygunluğu modellenebilir. Böylelikle, parametrelerdeki belirsizlik belirgin bir hale getirilerek modellenebilir. Öğrenme etkisi bir işin sürekli olarak yapılan tekrarları neticesinde, iş yapan birimin işi her seferde kazandığı tecrübe ile daha kısa sürede yapmasını ifade etmektedir. Yapılan iş tekrarı artıkça işlem iş tekrarlarındaki işlem süresi giderek azalacaktır. Bozulma etkisi ise iş parçasının işlem için kuyrukta beklerken veya işlenirken, çevre koşulları ya da sistem karakteristikleri gereği işlem süresinin giderek artmasıdır. Bu çalışmada işlem süreleri, teslim tarihleri, bozulma etkisi ve öğrenme etkisi bulanık sayılar ile ifade edilmiştir. Bulanık sayılar ile ifade edilen bir parametreye ait bir değerin gerçekleşme olayının şans değeri ise güvenilirlik fonksiyonu ile kurgulanmış ve güvenirlik temelli şans kısıtlı algoritma tekniği ile model oluşturulmuştur. Son olarak tam sayılı bulanık doğrusal olmayan matematiksel model sunulmuş ve örnek veri seti ile problem çözülmüştür. 

Keywords

• Tek makine,erken ve geç tamamlanma,bulanık parametreler,şans kısıtlı programlama,karma tam sayılı doğrusal olmayan bulanık programlama

Fuzzy chance constrained programming technique for single machine earliness/tardiness scheduling problem under effects of fuzzy learning and deterioration

Abstract

To minimize total weighted earliness/tardiness costs of the jobs under effects of deterioration and learning on a single machine in a fully fuzzy environment, a mixed integer fuzzy non-linear mathematical programming model is presented in this study. Parameters in this study such as processing times, learning effect and deterioration effect are considered as fuzzy numbers because of their uncertainties. Learning and deterioration effects have been considered in scheduling problems for twenty years. Earliness/tardiness scheduling problems are significant for manufactures that adopt themselves in Just-in-Time philosophy. In order to model the real life complexity of Just-in-Time manufactures, earliness/tardiness scheduling problems can be used with mixed integer mathematical programming models. In this study, fuzzy chance constrained mathematical programming technique is used to find crisp equivalent of the proposed mixed integer fuzzy non-linear mathematical programming model and solve it.  

Keywords

• Single machine,earliness and tardiness,fuzzy parameters,chance constrained programming,fuzzy mixed integer nonlinear programming

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