Oğuzhan Ahmet ARIK, Mehmet Duran TOKSARI

BOZULMA VE ÖĞRENME ETKİLERİ ALTINDAKİ BULANIK İŞLEM SÜRELERİ İLE ÇİZELGE TAMAMLANMA SÜRESİNİN EN AZA İNDİRİLMESİ

Bu çalışma tek makine çizelgeleme problemlerinde öğrenme ve bozulma etkileri altındaki belirsiz işlem sürelerini incelemektedir. Öğrenme etkisi, bozulma etkisi ve işlem süresi gibi parametrelerdeki belirsizliği ifade edebilmek için bulanık sayılar kullanılmıştır. Çalışmaya konu olan ve belirsiz parametrelere sahip problemin amaç fonksiyonu çizelge tamamlanma süresinin en aza indirilmesidir. Literatürde birçok tek makine çizelgeleme problemi deterministik parametreler ile incelenmiştir. Bu çalışmada ise karar vericilerin öğrenme ve bozulma etkileri altındaki gerçek hayat tek makine çizelgeleme problemlerinin belirsizliği ile başa çıkabilmelerine olanak tanıyacak bir metot tanıtılmaktadır. Problemin karmaşıklığı nedeni ile birçok kısıt doğrusal değildir. Bulanık doğrusal olmayan karma tam sayılı bir matematiksel model problemin çözümü için önerilmiştir ve ayrıca bir sayısal örnek çalışma içerisinde verilmiştir.

Anahtar Kelimeler:

Çizelgeleme, Bulanık, Bozulma, Öğrenme Etkisi

MINIMIZING MAKESPAN WITH FUZZY PROCESSING TIMES UNDER JOB DETERIORATION AND LEARNING EFFECT

This paper proposes a single machine/processor scheduling problem considering uncertain processing times under job deterioration and learning effect. In order to express uncertainty of parameters such as processing times, effects of deterioration and learning, fuzzy numbers are used. The objective function in this study is to minimize the makespan (maximum completion time) where the parameters of the problem are fully uncertain. In the literature, many single machine scheduling problems have been interested in deterministic model parameters such as processing times, due dates and release dates. This study introduces a way for decision makers to cope with real life ambiguity and imprecision in single machine scheduling problems with uncertain processing time under uncertain effects of job deterioration and learning. Due to complexity of the problem, most of constraints are non-linear. A numerical example is illustrated and a fuzzy mixed integer nonlinear programming model is proposed in this study.

Keywords:

Scheduling Fuzzy, Job Deterioration, Learning Effect, Mixed Integer Nonlinear Programming,

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