Zamana-bağımlı öğrenme etkili çizelgeleme probleminde maksimum gecikme minimizasyonu: Doğrusal olmayan programlama modeli

Çizelgeleme literatürünün çoğunda işlerin işlem zamanları sabit kabul edilmiştir. Ancak işlerin işlem zamanlarında, başlama zamanı veya pozisyonuna bağlı olarak azalma görülebilmektedir. Bu olgu literatürde öğrenme etkisi olarak bilinmektedir. Bu çalışmada da zamana-bağımlı öğrenme etkili tek makineli çizelgeleme problemi ele alınacaktır. Ele alınan problemin amaç fonksiyonu maksimum gecikme minimizasyonudur. Çalışmada problemin klasik (öğrenme etkisiz) durumunda en iyi çözümü garanti eden EDD (en erken teslim tarihi) kuralının, zamana-bağımlı öğrenme etkili durumda optimal çözümü garanti etmediği gösterilmiştir. Ayrıca problemi çözmek için doğrusal-olmayan programlama modeli geliştirilmiş ve geliştirilen modelle 14 işe kadar optimal çözümler bulunmuştur.

Minimizing the maximum lateness in a scheduling problem with a time-dependent learning effect: A non-linear programming model

In traditional scheduling problems, most literature assumes that the processing time of a job is fixed. However, there are many situations where the processing time of a job depends on the starting time or the position of the job in a sequence. In such situations, the actual processing time of a job may be more or less than its normal processing time if it is scheduled later. This phenomenon is known as the ‘‘learning effect’’. In this study, we introduce a time-dependent learning effect into a single-machine scheduling problem. The objective function of the problem is minimization of the maximum lateness. This study shows that EDD rule, which guarantees the best solution in classical situation (without learning effect), can not guarantee the best results in the situation with learning effect. In addition, a non-linear programming model is proposed for this problem, and solutions are found for problems which have up to 14 jobs.

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