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

Year 2018, Volume: 22 Issue: 2, 650 - 660, 01.04.2018

Oğuzhan Ahmet Arık , Mehmet Duran Toksarı

https://doi.org/10.16984/saufenbilder.299354

Cited By: 3

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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