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Journals / Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi / 2024 / Cilt: 40 Sayı: 1

A lagrange relaxation based algorithm for parallel injection machine scheduling problem

Paralel enjeksiyon makine çizelgeleme problemi için lagrange gevşetme temelli bir algoritma

Oğuzhan Ahmet Arık(ERCIYES UNIVERSITY)0000-0002-7088-2104
Pages
277–286
Publication Date
2024-08-16
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It has been observed that the Lagrange relaxation-based algorithm converges better to the optimum solution, and the performance of the proposed algorithm has been determined to be better than the mathematical model.

📌 3 Key Takeaways

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Objective & Hypothesis:Plastic injection machines produce semi-finished products and products required for many sectors.
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Key Findings & Data:The workshops where these machines come together and produce customer orders in parallel are called parallel injection machine workshops.
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Conclusion & Impact:It has been observed that the Lagrange relaxation-based algorithm converges better to the optimum solution, and the performance of the proposed algorithm has been determined to be better than the mathematical model.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Plastik enjeksiyon · paralel makine · iş bölüştürme

Abstract

Plastic injection machines produce semi-finished products and products required for many sectors. The workshops where these machines come together and produce customer orders in parallel are called parallel injection machine workshops. The problem of parallel injection machine scheduling is how the orders will be produced in which order and on which machine. Connecting injection molds to machines in the production of orders and modeling whether these molds are suitable for the machines are highly addressed in parallel injection machine scheduling problems. Again, sequence-dependent preparation or mold change time is also examined extensively in the literature. This study was inspired by a parallel injection machine workshop where plastic products for the healthcare industry are produced. The problem addressed is strikingly different from the problems examined in the literature in many aspects. A parallel process that includes differences such as dividing the order into machines, processing the batch of different orders, labor costs required for production, penalty costs for products produced after the delivery time, injection machines with different production speeds, energy costs and consideration of order-mould-machine compatibility. A mathematical model is proposed for the injection machine scheduling problem. In addition, the proposed mathematical model was ensured to be linear with all its constraints and objective function. A tool has been developed to solve real-life problems by solving the mathematical model proposed for the problem under consideration with Lagrange relaxation. Test problems of different sizes were created to test the validity of the established mathematical model and the Lagrange relaxation-based algorithm. It has been observed that the Lagrange relaxation-based algorithm converges better to the optimum solution, and the performance of the proposed algorithm has been determined to be better than the mathematical model.

Özet

Plastik enjeksiyon makineleri bir çok sektör için gerekli olan yarı mamul ve mamulleri üretmektedir. Bu makinelerin bir araya gelerek paralel bir şekilde müşteri siparişlerini ürettikleri atölyelere paralel enjeksiyon makine atölyesi olarak adlandırılmaktadır. Siparişlerin hangi sıra ile hangi makinede üretileceği ise paralel enjeksiyon makinesi çizelgeleme problemidir. Siparişlerin üretilmesinde enjeksiyon kalıplarının makinelere bağlanması ve bu kalıpların makineler için uygun olup olmadığının modellenmesi paralel enjeksiyon makine çizelgeleme problemlerinde oldukça ele alınmaktadır. Yine sıra bağımlı hazırlık veya kalıp değişim süresi de literatürde oldukça fazla incelenmektedir. Bu çalışmaya sağlık sektörü için plastik ürünlerin üretimin gerçekleştiği bir paralel enjeksiyon makinesi atölyesinden esinlenmiştir. Ele alınan problem bir çok yönü ile literatürdeki incelenen problemlerden dikkat çekici oranda farklıdır. Siparişin makinelere bölünmesi, farklı siparişlerin oluşturduğu yığının işlenmesi, üretim için gerekli işgücü maliyetleri, teslim zamanından sonra üretilen ürünlere ait olan ceza maliyetleri, farklı üretim hızlarına sahip enjeksiyon makinaları, enerji maliyetleri ve sipariş-kalıp-makine uygunluğunun göz önünde bulundurulması gibi farklılıkları içeren bir paralel enjeksiyon makine çizelgeleme problemi için matematiksel model önerilmiştir. Ayrıca önerilen matematiksel modelin tüm kısıtları ve amaç fonksiyonu ile beraber doğrusal olması sağlanmıştır. Ele alınan problem için önerilen matematiksel modelin Lagrange gevşetme ile çözülmesini sağlayarak gerçek hayat problemlerin çözülebilmesi için bir araç geliştirilmiştir. Kurulan matematiksel modelin ve Lagrange gevşetme temelli algoritmanın geçerliliklerini test etmek için farklı büyüklüklerde test problemleri oluşturulmuştur. Lagrange gevşetme temelli algoritmanın optimum çözüme daha iyi yakınsadığı gözlemlenmiş ve önerilen algoritmanın performansının matematiksel modelden daha iyi olduğu belirlenmiştir.

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Cite This Article

Arık, O. A. (2024). A lagrange relaxation based algorithm for parallel injection machine scheduling problem. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, Cilt: 40 Sayı: 1, 277–286. https://doi.org/10.17341/gazimmfd.1425180

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