# Mathematical Model and Algorithm for sequencing operations in the machine building industry

Document Type : research paper

Authors

Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

In this paper, the problem of sequencing machines in the final assembly line with regard to the supply of parts has been investigated. For this reason, a basic integer linear programming model has been developed and based on this, the problem-solving algorithm is developed in accordance with the reaction-based approach based on the renewal of the sequence of operations. Also, due to the Np-hardness of the problem, a meta-innovative method based on the variable-neighborhood search algorithm is presented. To evaluate the proposed solution method, a sample of library issues was used and to simulate the disruption event, test questions were designed in large, medium and small dimensions. The results show that, in three categories of problems, the proposed meta-innovation method is approaching it in a very appropriate way compared to the best available method. In addition, due to the solving time, it is much more efficient than the optimal solution method and is responsive. The immediate needs are to update the sequence of operations in the face of disturbances created in the car production line.

Keywords

Article Title [فارسی]

### ارایه مدل ریاضی و الگوریتم فراابتکاری جهت تعیین توالی عملیات در صنعت ماشین سازی

Authors [فارسی]

• محمد فلاح
• ندا گورانی
گروه مهندسی صنایع، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران
Abstract [فارسی]

میزان در اﯾﻦ ﻣﻘﺎﻟﻪ ﻣﺴﺌﻠﻪ ﺗﻌﯿﯿﻦ ﺗﻮاﻟﯽ ماشین‌ها در ﺧﻂ ﻣﻮﻧﺘﺎژ ﻧﻬﺎﯾﯽ ﺑﺎ در ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺗﺎﻣﯿﻦ ﻗﻄﻌﺎت ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ. ﺑﺪﯾﻦ ﺟﻬﺖ ﯾﮏ ﻣﺪل ﭘﺎﯾﻪ ای ﺑﺮﻧﺎﻣﻪ رﯾﺰی ﺧﻄﯽ ﻋﺪد ﺻﺤﯿﺢ ﺗﻮﺳﻌﻪ ﯾﺎﻓﺘﻪ و ﺑﺮ ﻣﺒﻨﺎی آن، اﻟﮕﻮرﯾﺘﻢ ﺣﻞ ﻣﺴﺌﻠﻪ ﻣﻄﺎﺑﻖ ﺑﺎ روﯾﮑﺮد واﮐﻨﺸﯽ و ﻣﺒﺘﻨﯽ ﺑﺮ ﺗﺠﺪﯾﺪ ﺗﻮاﻟﯽ ﻋﻤﻠﯿﺎت، ﺗﻮﺳﻌﻪ ﯾﺎﻓﺘﻪ اﺳﺖ. ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ Np-hard ﺑﻮدن ﻣﺴﺌﻠﻪ، ﯾﮏ روش ﻓﺮا اﺑﺘﮑﺎری ﻣﺒﺘﻨﯽ ﺑﺮ اﻟﮕﻮرﯾﺘﻢ ﺟﺴﺘﺠﻮی ﻫﻤﺴﺎﯾﮕﯽ ﻣﺘﻐﯿﺮ ارائه گردیده است. ﺟﻬﺖ ارزﯾﺎﺑﯽ روش ﺣﻞ ﭘﯿﺸﻨﻬﺎدی، از ﻧﻤﻮﻧﻪ ﻣﺴﺎﺋﻞ ﮐﺘﺎﺑﺨﺎﻧﻪ ای بهره گرفته و ﺟﻬﺖ ﺷﺒﯿﻪ ﺳﺎزی رﺧﺪاد اﺧﺘﻼل، ﻣﺴﺎﺋﻞ آزﻣﻮن در اﺑﻌﺎد ﺑﺰرگ، ﻣﺘﻮﺳﻂ و ﮐﻮﭼﮏ ﻃﺮاﺣﯽ ﺷﺪه اﻧﺪ. ﻧﺘﺎﯾﺞ ﺑﺪﺳﺖ آﻣﺪه ﺑﯿﺎﻧﮕﺮ آن اﺳﺖ ﮐﻪ در ﺳﻪ دﺳﺘﻪ ﻣﺴﺎﺋﻞ، روش ﻓﺮا اﺑﺘﮑﺎری ﭘﯿﺸﻨﻬﺎدی در ﻣﻘﺎﯾﺴﻪ ﺑﺎ ﺑﻬﺘﺮﯾﻦ روش ﻣﻮﺟﻮد، ﺗﺎ ﺣﺪ ﺑﺴﯿﺎر ﻣﻨﺎﺳﺒﯽ ﺑﻪ آن ﻧﺰدﯾﮏ ﺷﺪه و ﻋﻼوه ﺑﺮ اﯾﻦ، از ﺟﻬﺖ زﻣﺎن ﺣﻞ ﻧﯿﺰ ﺑﺴﯿﺎر ﮐﺎراﺗﺮ از روش ﺣﻞ ﺑﻬﯿﻨﻪ ﺑﻮده و ﭘﺎﺳﺨﮕﻮی ﻧﯿﺎزﻫﺎی آﻧﯽ ﺑﻪ روزآوری ﺗﻮاﻟﯽ ﻋﻤﻠﯿﺎت در ﻣﻮاﺟﻬﻪ ﺑﺎ اﺧﺘﻼﻻت اﯾﺠﺎد ﺷﺪه در ﺧﻂ ﺗﻮﻟﯿﺪ ﺧﻮدرو ﻣﯽﺑﺎشد

Keywords [فارسی]

• ﺗﻌﯿﯿﻦ ﺗﻮاﻟﯽ ﻋﻤﻠﯿﺎت ماشین سازی
• اﺧﺘﻼل ﺗﺎﻣﯿﻦ
• ﺛﺒﺎت
• روﯾﮑﺮد واﮐﻨﺸﯽ

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