A New Mathematical Model in Cell Formation Problem with Consideration of Inventory and Backorder: Genetic and Particle Swarm Optimization Algorithms

Document Type : Research Paper


1 Faculty of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 Faculty of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran


Cell Formation (CF) is the initial step in the configuration of cell assembling frameworks. This paper proposes a new mathematical model for the CF problem considering aspects of production planning, namely inventory, backorder, and subcontracting. In this paper, for the first time, backorder is considered in cell formation problem. The main objective is to minimize the total fixed and variable costs, including the machine related costs, intercellular movements, deviation between the levels of cell utilizations, inventory, backorder, and sub-contracting costs. The presented mathematical model is validated using GAMS software, and various test problems are solved by Genetic Algorithm (GA) and Discrete Particle Swarm Optimization (DPSO) algorithm. The performance of the algorithms is compared with the results obtained by the GAMS. The results demonstrate, there is no significant difference between the results of algorithms. Finally, some sensitive analyses are carried out to analyze the effects of backorder and inventory holding costs. 


Main Subjects

Article Title [فارسی]

ارائه مدل ریاضی تشکیل سلول با در نظرگیری موجودی و پس‌افت از طریق الگوریتم‌های ژنتیک و بهینه‌سازی انبوه ذرات

Authors [فارسی]

  • مسعود ربانی 1
  • مهیار طاهری باویل علیائی 1
  • حامد فرخی اصل 2
  • مهدی مبینی 1
1 دانشکده مهندسی صنایع، پردیس فنی دانشگاه تهران، تهران، ایران
2 دانشکده مهندسی صنایع، دانشگاه علم و صنعت، تهران، ایران
Abstract [فارسی]

مسأله تشکیل سلول نخستین مرحله اولیه در مسأله تولید سلولی می­باشد. در این مقاله یک مدل ریاضی جدید برای مسأله تشکیل سلول با توجه به جنبه­های برنامه­ریزی تولید شامل میزان موجودی، تقاضای پس­افت و برون­سپاری ارائه گردیده­است. برای نخستین بار در این مقاله، تقاضای پس­افت در مسأله تشکیل سلول در نظر گرفته شده­است. هدف مدل ارائه شده کاهش کل هزینه­های ثابت و متغیر اعم از هزینه­های مربوط به ماشین­آلات، جابجایی بین­سلولی، انحراف بین سطوح استفاده از سلول، میزان موجودی، تقاضای پس­افت و برون­سپاری می­باشد. مدل ریاضی ارائه شده با استفاده از نرم افزار GAMS اعتبار سنجی شده و سپس به حل چند مسأله آزمایشی با استفاده از الگوریتم ژنتیک (GA) و الگوریتم گسسته بهینه­سازی ذرات (DPSO) پرداخته شده­است. عملکرد الگوریتم­ها با نتایج حاصل از نرم افزار GAMS مقایسه شده­است که نتایج حاصل نشان­دهنده این امر می­باشد که تفاوت معناداری در نتایج الگوریتم­ها وجود ندارد. در نهایت، برای تجزیه و تحلیل تأثیر هزینه­های نگهداری و تقاضای پس­افت، تحلیل حساسیت صورت گرفته شده­است. 

Keywords [فارسی]

  • تشکیل سلول
  • تقاضای پس‌افت
  • میزان موجودی
  • برنامه‌ریزی تولید
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