توسعه روش آزادسازی لاگرانژین برای حل مسأله زمانبندی در محیط جریان کارگاهی انعطاف پذیر

نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشگاه صنعتی نوشیروانی بابل

2 دانشگاه تربیت مدرس تهران

چکیده

 مسأله زمانبندی در محیط جریان کارگاهی انعطاف­پذیر شامل تعیین توالی در یک مسأله جریان کارگاهی می­باشد که در هر مرحله حداقل یک یا چند ماشین موازی غیرمشابه وجود دارد. تابع هدف مسأله کمینه­سازی حداکثر زمان تکمیل کارها می­باشد. برای حل این مسأله از روش آزادسازی لاگرانژین استفاده‌شده است. برای حل زیرمسأله­های تولیدشده با استفاده از روش آزادسازی لاگرانژین نیز از دو رویکرد ساده­سازی زیرمسأله­ها و توسعه قوانین چیرگی استفاده‌شده است. نتایج نشان می­دهد که هر دو روش می­توانند به جواب­های نزدیک به بهینه در زمان­های نسبتاً معقول دست پیدا کنند ولی تفاوت معناداری با یکدیگر ندارند. همچنین روش ساده­سازی زیرمسأله‌ها در مدت زمان کوتاه­تری می­تواند به جواب­های مورد نظر دست یابند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Developing a Lagrangian Relaxation Method for Flexible Flowshop Scheduling Problem

نویسندگان [English]

  • Ebrahim Asadi Gangraj 1
  • Nasim Nahavandi 2
1 Babol University of Technology
2 Tarbiat Modares University
چکیده [English]

Flexible flow shop scheduling problem (FFS) with unrelated parallel machines contains sequencing in flow shop where, at any stage, there exists one or more unrelated parallel machines. The objective consists of minimizing the maximum completion time. A new Lagrangian relaxation (LR) method is developed to solve the candidate problem. To solve the sub-problems in LR, we use two approaches such as, simplicity of sub-problems and dominance rules. The results show that the both approaches can achieve the near-optimal solution in reasonable time; but there is no significant difference between them. On the other side, simplicity of sub-problems can achieve the solution in reasonable time.

کلیدواژه‌ها [English]

  • Flow Shop
  • Makespan
  • Lagrangian Relaxation
  • Dominance Rules

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