الگوریتم ژنتیک برای مسئله زمان بندی تک ماشین با جرایم زودکرد، و توان دوم دیرکرد و با در نظر گرفتن زمان بیکاری و شکست کار

نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار دانشکده مهندسی، گروه مهندسی صنایع، دانشگاه یزد

2 دانشجوی کارشناسی ارشد مهندسی صنایع، دانشگاه یزد

چکیده

  در این مقاله، مسئله زمانبندی تک ماشین با هزینه‌های زودکرد خطی و دیرکرد توان دوم، با در نظر گرفتن شکست کار و بیکاری مجاز مورد بررسی قرار گرفته و یک مدل ریاضی غیرخطی جدیدی برای مسئله زمان‌بندی تک ماشین ارائه شده است. با در نظر داشتن پیچیدگی در حل، این مسئله به عنوان مسائل NP-hard تلقی می‌گردد. بنابراین استفاده از روش‌هایی که نتایج بهینه تولید می‌کنند، تنها برای مسئله های با اندازه کوچک مناسب است. براین اساس یک الگوریتم ژنتیک برای حل این مسئله در اندازه‌های متوسط و بزرگ ارائه شده است به طوری که زمان حل به میزان بهینه یا نزدیک به آن کاهش پیدا کرده است. نمونه‌های عددی نشان می‌دهد که الگوریتم ارائه شده کارا و مؤثر می‌باشد.  

کلیدواژه‌ها


عنوان مقاله [English]

A genetic Algorithm for the Single Machine Scheduling Problem with Linear Earliness and Quadratic Tardiness Penalties with Consideration of Preemption and Idle Time

نویسندگان [English]

  • Mohamad_Bagher Fakhrzad 1
  • Mehdi Azimzade 2
1 Assistant Professor, Faculty of Industrial Engineering, Yazd University
2 M.Sc. in Industrial Engineering, Yazd University
چکیده [English]

In this paper, a non linear mathematical model has been proposed for solving a single machine scheduling problem with a linear earliness and quadratic tardiness cost, where machine idle time and preemptions are allowed. As the model is complex and cannot be solved in polynomial time, it has been assumed to be a NP hard problem, so the known optimal solution methods may not be applicable for its solution. A Genetic Algorithm approach has been developed for solving the model and numerical examples has been presented, which imply that the proposed method is efficient and effective.

کلیدواژه‌ها [English]

  • Single machine
  • Genetic Algorithm
  • Linear earliness
  • Quadratic tardiness
  • Machine idle time and preemption

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