زمان‌بندی چندعاملی ماشین‌های موازی ناهمگن با در نظر گرفتن هزینه انرژی و کارهای به‌هنگام

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه بوعلی سینا، همدان، ایران

2 استادیار گروه صنایع دانشکده مهندسی دانشگاه بوعلی سینا

10.22084/ier.2019.17391.1796

چکیده

در مدل­های کلاسیک، معمولاً تمرکز بر ارائه برنامه زمان‌بندی با اهداف متناظر با زمان تکمیل کارها است حال‌آنکه با توجه به ارتباط بین اقتصاد، انرژی و نگرانی­های زیست‌محیطی، توجه به انرژی مصرفی ماشین­آلات در سالیان اخیر موردتوجه محققین حوزه‌های مختلف قرار گرفته است. همچنین در تحقیقات عموماً فرض بر آن بوده است که یک عامل (تولیدکننده) به‌تنهایی سعی در بهینه­سازی هدف خود داشته حال‌آنکه در واقعیت ممکن است چندین عامل تولیدی به دلیل محدودیت‌های خود به‌ناچار از منابع مشترک جهت پردازش کارها استفاده کنند. در همین راستا در پژوهش حاضر، مساله زمان‌بندی دوعاملی در کارگاه ماشین­های موازی ناهمگن موردبررسی قرار گرفته و ازآنجاکه انرژی مصرفی ماشین­ها با سرعت پردازش آن‌ها رابطه­ای مستقیم دارد، هزینه انرژی نیز مورد قرار گرفته است. در اینجا فرض شده است که عامل اول درصدد کمینه­سازی مجموع جریمه­های دیرکرد و هزینه انرژی و عامل دوم درصدد کمینه­سازی مجموع جریمه­های دیرکرد و زودکرد است. از آنجائیکه مساله فوق یک مساله Np-hard است، علاوه بر مدل‌سازی و حل آن، جهت ارائه راه‌حل‌های مناسب برای ابعاد بزرگ، الگوریتم فراابتکاری ممتیک پیشنهاد و به‌منظور بررسی عملکرد آن، نتایج حاصل با نتایج خروجی نرم­افزار گمز و فراابتکاری دیگر مقایسه شده است. با توجه به نتایج حاصل، مشاهده گردید که الگوریتم پیشنهادی در ابعاد مختلف مساله عملکرد مناسبی داشته بطوریکه در ابعاد کوچک، در مقایسه نتایج با روش Lp-Metric وزنی، و در ابعاد بزرگ، با در نظر گرفتن چندین معیار عملکردی مطرح در ادبیات، الگوریتم پیشنهادی کارایی بسیار مناسبی داشته است.

کلیدواژه‌ها


عنوان مقاله [English]

Multi-agent heterogeneous parallel machines scheduling problem with energy cost and just-in-time jobs

نویسندگان [English]

  • Amir Afsar 1
  • Javad Behnamian 2
1 Department of Industrial Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran
2 Department of Industrial Engineering, Faculty of Engineering, Bu-Ali Sina University
چکیده [English]

In the classic models of scheduling problems, researchers mostly concentrate on the objectives considering jobs completion time. Due to the relation among economy, energy and environmental concerns, attention to the energy use of machines have been considered by researchers in the field of scheduling in recent years. Also, In the literature of scheduling problems, it is mostly assumed that one agent try to optimize the problem. But, occasionally there are several agents that each has their own jobs and they must use a series of common resources to process them. In this study, a two-agent heterogeneous parallel-machines scheduling problem is studied in which the process speed of each job on each machine is adjustable. Since there is a direct link between the energy used in machines and process speed, the used energy costs affect on scheduling problem. In this study, the first agent is tried to minimize total tardiness penalty as well as energy costs of production machines and the second agent is tried to minimize total tardiness and earliness. The suitable schedule should be considered to allocate and sequence jobs of agents to the common resources to optimize appropriately the agent’s objective functions. Since the proposed problem is Np-hard, in order to solve it in large scale problems, a Memetic algorithm is developed and to verify the performance of this algorithm, we take into comparison the results of Memetic algorithm with the results of GAMS software and of another meta-heuristic algorithm.

کلیدواژه‌ها [English]

  • Multi-Agent scheduling
  • Parallel-machines scheduling
  • Energy cost
  • Just-in-time jobs
  • Memetic algorithm
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