برنامه‌ریزی سیستم تولید اقتصادی با در نظر گرفتن تقاضای متغیر و خرابی تصادفی ماشین‌

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران.

2 دانشیار، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران.

3 دانش‌آموخته کارشناسی ارشد، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران.

4 دانشجوی دکتری، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران.

چکیده

در پژوهش حاضر یک مسئله تولید اقتصادی با درنظرگرفتن محصولات معیوب حین تولید و همچنین خرابی ماشین و تقاضای متغیر بررسی شده است. در این پژوهش فرض شده است که محصولات با نرخ ثابتی تولید می­‌شوند؛ ولی ماشین حین تولید ممکن است دچار خرابی شود. خراب‌­شدن ماشین در حین تولید، یک متغیر تصادفی است که از توزیع نمایی با پارامتر مشخص پیروی می­‌کند. همچنین فرض شده است زمان تعمیر ماشین یک مقدار ثابت و مشخص است. برخلاف مدل‌های کلاسیک، تقاضا برای محصول تولیدی به‌صورت تابعی غیر­افزایشی از زمان بیان شده است. هدف اصلی، تعیین سیاست­‌های بهینه بازپرسازی مسئله بیان­‌شده به‌گونه‌ای است که کل هزینه سالیانه حداقل شود. به این منظور ابتدا یک مدل ریاضی ارائه می­‌شود؛ سپس مقدار متوسط هزینه در واحد زمان تعیین شده و بر اساس مفاهیم بهینه­‌سازی سراسری، مقادیر بهینه مشخص خواهد شد. درنهایت با حل یک مثال عددی به تجزیه‌وتحلیل مسئله بیان شده پرداخته می­‌شود. بر اساس نتایج، مدت‌زمان تعمیر تأثیر بسزای در هزینه کل سیستم دارد و در صورت افزایش آن هزینه‌های سیستم روند افزایشی به‌صورت نمایی خواهد داشت.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Production Planning System with Variable Demand and Stochastic Machine Breakdown

نویسندگان [English]

  • Heibatolah Sadeghi 1
  • Hiwa Farughi 2
  • Faezeh Kalevandi 3
  • Maryam Solgi 4
1 Assistant Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.
2 Associate Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.
3 Graduated Master, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.
4 PhD Student, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.
چکیده [English]

In this paper, the economic production is considered by considering defective products during production, a percentage of which can be recycled at a fixed cost, also machine failure, and variable demand. It is assumed that the products are produced at a fixed rate, but the machine may break down during production. Machine failure during production is a random variable that follows an exponential distribution with a specified parameter. If the machine breaks down during production, production stops immediately and the machine is repaired, and this study assumes that the machine repair time is a fixed value. Also, unlike the classical models, the demand for the manufactured product is expressed as a non-incremental function of time. The main goal is to determine the optimal policies for reproducing the problem in such a way that the total annual cost is minimized. For this purpose, first, a mathematical model is presented, then, the average cost per unit of time is determined, and based on the concepts of global optimization, the optimal values are determined. Finally, by solving a numerical example, the problem is analyzed. The results show that, the repair time has a great impact on the cost of the entire system, and as it increases, the system cost increases exponentially.

کلیدواژه‌ها [English]

  • Economic Production Model
  • Defective Products
  • Random Machine Failure
  • Variable Demand
  • Replenishment

مراجع

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