A Lot-Sizing Model for Non-Instantaneous Deteriorating Products Under Advance Payment and Non-Linear Partial Backlogging

Document Type : Research Paper


1 School of Industrial and Systems Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 Department of Industrial Engineering, KHATAM University, Tehran, Iran


In real life conditions, the buyers sometimes pay all or a percentage of the product price before receiving it, and the wholesaler sometimes allows them to prepay it at equal intervals. The present study develops a new mathematical model for products with non-instantaneous deteriorating rates by considering consecutive advance payments. In the proposed inventory model, the shortage is consisting of lost sales along with backorders simultaneously. In addition, the model considers the backlogging as totally dependent on the waiting time for the further cycle. In addition, the appropriate conditions to achieve the optimal solutions have been developed, and numerical instances have been provided to verify and evaluate the results and solution method. The useful methods to effectively reduce the annual total cost are provided according to the results of the sensitivity analysis.


Main Subjects

Article Title [فارسی]

مدل تعیین اندازه دسته تولید برای محصولات زوال‌پذیر غیر آنی تحت پیش‌پرداخت و پشتیبانی جزئی غیر خطی

Authors [فارسی]

  • سارا توسلی 1
  • ندا معنوی زاده 2
  • آیدا رضائی 1
  • مسعود ربانی 1
1 دانشکده مهندسی صنایع و سیستم‌ها، دانشکده فنی، دانشگاه تهران، تهران، ایران
2 گروه مهندسی صنایع، دانشگاه خاتم، تهران، ایران
Abstract [فارسی]

در واقعیت، گاهی خریداران تمام یا درصدی از قیمت محصول را قبل از دریافت آن می‌پردازند و گاهی عمده‌فروش به آن‌ها اجازه می‌دهد تا در بازه‌های زمانی مساوی پیش‌پرداخت را انجام دهند. مطالعه حاضر با در نظر گرفتن پیش‌پرداخت‌های متوالی، یک مدل ریاضی جدید برای محصولات با نرخ زوال غیر آنی ارائه می‌کند. در مدل موجودی پیشنهادی، کمبود بصورت ترکیبی از فروش از دست‌رفته و پس‌افت بطور همزمان می‌باشد. همچنین، مدل، پشتیبانی را کاملاً وابسته به زمان انتظار برای چرخه بعدی می‌داند. علاوه بر این، شرایط مناسب برای دستیابی به راه حل‌های بهینه ایجاد و مثال‌های عددی برای تصدیق و ارزیابی نتایج و روش حل ارائه شده است. راهکارهای موثر برای کاهش هزینه کل سالانه بر اساس نتایج تحلیل حساسیت ارائه شده است.

Keywords [فارسی]

  • مقدار سفارش اقتصادی
  • پشتیبانی جزئی غیر خطی
  • زوال‌پذیری غیر آنی
  • پیش‌پرداخت
  • اقلام زوال‌پذیر
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