Optimization of the Inflationary Inventory Control Model under Stochastic Conditions with Simpson Approximation: Particle Swarm Optimization Approach

Document Type: Review article


1 Faculty of Industrial Engineering, Islamic Azad University, Science and Research Branch, Saveh, Iran

2 Faculty of Industrial Engineering, Kharazmi University, Tehran, Iran

3 Faculty of Industrial Engineering, Islamic Azad University, Karaj Branch, Iran

4 Department of Information Technology of Sufi Razi, Zanjan, Iran


In this study, we considered an inflationary inventory control model under non-deterministic conditions. We assumed the inflation rate as a normal distribution, with any arbitrary probability density function (pdf). The objective function was to minimize the total discount cost of the inventory system. We used two methods to solve this problem. One was the classic numerical approach which turned out to be prohibitively difficult. The other was a proposed combination method which used Simpson approximation and particle swarm optimization (PSO). To illustrate the theoretical results, we have provided numerical examples.


Main Subjects

Article Title [Persian]

بهینه‌سازی مدل کنترل موجودی تورمی تحت شرایط احتمالی با رویکرد تقریب سیمپسون : بهینه‌سازی ازدحام ذرات

Authors [Persian]

  • سید مصطفی اورند 1
  • ابوالفضل میرزازاده 2
  • فرزانه احمدزاده 3
  • فرید طالب لو 4
1 دانشکدة مهندسی صنایع، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات، ساوه، ایران
2 دانشکدة مهندسی صنایع، دانشگاه خوارزمی، تهران، ایران
3 دانشکدة مهندسی صنایع، دانشگاه آزاد اسلامی، واحد کرج، ایران
4 گروه فناوری اطلاعات، دانشگاه صوفی رازی، زنجان، ایران
Abstract [Persian]

این مقاله یک مدل کنترل موجودی تورمی تحت شرایط غیرقطعی در نظر می‌گیرد. فرض می‌کنیم نرخ تورم از تابع توزیع نرمال، با هر تابع چگالی احتمال دلخواه (PDF) پیروی می‌کند. تابع هدف به حداقل رساندن هزینة تخفیف کل سیستم موجودی است. از دو روش جهت حل این مسئله استفاده شد: رویکرد کلاسیک عددی که معلوم می‌شود روش دشواری است؛ و روش ترکیبی پیشنهادی با استفاده از تقریب سیمپسون و بهینه‌سازی ازدحام ذرات (PSO). مثال‌های عددی جهت نشان دادن نتایج نظری ارائه شده است.

Keywords [Persian]

  • احتمالی
  • ازدحام ذرات
  • بهینه‌سازی تقریب سیمپسون
  • تورم
  • سیستم موجودی
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