برنامه‌ریزی کنترل موجودی مسئله تولید اقتصادی محصولات فاسد شدنی با در نظر گرفتن تقاضای تصادفی

میرزایی, رضا; صادقی, هیبت اله

doi:10.66224/jii.3.2.99

برنامه‌ریزی کنترل موجودی مسئله تولید اقتصادی محصولات فاسد شدنی با در نظر گرفتن تقاضای تصادفی

نوع مقاله : مقاله پژوهشی

نویسندگان

رضا میرزایی ¹

هیبت اله صادقی ²

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

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

10.66224/jii.3.2.99

چکیده

از جمله مسائل کلیدی در اقتصاد امروز و مدیریت موجودی، تعیین مقدار تولید اقتصادی برای کالاهای فاسدشدنی است. این مسئله به دلیل چالش‌هایی مانند فسادپذیری محصولات، تولید معیوب، تقاضای تصادفی و وابستگی آن به قیمت، اهمیت ویژه‌ای دارد. در این پژوهش، مسئله تولید اقتصادی کالاهای فاسدشدنی تحت تقاضای تصادفی، با در نظر گرفتن فرضیات واقعی شامل فسادپذیری کالاها با نرخ ثابت، دوباره‌کاری محصولات معیوب، مجاز بودن کمبود به‌صورت پس‌افت کامل، وابستگی تقاضا به قیمت فروش تحت رفتار حرکت براونی و نرخ تولید کاهشی نمایی برای مدل‌سازی فرسودگی تجهیزات بررسی می‌شود.
در این مسئله، سیستم تولیدی کالاهای فاسدشدنی تولید می‌کند که بخشی از آنها معیوب است. سیستم دوباره‌کاری را بر روی اقلام معیوب انجام می‌دهد تا آنها را به محصولات سالم تبدیل کند، درحالی‌که کاهش تدریجی نرخ تولید را نیز لحاظ می‌نماید. برای بیشینه‌سازی سود متوسط بلندمدت و جلوگیری از افزایش هزینه‌ها، اندازه انباشته تولید، سطح کمبود، پارامترهای چرخه و سیاست قیمت‌گذاری پویا باید بهینه تعیین شود. برای این منظور، مدل ریاضی غیرخطی تصادفی جامعی با افق برنامه‌ریزی نامحدود ارائه می‌گردد. مدل با رویکرد ترکیبی شبیه‌سازی مونت‌کارلو و گرادیان نزولی حل‌شده، با مثال عددی اجرا می‌شود. نتایج عددی نشان می‌دهد که نرخ کاهش تولید و اقلام غیرقابل دوباره‌کاری بیشترین تأثیر منفی بر سودآوری دارند، درحالی‌که کشش قیمتی تقاضا بر نرخ فساد غلبه کرده و کاهش تدریجی قیمت در بازارهای حساس، سود را به‌طور قابل‌توجهی افزایش می‌دهد.

کلیدواژه‌ها

تقاضای براونی

کالاهای فاسدشدنی

سیستم تولید اقتصادی

شبیه‌سازی مونت‌کارلو

گرادیان نزولی

عنوان مقاله English

Inventory Control Planning of Economic Production Quantity for Perishable Products under Stochastic Demand

نویسندگان English

Reza Mirzaie ¹

heibatolah Sadeghi ²

¹ Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran.

² Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran.

چکیده English

One of the key issues in contemporary economics and inventory management is the determination of the economic production quantity for perishable products. This problem holds particular significance due to challenges such as product deterioration, imperfect production, stochastic demand, and its dependency on price, which complicate optimal decision-making in real-world supply chains.
In this research, the economic production quantity problem for perishable items under stochastic demand is examined, incorporating realistic assumptions including a constant deterioration rate for products, rework of defective items, full backordering of shortages, demand dependency on selling price under Brownian motion behavior, and an exponentially declining production rate to simulate the progressive deterioration of production equipment over time.
In this problem, the production system manufactures perishable products, a portion of which are defective due to imperfect processes. The system performs rework on defective items to convert them back to perfect-quality products, while also accounting for the gradual decline in production rate resulting from equipment aging. To maximize long-run average profit and prevent excessive costs associated with holding, shortages, and deterioration, the production lot size, backorder level, cycle parameters, and dynamic pricing policy must be optimally determined through joint optimization.
For this purpose, a comprehensive nonlinear stochastic mathematical model is developed with an infinite planning horizon to capture long-term behavior. The model is solved using a hybrid approach combining Monte Carlo simulation for handling stochastic elements and gradient descent for efficient optimization and is executed with a numerical example to demonstrate its applicability. Numerical results indicate that the production decline rate and non-reworkable defective items exert the most significant negative impact on profitability, whereas demand price elasticity dominates the deterioration rate in influencing optimal policies, and gradual price reduction in price-sensitive markets substantially increases profit by stimulating demand and mitigating losses from deterioration.

کلیدواژه‌ها English

Brownian demand

Perishable items

Economic production system

Monte Carlo simulation

Gradient descent

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