IJE TRANSACTIONS A: Basics Vol. 29, No. 4 (April 2016) 524-529   

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H. Mokhtari
( Received: March 09, 2016 – Accepted in Revised Form: April 14, 2016 )

Abstract    The production planning is an important problem in most of manufacturing systems in practice. Unlike many researches existing in literature, this problem encounters with great uncertainties in parameters and input data. In this paper, a single machine capacitated production planning problem is considered and a linear programming formulation is presented. The production costs are assumed to be uncertain parameters. To handle the uncertainties in the model, the grey systems theory is employed and the concept of grey numbers is incorporated into an optimization framework. In such systems, the uncertain parameters with unknown distributions can be handled by grey numbers. The grey linear programming (GLP) is a development of the classical linear programming which allows uncertainty to be effectively communicated into the optimization process. Finally, the uncertain problem is transformed into a GLP, and is solved by two linear deterministic sub-models.


Keywords    Grey Systems Theory; Linear Programming; Single Machine Production System; Uncertain Parameters


چکیده    برنامه‌ریزی تولید یکی از مسایل مهم در اکثر سیستم‌های تولیدی در عمل است. برخلاف اکثر تحقیقاتی که در ادبیات وجود دارند، این مسأله مواجه با عدم قطعیت زیادی در پارامترها و داده‌های ورودیش است. در تحقیق حاضر، یک مسأله برنامه‌ریزی تولید تک ماشینه با ظرفیت محدود مورد توجه قرار گرفته است و یک فرمول­بندی برنامه‌ریزی خطی برای آن ارایه شده است. فرض شده است که هزینه‌های تولید پارامترهای غیرقطعی مسأله هستند. به منظور مواجهه با این عدم قطعیت‌ها در مدل مسأله، تئوری سیستم‌های خاکستری به کار گرفته و مفهوم اعداد خاکستری با یک رویکرد بهینه‌سازی ترکیب شد. در چنین سیستم‌هایی، پارامترهای غیرقطعی با توزیع نامعلوم را می‌توان توسط اعداد خاکستری مدل­سازی کرد. برنامه‌ریزی خطی خاکستری، توسعه‌ی برنامه‌ریزی خطی کلاسیک است که اجازه می‌دهد عدم قطعیت به طور موثری در فرآیند بهینه‌سازی لحاظ گردد. نهیاتاً، مسأله‌ی غیرقطعی به یک مسأله برنامه‌ریزی خطی خاکستری تبدیل شده و توسط دو زیرمدل خطی حل می‌شود.


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