نشریه پژوهش های مهندسی صنایع در سیستم های تولید

نشریه پژوهش های مهندسی صنایع در سیستم های تولید

مدل‌سازی مسأله‌‌ی مدیریت زنجیره‌ی تأمین کالا به‌صورت بازی استکلبرگ دوسطحی و حل آن بااستفاده از شرایط بهینگی کاروش-کان-تاکر

نوع مقاله : مقاله پژوهشی

نویسندگان
1 گروه ریاضی، دانشکدۀ علوم ریاضی و آمار، دانشگاه بیرجند، بیرجند، ایران
2 گروه مهندسی صنایع، دانشکدۀ کامپیوتر و مهندسی صنایع، دانشگاه صنعتی بیرجند، بیرجند، ایران
چکیده
در مسائل زنجیره‌تأمین کالا در دنیای واقعی، گاهی با مسائلی با دو تأمین‌کننده در دو سطح مختلف مواجه می‌شویم که به‌دلیل جایگاه‌شان در تأمین کالا، یکی نقش رهبر و دیگری نقش پیرو را دارد، لذا مسأله به‌صورت مدل بازی استکلبرگ دوسطحی فرمول‌بندی می‌شود. به‌عنوان مثال، برخی از کالاها در داخل کشور تولید می‌شوند اما کل نیاز بازار تأمین نمی‌شود و کمبود کالا باید از طریق واردات تأمین شود، و برخی از کالاها در داخل کشور تولید نمی‌شوند (یا تولید ناچیزی دارند) و کل نیاز بازار از طریق واردات تأمین می‌شود و ممکن است قاچاق‌چیان نیز دست به واردات کالا بزنند، که منجر به پیامدهای منفی اقتصادی و اجتماعی می‌شود. در این مقاله دو دسته مسأله‌ی تأمین کالا بین دو تأمین‌کننده در دو سطح متفاوت ارائه می‌شود. در دسته‌ی اول تولیدکننده در سطح اول و واردکننده در سطح دوم قراردارد و هدف تأمین‌کنندگان بیشینه‌سازی سودشان می‌باشد. در دسته‌ی دوم واردکننده در سطح اول و قاچاق‌چی در سطح دوم قراردارد که واردکننده دو هدف بیشینه‌سازی سود خود و جلوگیری از قاچاق کالا را با کمینه‌سازی سود قاچاق‌چی دنبال می‌کند، در حالی‌که قاچاق‌چی به‌دنبال بیشینه‌سازی سودش است، لذا با یک مسأله‌ی ممانعت مواجه هستیم. این دو نوع مسأله به‌صورت مسائل بازی استکلبرگ دوسطحی مدل‌سازی گردیده و سپس بااستفاده از شرایط بهینگی کاروش-کان-تاکر به مدل‌های یک‌سطحی تبدیل و حل می‌شوند. در پایان برای تشریح روش، مثال‌هایی از هردو مدل ارائه و ضمن حل، تحلیل حساسیت نیز می‌گردد.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

Modeling Supply Chain Management Problem as a Bi-Level Stackelberg Game and Solving it Using Karush-Kahn-Tucker Optimality Conditions

نویسندگان English

Narges Mirazizi 1
Hassan Hassanpour 1
Javad Tayyebi 2
1 Department of Mathematics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran
2 Department of Industrial Engineering, Faculty of Computer and Industrial Engineering, Birjand University of Technology, Birjand, Iran
چکیده English

In real-world supply chain problems, we sometimes encounter problems with two suppliers at two different levels, one of which plays the role of leader and the other of follower due to their position in the supply of goods, so the problem is formulated as a bi-level Stackelberg game model. For example, some goods are produced domestically, but the entire market demand is not met and the shortage of goods must be met through imports, and some goods are not produced domestically (or have a small production) and the entire market demand is met through imports, and smugglers may also import goods, which leads to negative economic and social consequences. In the paper two categories of the supply problem between two suppliers at two different levels. In the first category, the producer is at the first level and the importer is at the second level, and the suppliers' goal is to maximize their profits. In the second group, the importer is at the first level and the smuggler is at the second level. The importer pursues two goals: maximizing his profit and preventing smuggling by minimizing the smuggler's profit, while the smuggler seeks to maximize his profit, so we are faced with an obstacle problem. These two types of problems are modeled as bi-level Stackelberg game problems and then converted into one-level models using the Karush-Kahn-Tucker optimality conditions and solved. Finally, examples of both models are presented to explain the method and a sensitivity analysis is also performed.

کلیدواژه‌ها English

Stackelberg Game Problem
Bi-Level Game
Karush-Kahn-Tucker's Conditions
Supply Chain Management
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