نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی کاربردی، دانشکده علوم پایه مهندسی، دانشگاه صنعتی سهند ، تبریز، ایران.

2 گروه ریاضی کاربردی، دانشکده علوم پایه مهندسی، دانشگاه صنعتی سهند، تبریز، ایران.

چکیده

در این مقاله، مسئله مکان‌یابی سرویس‌دهنده غیر ظرفیت‌دار -کالایی و -حالتی مورد بررسی قرار می‌گیرد.  به‎عبارت دقیق‌تر، فرض می‌شود که یک مشتری می‌تواند  کالای متفاوت را در یک شبکه -حالتی تقاضا کند. ابتدا یک فرمول‌بندی ریاضی برای مسئله مکان‌یابی سرویس‌دهنده غیر ظرفیت‌دار -کالایی و -حالتی با هزینه‌های قطعی ارائه می‌شود. همچنین، نشان داده می‌شود که این مسئله یک مسئله Np -سخت است. با توجه به این‌که در بیشتر مسائل دنیای واقعی داده‌های ورودی اغلب مبهم و غیرقطعی هستند، ما در ادامه مسئله مکان‌یابی سرویس‌دهنده غیر ظرفیت‌دار -کالایی و -حالتی که در آن هزینه‌های تاسیس سرویس‌دهنده‌ها و هزینه‌های سرویس‌دهی مشتریان متغیرهای تصادفی فازی هستند را مورد تحلیل و ارزیابی قرار می‌دهیم. با بکاربردن سه معیار احتمال-امکان، احتمال-الزام و احتمال-اعتبار، مدل مکان‌یابی سرویس‌دهنده غیر ظرفیت‌دار -‎کالایی و -‎حالتی تصادفی فازی به یک مسئله برنامه‌ریزی درجه دوم قطعی تبدیل می‌شود. درنهایت، یک مثال کاربردی برای نشان دادن کارآیی رویکردهای پیشنهادی ارائه می‌شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

The k- product and t-state uncapacitated facility location problem with fuzzy random costs

نویسندگان [English]

  • Sepideh Taghikhani 1
  • Fahimeh Baroughi 1
  • Behrooz Alizadeh 2

1 Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

2 Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

چکیده [English]

In this paper, the -product and t-state uncapacitated facility location problem is investigated. To be more precise, it is assume that each customer can request  different products in a -state network. First, the mathematical formulation for the -product and t-state uncapacitated facility location problem with certain costs is proposed. Also, it is shown that this paoblem is NP-hard. Since in most real-world problems the input of data are often ambiguous and uncertain, we study the -product and -state uncapacitated facility location problem in which the facility set-up costs and customer service costs are fuzzy random variables. Using three criteria, ‎probability-possibility‎, ‎probability-necessity‎ and ‎probability-credibility, the -product and‌‌ -state uncapacitated facility location problem is formulated as a quadratic programming. Finally, a practical example is given to illustrate the efficiency of the proposed approaches.

کلیدواژه‌ها [English]

  • Uncapacitated facility location problem
  • fuzzy random variable
  • ‎Probability-possibility
  • ‎Probability-necessity
  • Probability-credibility
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