fa کمینه‌سازی حداکثر زمان تکمیل در مسأله زمانبندی تولید کارگاهی با ماشینهای موازی پژوهشي Research <p align="right"><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt">در این مقاله، مسأله زمانبندی تولید کارگاه منعطف </span><span dir="ltr"></span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin"><span dir="ltr"></span>(Flexible Job Shop)</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> با تعریف جدیدی از انعطاف پذیری مورد بررسی قرار می­گیرد. در این نوع انعطاف پذیری برای مساله فرض می­شود که در هر ایستگاه عملیاتی چند ماشین وجود دارند که کارها در هر ایستگاه می­توانند به یکی از آنها تخصیص داده شود. تابع هدف کمینه­سازی بازه ساخت </span><span dir="ltr"></span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin"><span dir="ltr"></span>(make span)</span><span dir="rtl"></span><span dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> <span lang="FA"><font face="Nazanin" size="3">است. ابتدا مدل ریاضی مساله ارائه شده و سپس</font></span></span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">NP-hard</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> بودن مسأله نشان داده می­شود. بعلت </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">NP-hard</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> بودن مساله استفاده از روشهای دقیق برای حل آن در زمان چندجمله­ای ممکن نیست و باید از الگوریتمهای ابتکاری برای حل آن استفاده نمود. ­به این منظور دو الگوریتم ابتکاری به نامهای </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H1</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> و </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H2</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> به ترتیب برای مسائل با ابعاد بزرگ و معمولی برای حل مساله ارائه می­شود. بعلت اینکه این مسأله تا کنون در ادبیات موضوع مورد مطالعه قرار نگرفته است، معیار مناسبی برای ارزیابی الگوریتم­های ارائه شده وجود ندارد. بنابراین بمنظور ارزیابی الگوریتمهای ارائه شده، سه الگوریتم ابتکاری با نامهای </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H3</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span>، </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H4</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> و </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H5</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> و همچنین یک کران پایین برای آن ارائه می­شود و نتایج الگوریتمهای </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H1</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> و </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H2</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> با آنها مقایسه شده است. نتایج محاسبات نشان می­دهد که الگوریتم پیشنهادی </span><span dir="ltr"></span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin"><span dir="ltr"></span><font face="Times New Roman"><span style="mso-spacerun: yes"> </span>H2</font></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt">برای مسائل با ابعاد کوچک، جوابهای بهتری را نسبت به الگوریتمهای دیگر ارائه می­دهد. اما در مسائل با ابعاد بزرگ </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H1</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> به طور مجانبی کاراتر از </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H2</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> است. همچنین کارائی الگوریتم </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-bidi-font-size: 11.0pt mso-bidi-font-family: Nazanin">H3</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-fareast-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US mso-bidi-language: FA mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-font-size: 9.0pt"><span dir="rtl"></span> پایین­تر از سایر الگوریتمها است.</span></p> تولید کارگاهی انعطاف‌پذیر ، ماشینهای موازی، مدلسازی ریاضی، الگوریتمهای ابتکاری Flexible Job Shop, Parallel Machines, Mathematical Modeling, Heuristic Algorithms 11 21 http://ijiepm.iust.ac.ir/browse.php?a_code=A-10-1-101&slc_lang=fa&sid=1 S. H. Zegordi zegordi@modares.ac.ir . 180031947532846001354 180031947532846001354 Yes M.A. BeheshtiNia beheshtinia@modares.ac.i 180031947532846001421 180031947532846001421 No N. Jafari Hajagha n_jafari@modares.ac.ir 180031947532846001422 180031947532846001422 No