fa کمینه‌سازی حداکثر دیرکرد کارها در مسأله زمانبندی جریان کارگاهی جایگشتی دوباره وارد شونده چند ماشینه سایر موضوعاتی که به مرزهای دانش در مهندسی صنایع و تولید کمک می کند Other related Industrial and production reserach subjects in which has direct relation to the state-of-the art of the IE كاربردي Applicable <p align="right"><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">در</span><b><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"> </span></b><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">این مقاله، مسأله زمانبندی </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">جریان کارگاهی </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">جایگشتی دوباره وارد شونده با هدف کمینه­سازی </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Arial mso-hansi-font-family: Arial mso-ansi-language: EN-US mso-fareast-language: EN-US">حداکثر </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">دیرکرد کارها مورد بررسی قرار می­گیرد. محیط </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">جریان کارگاهی دوباره </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">وارد</span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"> شونده (</span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">RFS</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"><span dir="rtl"></span>) همان جریان کارگاهی است با این تفاوت که کارها، ماشین­های مشخصی را بیش از یک بار ملاقات می­کنند. در نوع </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">RFS</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"><span dir="rtl"></span>، اگر ترتیب کار روی هر ماشین در هر سطح یکسان باشد، به چنین مسایلی، مسأله جریان کارگاهی جایگشتی دوباره وارد شونده (</span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">RPFS</span><span dir="rtl"></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"><span dir="rtl"></span>) عنوان می­گردد. در این مقاله، ابتدا مدل ریاضی مسأله کمینه­سازی</span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Arial mso-hansi-font-family: Arial mso-ansi-language: EN-US mso-fareast-language: EN-US"> حداکثر </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">دیرکرد کارها در</span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"> </span><span style="FONT-SIZE: 9pt FONT-FAMILY: "Times New Roman" mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">RPFS</span><span dir="rtl"></span><span dir="rtl" style="FONT-SIZE: 9pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US"><span dir="rtl"></span> </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">چند ماشینه، توسعه داده می­شود. </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">برای حل این مسأله، سه الگوریتم فراابتکاری مبتنی بر الگوریتم­ ژنتیک، شبیه­سازی تبرید و جستجوی ممنوع طراحی و بکار گرفته می­شود.</span><span dir="ltr"></span><span lang="FA" style="FONT-SIZE: 11pt FONT-FAMILY: "Times New Roman" mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US"><span dir="ltr"></span> </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">الگوریتم­های فراابتکاری </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">همچنین</span><span dir="ltr"></span><span lang="FA" style="FONT-SIZE: 11pt FONT-FAMILY: "Times New Roman" mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US"><span dir="ltr"></span> </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">با حل­های بهینه ایجاد شده توسط رویکرد برنامه­ریزی عدد صحیح مقایسه می­گردند.</span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US"> </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">نتایج آزمایشی نشان می­دهد که الگوریتم ژنتیک در اکثر موارد کارایی بهتری نسبت به </span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: Bnazanin mso-hansi-font-family: Bnazanin mso-ansi-language: EN-US mso-fareast-language: EN-US">الگوریتم</span><span style="FONT-SIZE: 11pt FONT-FAMILY: Bnazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-bidi-font-family: Nazanin mso-ansi-language: EN-US mso-fareast-language: EN-US"><font face="Times New Roman">­</font></span><span lang="FA" dir="rtl" style="FONT-SIZE: 11pt FONT-FAMILY: Nazanin mso-bidi-language: FA mso-fareast-font-family: 'Times New Roman' mso-ascii-font-family: 'Times New Roman' mso-hansi-font-family: 'Times New Roman' mso-ansi-language: EN-US mso-fareast-language: EN-US">های تست شده دیگر دارد.</span></p> <p> <i> This investigation considers a reentrant permutation flowshop scheduling problem whose performance criterion is maximum tardiness. The reentrant flowshop (RFS) is a natural extension of the classical flowshop by allowing a job to visit certain machines more than once. The RFS scheduling problem, in which the job order is the same for each machine in each layer, is called a reentrant permutation flowshop (RPFS) problem. In this paper, a mathematical model is extended to solve the given problem minimizing the maximum tardiness on an m-machine RPFS problem. This problem is solved by three meta-heuristic algorithms, namely genetic algorithm, simulated annealing and tabu search. The results of these algorithms are compared to the optimal solutions obtained by the integer programming approach. The experimental results show that the genetic algorithm has a better performance than the others tested </i><i>. </i></p> زمانبندی،جریان کارگاهی جایگشتی دوباره واردشونده،حداکثر دیرکرد کارها،الگوریتم‌های فراابتکاری Flowshop scheduling,Reentrant permutation, Maximum tardiness, Meta-heuristic algorithms 179 190 http://ijiepm.iust.ac.ir/browse.php?a_code=A-10-231-3&slc_lang=fa&sid=1 M. Fasihi maede.fasihi@gmail.com 180031947532846001813 180031947532846001813 No F. Jolai fjolai@ut.ac.ir 180031947532846001814 180031947532846001814 Yes R. Tavakkoli-Moghaddam tavakoli@ut.ac.ir 180031947532846001815 180031947532846001815 No