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A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information
<!DOCTYPE html> <!--[if IE 8]> <html class="ie ie8"> <![endif]--> <!--[if IE 9]> <html class="ie ie9"> <![endif]--> <!--[if gt IE 9]><!--> <html> <!--<![endif]--> <head> <meta charset="utf-8" /> <title>A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information</title> <!-- favicon --> <link rel="shortcut icon" type="image/ico" href="./data/ijsom/coversheet/favicon.ico" /> <!-- mobile settings --> <meta name="viewport" content="width=device-width, maximum-scale=1, initial-scale=1, user-scalable=0" /> <!--[if IE]><meta http-equiv='X-UA-Compatible' content='IE=edge,chrome=1'><![endif]--> <!-- user defined metatags --> <meta name="keywords" content="Pull system,Kanban,Buffer,Dynamic environment,Markov chain" /> <meta name="description" content="The pull system produces products based on customer demands. Each station is isolated until a customer order is placed; then a signal or Kanban is sent from downstream station to upstream station and continues until the first station. Most of the papers studied pull system in deterministic environment while many real production lines are subjected to different types of uncertainties. The objective of this paper is to apply a dynamic Kanban system that changes the information on the Kanban cards based on the remained inventory in the buffer. The proposed approach uses a Markov chain analysis to compare effectiveness of the Kanban card with dynamic information with the Kanban card with static information. In this paper the production line of two work stations and two inventory buffer is modeled. Throughput, shortage, work-in-process and cycle time are the model measurement parameters and the results show the advantages of the proposed approach." /> <meta name="title" content="A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information" /> <meta name="googlebot" content="NOODP" /> <meta name="citation_title" content="A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information" /> <meta name="citation_author" content="Tanhaie, Fahimeh" /> <meta name="citation_author_institution" content="School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran" /> <meta name="citation_author" content="Jolai, Fariborz" /> <meta name="citation_author_institution" content="School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran" /> <meta name="citation_author" content="Rabbani, Masoud" /> <meta name="citation_author_institution" content="School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran" /> <meta name="citation_abstract" content="The pull system produces products based on customer demands. Each station is isolated until a customer order is placed; then a signal or Kanban is sent from downstream station to upstream station and continues until the first station. Most of the papers studied pull system in deterministic environment while many real production lines are subjected to different types of uncertainties. The objective of this paper is to apply a dynamic Kanban system that changes the information on the Kanban cards based on the remained inventory in the buffer. The proposed approach uses a Markov chain analysis to compare effectiveness of the Kanban card with dynamic information with the Kanban card with static information. In this paper the production line of two work stations and two inventory buffer is modeled. Throughput, shortage, work-in-process and cycle time are the model measurement parameters and the results show the advantages of the proposed approach." /> <meta name="citation_id" content="2733" /> <meta name="citation_publication_date" content="2017/08/01" /> <meta name="citation_date" content="2017-08-01" /> <meta name="citation_journal_title" content="International Journal of Supply and Operations Management" /> <meta name="citation_issn" content="23831359" /> <meta name="citation_volume" content="4" /> <meta name="citation_issue" content="3" /> <meta name="citation_firstpage" content="215" /> <meta name="citation_lastpage" content="228" /> <meta name="citation_publisher" content="Kharazmi University" /> <meta name="citation_doi" content="10.22034/2017.3.03" /> <meta name="DC.Identifier" content="10.22034/2017.3.03" /> <meta name="citation_abstract_html_url" content="http://www.ijsom.com/article_2733.html" /> <meta name="citation_pdf_url" content="http://www.ijsom.com/article_2733_de18891b7d836ce4315273208a61ff26.pdf" /> <meta name="DC.Title" content="A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information" /> <meta name="DC.Source" content="International Journal of Supply and Operations Management" /> <meta name="DC.Date" content="01/08/2017" /> <meta name="DC.Date.issued" content="2017-08-01" /> <meta name="DC.Format" content="application/pdf" /> <meta name="DC.Contributor" content="Tanhaie, Fahimeh" /> <meta name="DC.Contributor" content="Jolai, Fariborz" /> <meta name="DC.Contributor" content="Rabbani, Masoud" /> <meta name="og:title" content="A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information" /> <meta name="og:description" content="The pull system produces products based on customer demands. Each station is isolated until a customer order is placed; then a signal or Kanban is sent from downstream station to upstream station and continues until the first station. Most of the papers studied pull system in deterministic environment while many real production lines are subjected to different types of uncertainties. The objective of this paper is to apply a dynamic Kanban system that changes the information on the Kanban cards based on the remained inventory in the buffer. The proposed approach uses a Markov chain analysis to compare effectiveness of the Kanban card with dynamic information with the Kanban card with static information. In this paper the production line of two work stations and two inventory buffer is modeled. Throughput, shortage, work-in-process and cycle time are the model measurement parameters and the results show the advantages of the proposed approach." /> <meta name="og:url" content="http://www.ijsom.com/article_2733.html" /> <!-- WEB FONTS : use %7C instead of | (pipe) --> <link href="./themes/base/front/assets/css/social-icon-font.css" rel="stylesheet" type="text/css" /> <!-- CORE CSS --> <link href="./themes/base/front/assets/plugins/bootstrap/css/bootstrap.min.css?v=0.02" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/header.css?v=0.05" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/footer.css" rel="stylesheet" type="text/css" /> <link href="./inc/css/essentials.css?v=0.2" rel="stylesheet" type="text/css" /> <link href="./inc/css/cookieconsent.min.css" rel="stylesheet" type="text/css" /> <link href="./inc/css/print.css" rel="stylesheet" type="text/css" media="print"/> <!-- RTL CSS --> <link href="./themes/base/front/assets/plugins/bootstrap/css/bootstrap-ltr.min.css" rel="stylesheet" type="text/css" /> <link href=" ./themes/base/front/assets/css/gfonts-OpenSans.css" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/accordian.css" rel="stylesheet" type="text/css" /> <link href="./themes/base/front/assets/css/academicons.min.css" rel="stylesheet" type="text/css" /> <!-- user defined metatags--> <meta name="google-site-verification" content="UlbWpwabckk_wTgRmzoJCVPEYKnomtCLcftujpXdou4" /> <link href="./data/ijsom/coversheet/stl_front.css?v=0.78" rel="stylesheet" type="text/css" /> <link href="./data/ijsom/coversheet/stl.css" rel="stylesheet" type="text/css" /> <!-- Feed--> <link rel="alternate" type="application/rss+xml" title="RSS feed" href="ju.rss" /> <script type="text/javascript" src="./themes/base/front/assets/plugins/jquery/jquery.min.js?v=0.5"></script> <script type="text/javascript" src="./inc/js/common.js?v=0.1"></script> <script type="text/javascript" src="./inc/js/jquery/cookieconsent.min.js"></script> <!-- Extra Style Scripts --> <!-- Extra Script Scripts --> <script src="inc/js/article.js?v=0.31" type="text/javascript" ></script> </head> <body class="ltr len"> <div class="container" id="header"> <div class="row"> <div class="col-xs-12 text-center"> <img src="./data/ijsom/coversheet/head_en.jpg" class="img-responsive text-center" style="display:-webkit-inline-box; 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Each station is isolated until a customer order is placed; then a signal or Kanban is sent from downstream station to upstream station and continues until the first station. Most of the papers studied pull system in deterministic environment while many real production lines are subjected to different types of uncertainties. The objective of this paper is to apply a dynamic Kanban system that changes the information on the Kanban cards based on the remained inventory in the buffer. The proposed approach uses a Markov chain analysis to compare effectiveness of the Kanban card with dynamic information with the Kanban card with static information. In this paper the production line of two work stations and two inventory buffer is modeled. Throughput, shortage, work-in-process and cycle time are the model measurement parameters and the results show the advantages of the proposed approach.</div> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Keywords</strong></p> <ul class="block list-inline list-inline-seprator margin-bottom-6 ltr"> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105808&_kw=Pull+system" >Pull system</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105809&_kw=Kanban" >Kanban</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105810&_kw=Buffer" >Buffer</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105811&_kw=Dynamic+environment" >Dynamic environment</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105077&_kw=Markov+chain" >Markov chain</a> </li> </ul> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Main Subjects</strong></p> <ul class="block list-inline list-inline-seprator margin-bottom-6"> <li class="padding-3"> <a href="./?_action=article&sb=158&_sb=operations+planning%2Cscheduling+%26amp%3B+control" >operations planning,scheduling & control</a> </li> </ul> </div> <hr> <div class="page_break"></div> <div class="panel"> <div class="panel-heading card-header"> <h4 class="panel-title "> <a data-toggle="collapse" data-parent="#accordions" href="#collapsesRef"><i class="fa fa-plus"></i> References</a> </h4> </div> <div id="collapsesRef" class="panel-collapse collapse"> <div class="panel-body justify"> <div class="padding-3 margin-top-3 ltr justify">Bitran, G., and Chang, L. (1987). A Mathematical Programming Approach to a Deterministic Kanban System. <em>Management Science</em>, Vol. 33(4), pp. 427-441. </div> <div class="padding-3 margin-top-3 ltr justify">Framinan, J., González, P., and Ruiz-Usano, R. (2003). The CONWIP production control system: Review and research issues. <em>Production Planning & Control</em>, Vol. 14(3), pp. 255-265. </div> <div class="padding-3 margin-top-3 ltr justify">Framinan, J., González, P., and Ruiz-Usano, R. (2006). Dynamic card controlling in a Conwip system. <em>International Journal of Production Economics</em>, Vol. 99(1-2), pp. 102-116. </div> <div class="padding-3 margin-top-3 ltr justify">Gong, Q., Yang, Y., and Wang, S. (2014). Information and decision-making delays in MRP, KANBAN, and CONWIP. <em>International Journal of Production Economics</em>, Vol. 156, pp. 208-213. </div> <div class="padding-3 margin-top-3 ltr justify">González-R, P., Framinan, J., and Pierreval, H. (2011). Token-based pull production control systems: an introductory overview. <em>Journal of Intelligent Manufacturing</em>, Vol. 23(1), pp. 5-22. </div> <div class="padding-3 margin-top-3 ltr justify">Gupta, S., and Al-Turki, Y. (1997). An algorithm to dynamically adjust the number of Kanbans in stochastic processing times and variable demand environment. <em>Production Planning & Control</em>, Vol. 8(2), pp. 133-141. </div> <div class="padding-3 margin-top-3 ltr justify">Gupta, M. (2003). Constraints management--recent advances and practices. <em>International Journal of Production Research</em>, Vol. 41(4), pp. 647-659. </div> <div class="padding-3 margin-top-3 ltr justify">Hopp, W., and Roof, M. (1998). Setting WIP levels with statistical throughput control (STC) in CONWIP production lines. <em>International Journal of Production Research</em>, Vol. 36(4), pp. 867-882. </div> <div class="padding-3 margin-top-3 ltr justify">Huang, Y., Wan, H., Kuriger, G., and Chen, F. (2013). Simulation Studies of Hybrid Pull Systems of Kanban and CONWIP in an Assembly Line. <em>Advances in Sustainable and Competitive Manufacturing Systems</em>, pp. 1553-1563. </div> <div class="padding-3 margin-top-3 ltr justify">Jou Lin, C., Frank Chen, F., and Min Chen, Y. (2013). Knowledge kanban system for virtual research and development. <em>Robotics and Computer-Integrated Manufacturing</em>, Vol. 29(3), pp. 119-134. </div> <div class="padding-3 margin-top-3 ltr justify">Kemeny, J., & Snell, J. (1960). <em>Finite markov chains</em>. Princeton, N.J.: Van Nostrand. </div> <div class="padding-3 margin-top-3 ltr justify">Khojasteh-Ghamari, Y. (2008). A performance comparison between Kanban and CONWIP controlled assembly systems. <em>Journal of Intelligent Manufacturing</em>, Vol. 20(6), pp. 751-760. </div> <div class="padding-3 margin-top-3 ltr justify">Miltenburg, J. (1997). Comparing JIT, MRP and TOC, and embedding TOC into MRP. <em>International Journal of Production Research</em>, Vol. 35(4), pp. 1147-1169. </div> <div class="padding-3 margin-top-3 ltr justify">Moeeni, F., and Chang, Y. (1990). An Approximate Solution to Deterministic Kanban Systems. <em>Decision Sciences</em>, Vol. 21(3), pp. 596-607. </div> <div class="padding-3 margin-top-3 ltr justify">Renna, P. (2010). Dynamic Control Card in a Production System Controlled by Conwip Approach. <em>Jordan Journal of Mechanical and Industrial Engineering</em>, Vol. 4(4), pp.425-432. </div> <div class="padding-3 margin-top-3 ltr justify">Sato, R., and Khojasteh-Ghamari, Y. (2010). An integrated framework for card-based production control systems. <em>Journal of Intelligent Manufacturing</em>, Vol. 23(3), pp. 717-731. </div> <div class="padding-3 margin-top-3 ltr justify">Schmidbauer, H., and Rösch, A. (1994). A stochastic model of an unreliable Kanban production system. <em>OR Spektrum</em>, Vol. 16(2), pp. 155-160. </div> <div class="padding-3 margin-top-3 ltr justify">Sendil Kumar, C., and Panneerselvam, R. (2006). Literature review of JIT-KANBAN system. <em>Int J Adv Manuf Technol</em>, Vol. <em>32</em>(3-4), pp. 393-408. </div> <div class="padding-3 margin-top-3 ltr justify">Shahabudeen, P., Krishnaiah, K., and Thulasi Narayanan, M. (2003). Design of a Two-Card Dynamic Kanban System Using a Simulated Annealing Algorithm. <em>The International Journal of Advanced Manufacturing Technology</em>, Vol. 21(10-11), pp. 754-759. </div> <div class="padding-3 margin-top-3 ltr justify">Shahabudeen, P., and Sivakumar, G. (2008). Algorithm for the design of single-stage adaptive kanban system. <em>Computers & Industrial Engineering</em>, Vol. 54(4), pp. 800-820. </div> <div class="padding-3 margin-top-3 ltr justify">Spearman, M., Woodruff, D., and Hopp, W. (1990). CONWIP: a pull alternative to Kanban. <em>Int. J. Of Prodn. Res.</em>, Vol. 28(5), pp. 879-894. </div> <div class="padding-3 margin-top-3 ltr justify">Tardif, V., and Maaseidvaag, L. (2001). An adaptive approach to controlling Kanban systems. <em>European Journal of Operational Research</em>, Vol. 132(2), pp. 411-424.</div> </div> </div> </div> </div> </div> <!-- /CENTER --> <!-- LEFT --> <div class="col-lg-3 col-md-3 col-sm-4"> <div class="panel panel-default my_panel-default margin-bottom-10"> <div class="panel-body ar_info_pnl" id="ar_info_pnl_cover"> <div id="pnl_cover"> <div class="row" > <div class="col-xs-6 col-md-6 nomargin-bottom"> <a href="javascript:loadModal('International Journal of Supply and Operations Management', './data/ijsom/coversheet/cover_en.jpg')"> <img src="data/ijsom/coversheet/cover_en.jpg" alt="International Journal of Supply and Operations Management" style="width: 100%;"> </a> </div> <div class="col-xs-6 col-md-6 nomargin-bottom"> <h6><a href="./issue_506_509.html">Volume 4, Issue 3 - Serial Number 3</a><br/>August 2017<div id="sp_ar_pages">Pages <span dir="ltr">215-228</span></div></h6> </div> </div> </div> </div> </div> <!-- Download Files 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in"> <div class="panel-body ar_info_pnl"> <ul class="list-group list-group-bordered list-group-noicon" style="display:block !important;max-height:9999px"> <li class="list-group-item"><a class="tag_a">Article View: <i>2,557</i></a></li> <li class="list-group-item"><a class="tag_a">PDF Download: <i>1,188</i></a></li> </ul> </div> </div> </div> </div> <!-- /LEFT --> </div> </section> <div id="cite-apa" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <!-- Modal Header --> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">APA</h4> </div> <!-- Modal Body --> <div class="modal-body"> <p>Tanhaie, F., Jolai, F., & Rabbani, M. (2017). A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information. <em>International Journal of Supply and Operations Management</em>, 4(3), 215-228. doi: 10.22034/2017.3.03</p> </div> </div> </div> </div> <div id="cite-mla" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <!-- Modal Header --> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">MLA</h4> </div> <!-- Modal Body --> <div class="modal-body"> <p>Fahimeh Tanhaie; Fariborz Jolai; Masoud Rabbani. "A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information". <em>International Journal of Supply and Operations Management</em>, 4, 3, 2017, 215-228. doi: 10.22034/2017.3.03</p> </div> </div> </div> </div> <div id="cite-harvard" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <!-- Modal Header --> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">HARVARD</h4> </div> <!-- Modal Body --> <div class="modal-body"> <p>Tanhaie, F., Jolai, F., Rabbani, M. (2017). 'A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information', <em>International Journal of Supply and Operations Management</em>, 4(3), pp. 215-228. doi: 10.22034/2017.3.03</p> </div> </div> </div> </div> <div id="cite-vancouver" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <!-- Modal Header --> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">VANCOUVER</h4> </div> <!-- Modal Body --> <div class="modal-body"> <p>Tanhaie, F., Jolai, F., Rabbani, M. A Markov Chain Analysis of the Effectiveness of Kanban Card with Dynamic Information. <em>International Journal of Supply and Operations Management</em>, 2017; 4(3): 215-228. doi: 10.22034/2017.3.03</p> </div> </div> </div> </div> </div> </div> <!-- /MAIN CONTENT --> <!-- Subscribe --> <section class="alternate padding-xxs"> </section> <!-- /Subscribe --> <!-- FOOTER --> <div class="container"> <footer id="footer"> <div class="scrollup" id="scroll" href="#"><span></span></div> <div class="row"> <div class="col-md-2"> <!-- Links --> <h4 class="">Explore Journal</h4> <ul class="footer-links list-unstyled"> <li id="fli_home"><a href="./">Home</a></li> <li id="fli_about"><a href="./journal/about">About Journal</a></li> <li id="fli_Edb"><a href="./journal/editorial.board">Editorial Board</a></li> <li id="fli_submit"><a href="./author">Submit Manuscript</a></li> <li id="fli_contactus"><a href="./journal/contact.us">Contact Us</a></li> <li id="fli_glossary"><a href="./journal/glossary">Glossary</a></li> <li id="fli_order_hrdj"><a href="./journal/subscription.form">Hard Copy Subscription</a></li> <li id="fli_sitemap"><a href="./sitemap.xml?usr">Sitemap</a></li> </ul> <!-- /Links --> </div> <div class="col-md-3"> <!-- Latest News --> <h4 class="">Latest News</h4> <ul class="footer-posts list-unstyled"> <li> <a href="./news?newsCode=173">SD of ISC: Sustainable Development of Intelligent Supply Chains based on Trends and Future Directions: Application of Novel Solution Techniques</a> <small class="ltr">2023-03-05</small> </li> </ul> <!-- /Latest News --> </div> <div class="col-md-3"> <!-- Footer Note --> <div><p><a title="Linkedin" href="http://www.linkedin.com/company/ijsom?trk=eml-cp_mktg-btn-welcome-20120607%2F"><img src="images/linkedin.jpg" alt="linkedin" /></a></p></div> <!-- /Footer Note --> </div> <div class="col-md-4"> <!-- Newsletter Form --> <h4 class="">Newsletter Subscription</h4> <p>Subscribe to the journal newsletter and receive the latest news and updates</p> <form class="validate" action="" method="post" data-success="Subscription saved successfully." data-toastr-position="bottom-right"> <input type="hidden" name="_token" value="2d10b5e4d5b29fb0aaa4e0e0ba49e32c039e7136f67d6d08"/> <div class="input-group"> <span class="input-group-addon"><i class="fa fa-envelope"></i></span> <input type="email" id="email" name="email" required="required" class="form-control required sbs_email" placeholder="Enter your Email" oninvalid="this.setCustomValidity('Enter a valid email address.')" oninput="this.setCustomValidity('')"> <span class="input-group-btn"> <button class="btn btn-primary mybtn" type="submit">Subscribe</button> </span> </div> </form> <!-- /Newsletter Form --> <!-- Social Icons --> <div class="margin-top-20"> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Facebook"> <i class="fa fa-facebook-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Twitter"> <i class="fa fa-twitter-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Linkedin"> <i class="fa fa-linkedin-square" aria-hidden="true"></i> </a> <a class="noborder" href="./ju.rss" class="social-icon social-icon-border social-rss pull-left block" data-toggle="tooltip" data-placement="top" title="Rss"><i class="fa fa-rss-square" aria-hidden="true"></i></a> </div> </div> </div> <div class="copyright" style="position: relative"> <ul class="nomargin list-inline mobile-block"> <li>© Journal Management System. <span id='sp_crt'>Powered by <a target='_blank' href='https://www.sinaweb.net/'>Sinaweb</a></span></li> </ul> </div> </footer> </div> <!-- /FOOTER --> </div> <!-- /wrapper --> <!-- SCROLL TO TOP --> <a href="#" id="toTop_old"></a> <!-- PRELOADER --> <div id="preloader"> <div class="inner"> <span class="loader"></span> </div> </div><!-- /PRELOADER --> <!-- JAVASCRIPT FILES --> <script type="text/javascript">var plugin_path = './themes/base/front/assets/plugins/';</script> <script type="text/javascript" src="./themes/base/front/assets/js/scripts.js?v=0.02"></script> <!-- user defined scripts--> <!-- Extra Script Scripts --> <script type="text/javascript"> $('ul.nav li.dropdown').hover(function() { if (window.matchMedia('(max-width: 767px)').matches) return; 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