Document Zbl 1177.90130

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G.</a>; <a href="/authors/rong.y-l" title="Author Profile">Rong, Y. L.</a></div> <h2 class="title"> <strong>The reliable design of one-piece flow production system using fuzzy ant colony optimization.</strong> <i>(English)</i> <a class="label nowrap" href="/1177.90130">Zbl 1177.90130</a> </h2> <div class="source"> <a href="/serials/1149" title="Journal Profile">Comput. Oper. Res.</a> <a href="/?q=in%3A235364" title="Articles in this Issue">36, No. 5, 1656-1663 (2009)</a>. </div> <div class="abstract">Summary: One-piece flow production system is designed with the purpose of ensuring just-in-time production. Three approaches are applied to achieve the goal: adopting straightforward schedule policies, relaxing the Takt time and decreasing the risk of machine failures and operator mistakes. Consequently, a multi-objective design model is proposed, whose aim is to minimize cycle time, changeover count, cell load variation and the number of cells and maximize the extent to which items are completed in a cell. The fuzzy ant colony optimization (FACO) is also presented to solve the formulated problem. In FACO, the fuzzy logic controller (FLC) is used to adapt the evaporated and deposited value of pheromone trail based on the ant’s fitness and pheromone trail age. Furthermore, domain knowledge of facility layout, generated based on the travel chart method, is also adaptively injected to improve the performance of FACO. The proposed method is evaluated with the real-world data and experimental results demonstrate that our method outperforms many other methods in efficiency, solution quality and facilitation measures.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5383149">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B30" title="MSC2020">90B30</a> </td> <td class="space"> Production models </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C70" title="MSC2020">90C70</a> </td> <td class="space"> Fuzzy and other nonstochastic uncertainty mathematical programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aone-piece+flow">one-piece flow</a>; <a href="/?q=ut%3AFACO">FACO</a>; <a href="/?q=ut%3Ajust-in-time">just-in-time</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <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">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1177.90130" data-ciurl="/ci/05383149" data-biburl="/bibtex/05383149.bib" data-amsurl="/amsrefs/05383149.bib" data-xmlurl="/xml/05383149.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05383149.pdf" title="Zbl 1177.90130 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cor.2008.03.010" aria-label="DOI for “The reliable design of one-piece flow production system using fuzzy ant colony optimization”" title="10.1016/j.cor.2008.03.010">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Miltenburg, J., One-piece flow manufacturing on U-shaped production lines: a tutorial source, IIE Transactions, 33, 303-321 (2001)</td> </tr><tr> <td>[2]</td> <td class="space">Quintana, R., Recursive linear control of order release to manufacturing cells with random yield, IIE Transactions, 34, 489-500 (2002)</td> </tr><tr> <td>[3]</td> <td class="space">Stockton, D. J.; Ardon-Finch, J.; Khalil, R., Walk cycle design for flexible manpower lines using genetic algorithms, International Journal of Computer Integrated Manufacturing, 18, 15-26 (2005)</td> </tr><tr> <td>[4]</td> <td class="space">Bazargan-Lari, M.; Kaebernick, H.; Harraf, A., Cell formation and layout designs in a cellular manufacturing environment—a case study, International Journal of Production Research, 38, 1689-1709 (2000) · <a href="/0944.90541" class="nowrap">Zbl 0944.90541</a></td> </tr><tr> <td>[5]</td> <td class="space">Zhao, C.; Wu, Z. M., A genetic algorithm for manufacturing cell formation with multiple routes and multiple objectives, International Journal of Production Research, 38, 385-395 (2000) · <a href="/0944.90508" class="nowrap">Zbl 0944.90508</a></td> </tr><tr> <td>[6]</td> <td class="space">Solimanpur, M.; Vrat, P.; Shankar, R., A multi-objective genetic algorithm approach to the design of cellular manufacturing systems, International Journal of Production Research, 42, 1419-1441 (2004) · <a href="/1060.90084" class="nowrap">Zbl 1060.90084</a></td> </tr><tr> <td>[7]</td> <td class="space">Guerrero, F.; Lozano, S.; Smith, K.; Canca, D.; Kwok, T., Manufacturing cell formation using a new self-organizing neural network, Computers and Industrial Engineering, 42, 377-382 (2002)</td> </tr><tr> <td>[8]</td> <td class="space">Chen, C.-W.; Sha, D. Y., Heuristic approach for solving the multi-objective facility layout problem, International Journal of Production Research, 43, 4493-4507 (2005) · <a href="/1094.90019" class="nowrap">Zbl 1094.90019</a></td> </tr><tr> <td>[9]</td> <td class="space">Byrne, A., How Wiremold reinvented itself with kaizen, Target, 11, 8-14 (1995)</td> </tr><tr> <td>[10]</td> <td class="space">Dorigo, M.; Gambardella, L. M., Ant colony system: a cooperative learning approach to the traveling salesman problem, IEEE Transactions on Evolutionary Computation, 1, 53-66 (1997)</td> </tr><tr> <td>[11]</td> <td class="space">Liao, C.; Juan, H., An ant colony optimization for single-machine tardiness scheduling with sequence-dependent setups, Computers and Operations Research, 34, 1899-1909 (2007) · <a href="/1112.90030" class="nowrap">Zbl 1112.90030</a></td> </tr><tr> <td>[12]</td> <td class="space">Montemanni, R.; Gambardella, L. M.; Rizzoli, A. E.; Donati, A. V., Ant colony system for a dynamic vehicle routing problem, Journal of Combinatorial Optimization, 10, 327-343 (2005) · <a href="/1093.90094" class="nowrap">Zbl 1093.90094</a></td> </tr><tr> <td>[13]</td> <td class="space">Pour, H. D.; Nosraty, M., Solving the facility and layout and location problem by ant-colony optimization-meta heuristic, International Journal of Production Research, 44, 5187-5196 (2006) · <a href="/1128.90552" class="nowrap">Zbl 1128.90552</a></td> </tr><tr> <td>[14]</td> <td class="space">Liao, C. J.; Lin, H.-T., Just-in-time manufacture of home-use sewing machines using backward scheduling, International Journal of Production Research, 36, 1841-1855 (1998) · <a href="/0949.90633" class="nowrap">Zbl 0949.90633</a></td> </tr><tr> <td>[15]</td> <td class="space">Garcia-Martinez, C.; Cordon, O.; Herrera, F., A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP, European Journal of Operational Research, 180, 116-148 (2007) · <a href="/1114.90103" class="nowrap">Zbl 1114.90103</a></td> </tr><tr> <td>[16]</td> <td class="space">Dorigo, M.; Maniezzo, V.; Colorni, A., Ant system: optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 26, 29-41 (1996)</td> </tr><tr> <td>[17]</td> <td class="space">Stuetzle, T.; Hoos, H. H., MAX-MIN ant system, Future Generation Computer Systems, 16, 889-914 (2000)</td> </tr><tr> <td>[18]</td> <td class="space">Vlachos, A.; Moue, A., Max-min ant system applied in economic load dispatch, WSEAS Transactions on Computers, 4, 711-717 (2005)</td> </tr><tr> <td>[19]</td> <td class="space">Chu, S. C.; Roddick, J. F.; Pan, J. S., Ant colony system with communication strategies, Information Sciences, 167, 63-76 (2004) · <a href="/1094.90053" class="nowrap">Zbl 1094.90053</a></td> </tr><tr> <td>[20]</td> <td class="space">Li, S. G.; Wu, Z. M.; Pang, X. H., Parallel ant colony algorithm and its application in the capacitated lot sizing problem for an agile supply chain, Journal of Harbin Institute of Technology (New Series), 11, 573-578 (2004)</td> </tr><tr> <td>[21]</td> <td class="space">Ellabib, I.; Calamai, P.; Basir, O., Exchange strategies for multiple ant colony system, Information Sciences, 177, 1248-1264 (2007)</td> </tr><tr> <td>[22]</td> <td class="space">Li, S. G.; Wu, Z. M.; Pang, X. H., Job shop in real time case, International Journal of Advanced Manufacturing Technology, 26, 870-875 (2005)</td> </tr><tr> <td>[23]</td> <td class="space">Klir, G. J.; Yuan, B., Fuzzy sets and fuzzy logic: theory and applications (1995), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · <a href="/0915.03001" class="nowrap">Zbl 0915.03001</a></td> </tr><tr> <td>[24]</td> <td class="space">Grefenstette, J. J., Optimization of control parameters for genetic algorithm, IEEE Transactions on Systems, Man and Cybernetics, 16, 122-128 (1986)</td> </tr><tr> <td>[25]</td> <td class="space">Baraglia, R.; Hidalgo, J. I.; Perego, R., A hybrid heuristic for the traveling salesman problem, IEEE Transactions on Evolutionary Computation, 5, 613-622 (2001)</td> </tr><tr> <td>[26]</td> <td class="space">Liao, C. J.; Tseng, C. T.; Luarn, P., A discrete version of particle swarm optimization for flow shop scheduling problems, Computers and Operations Research, 34, 3099-3111 (2007) · <a href="/1185.90083" class="nowrap">Zbl 1185.90083</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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