Document Zbl 1407.90144

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J. Oper. Res.</a> <a href="/?q=in%3A424002" title="Articles in this Issue">35, No. 6, Article ID 1850048, 11 p. (2018)</a>. </div> <div class="abstract">Summary: In this paper, we consider the online single machine scheduling problem to minimize the maximum weighted completion time of the jobs. For the preemptive problem, we show that the LW (largest weight first) rule yields an optimal schedule. For the non-preemptive problem, <span class="zbmathjax-textit">W. Li</span> presented a lower bound 2 and then provided an online algorithm with a competitive ratio of 3 [ibid. 32, No. 4, Article ID 1550030, 10 p. (2015; <a href="/1325.90046">Zbl 1325.90046</a>)]. In this paper, we present two online algorithms with the best-possible competitive ratio of $2$ for the non-preemptive problem.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6991468">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B35" title="MSC2020">90B35</a> </td> <td class="space"> Deterministic scheduling theory in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W27" title="MSC2020">68W27</a> </td> <td class="space"> Online algorithms; streaming algorithms </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ascheduling">scheduling</a>; <a href="/?q=ut%3Aonline+algorithm">online algorithm</a>; <a href="/?q=ut%3Abest-possible+competitive+ratio">best-possible competitive ratio</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1325.90046">Zbl 1325.90046</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 1407.90144" data-ciurl="/ci/06991468" data-biburl="/bibtex/06991468.bib" data-amsurl="/amsrefs/06991468.bib" data-xmlurl="/xml/06991468.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06991468.pdf" title="Zbl 1407.90144 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/10.1142/S0217595918500483" aria-label="DOI for “Best-possible online algorithms for single machine scheduling to minimize the maximum weighted completion time”" title="10.1142/S0217595918500483">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">Albers, S.; Robert, Y.; Vivien, F., Introduction to Scheduling, Online scheduling, 57-84, (2009), Boca Raton: Chapman and Hall/CRC Press, Boca Raton</td> </tr><tr> <td>[2]</td> <td class="space">Anderson, EJ; Potts, CN, Online scheduling of a single machine to minimize total weighted completion time, Mathematics of Operations Research, 29, 686-697, (2004) · <a href="/1082.90033" class="nowrap">Zbl 1082.90033</a></td> </tr><tr> <td>[3]</td> <td class="space">van den Akker; Hoogeveen, MH; Vakhania, N., Restarts can help in the online minimization of the maximum delivery time on a single machine, Journal of Scheduling, 3, 333-341, (2000) · <a href="/0966.90033" class="nowrap">Zbl 0966.90033</a></td> </tr><tr> <td>[4]</td> <td class="space">Feng, Q.; Yuan, JJ, NP-hardness of a multicriteria scheduling on two families of jobs, OR Transactions, 11, 121-126, (2007)</td> </tr><tr> <td>[5]</td> <td class="space">Hoogeveen, JA; Vestjens, APA, A best possible deterministic online algorithm for minimizing maximum delivery time on a single machine, SIAM Journal on Discrete Mathematics, 13, 56-63, (2000) · <a href="/0944.90020" class="nowrap">Zbl 0944.90020</a></td> </tr><tr> <td>[6]</td> <td class="space">Li, WJ, A best possible online algorithm for the parallel-machine scheduling to minimize the maximum weighted completion time, Asia-Pacific Journal of Operational Research, 32, 4, 10, (2015) · <a href="/1325.90046" class="nowrap">Zbl 1325.90046</a></td> </tr><tr> <td>[7]</td> <td class="space">Nong, QQ; Cheng, TCE; Ng, CT, Two-agent scheduling to minimize the total cost, European Journal of Operational Research, 215, 39-44, (2011) · <a href="/1237.90094" class="nowrap">Zbl 1237.90094</a></td> </tr><tr> <td>[8]</td> <td class="space">Phillips, C.; Stein, C.; Wein, J., Minimizing average completion time in the presence of release dates, Mathematics Programming, 82, 199-223, (1998) · <a href="/0920.90074" class="nowrap">Zbl 0920.90074</a></td> </tr><tr> <td>[9]</td> <td class="space">Tian, J.; Fu, RY; Yuan, JJ, Online over time scheduling on parallel-batch machines: A survey, Journal of the Operations Research Society of China, 2, 445-454, (2014) · <a href="/1306.90060" class="nowrap">Zbl 1306.90060</a></td> </tr><tr> <td>[10]</td> <td class="space">van Stee, R.; Poutre, HL, Minimizing the total completion time online on a single machine using restarts, Journal of Algorithms, 57, 95-129, (2005) · <a href="/1101.68434" class="nowrap">Zbl 1101.68434</a></td> </tr><tr> <td>[11]</td> <td class="space">Vestjens, APA (1997). Online machine scheduling. Ph.D. thesis, Eindhoven University of Technology, The Netherlands. · <a href="/0941.68515" class="nowrap">Zbl 0941.68515</a></td> </tr><tr> <td>[12]</td> <td class="space">Yuan, JJ; Fu, RY; Ng, CT; Cheng, TCE, A best online algorithm for unbounded parallel-batch scheduling with restarts to minimize makespan, Journal of Scheduling, 14, 361-369, (2011) · <a href="/1229.90067" class="nowrap">Zbl 1229.90067</a></td> </tr><tr> <td>[13]</td> <td class="space">Zhang, GC; Cai, XQ; Wong, CK, Online algorithms for minimizing makespan on batch processing machines, Naval Research Logistics, 48, 241-258, (2001) · <a href="/1018.90017" class="nowrap">Zbl 1018.90017</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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