Document Zbl 0795.90032

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J. Oper. Res.</a> <a href="/?q=in%3A15161" title="Articles in this Issue">70, No. 1, 115-125 (1993)</a>. </div> <div class="abstract">Summary: We examine the complexity of scheduling problems when more than one measure of performance is appropriate. The criteria we study are maximal tardiness, flowtime, number of tardy jobs, tardiness, and the weighted counterparts of the last three measures. The machine environment is restricted to a single machine. Complexity results are given for secondary criterion, bicriteria and weighted criteria approaches for all combinations of measures. Of the problems examined, only six remain open.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A474829">Cited in <strong>35</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%3A90C60" title="MSC2020">90C60</a> </td> <td class="space"> Abstract computational complexity for mathematical programming problems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acomplexity+of+scheduling+problems">complexity of scheduling problems</a>; <a href="/?q=ut%3Amaximal+tardiness">maximal tardiness</a>; <a href="/?q=ut%3Aflowtime">flowtime</a>; <a href="/?q=ut%3Anumber+of+tardy+jobs">number of tardy jobs</a>; <a href="/?q=ut%3Atardiness">tardiness</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 0795.90032" data-ciurl="/ci/00474829" data-biburl="/bibtex/00474829.bib" data-amsurl="/amsrefs/00474829.bib" data-xmlurl="/xml/00474829.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00474829.pdf" title="Zbl 0795.90032 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/10.1016/0377-2217(93)90236-G" aria-label="DOI for “Complexity of single machine, multi-criteria scheduling problems”" title="10.1016/0377-2217(93)90236-G">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">Baker, K. R., Introduction To Sequenching And Scheduling (1974), Wiley: Wiley New York</td> </tr><tr> <td>[2]</td> <td class="space">Chen, C.-L.; Bulfin, R. L., Scheduling unit processing time jobs on a single machine with multiple criteria, Computers & Operations Research, 17, 1-17 (1989) · <a href="/0681.90049" class="nowrap">Zbl 0681.90049</a></td> </tr><tr> <td>[3]</td> <td class="space">Du, J.; Leung, J. Y.-T., Minimizing total tardiness on one machine is NP-hard, Mathematics of Operations Research, 15, 483-493 (1990) · <a href="/0714.90052" class="nowrap">Zbl 0714.90052</a></td> </tr><tr> <td>[4]</td> <td class="space">Emmons, H., One machine sequencing to minimize mean flow time with minimum number tardy, Naval Research Logistics Quarterly, 22, 585-592 (1975) · <a href="/0315.90032" class="nowrap">Zbl 0315.90032</a></td> </tr><tr> <td>[5]</td> <td class="space">Emmons, H., A note on a scheduling problem with dual criteria, Naval Research Logistics Quarterly, 22, 615-616 (1975) · <a href="/0314.90045" class="nowrap">Zbl 0314.90045</a></td> </tr><tr> <td>[6]</td> <td class="space">French, S., Sequencing and Scheduling (1986), Wiley: Wiley New York</td> </tr><tr> <td>[7]</td> <td class="space">Garey, M. R.; Johnson, D. S., Computers and Intractability (1979), Freeman: Freeman San Francisco, CA · <a href="/0411.68039" class="nowrap">Zbl 0411.68039</a></td> </tr><tr> <td>[8]</td> <td class="space">Goicoechea, A.; Hansen, D. R.; Duckstein, L., Multiobjective Decision Analysis with Engineering and Business Applications (1982), Wiley: Wiley New York · <a href="/0584.90045" class="nowrap">Zbl 0584.90045</a></td> </tr><tr> <td>[9]</td> <td class="space">Graham, R. L.; Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H.G., Optimization and approximation in deterministic sequencing and scheduling, Annals of Discrete Mathematics, 5, 287-326 (1979) · <a href="/0411.90044" class="nowrap">Zbl 0411.90044</a></td> </tr><tr> <td>[10]</td> <td class="space">Lageweg, B. J.; Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H.G., Computer aided complexity classification of deterministic scheduling problems (1981), Stichting Mathematisch Centrum: Stichting Mathematisch Centrum Amsterdam, Netherlands · <a href="/0452.90035" class="nowrap">Zbl 0452.90035</a></td> </tr><tr> <td>[11]</td> <td class="space">Lawler, E. L., Sequencing to minimize the weighted number of tardy jobs, Recherche Opérationnelle, 10, 17-33 (1976) · <a href="/0333.68044" class="nowrap">Zbl 0333.68044</a></td> </tr><tr> <td>[12]</td> <td class="space">Lenstra, J. K.; Rinnooy Kan, A. H.G.; Brucker, P., Complexity of machine scheduling problems, Annals of Discrete Mathematics, 1, 343-362 (1977) · <a href="/0301.90025" class="nowrap">Zbl 0301.90025</a></td> </tr><tr> <td>[13]</td> <td class="space">Panwalkar, S. S.; Dudek, R. K.; Smith, M. L., Sequencing research and the industrial scheduling problem, (Elmaghraby, S. E., Symposium on the Theory of Scheduling and its Application (1973), Springer-Verlag: Springer-Verlag New York), 29-38 · <a href="/0269.90025" class="nowrap">Zbl 0269.90025</a></td> </tr><tr> <td>[14]</td> <td class="space">Rinnooy Kan, A. H.G., Machine Scheduling Problems: Classification, Complexity and Computations (1976), Martinus Nijhoff: Martinus Nijhoff The Hague, Holland · <a href="/0366.90092" class="nowrap">Zbl 0366.90092</a></td> </tr><tr> <td>[15]</td> <td class="space">Smith, W. E., Various optimizers for single stage production, Naval Research Logistics Quaterly, 3, 59-66 (1956)</td> </tr><tr> <td>[16]</td> <td class="space">Steuer, R. E., Multiple Criteria Optimization: Theory, Computation, and Applications (1986), Wiley: Wiley New York · <a href="/0663.90085" class="nowrap">Zbl 0663.90085</a></td> </tr><tr> <td>[17]</td> <td class="space">Van Wassenhove, L. N.; Gelders, L. F., Solving a bicriteria scheduling problem, European Journal of Operational Research, 4, 42-48 (1980) · <a href="/0418.90054" class="nowrap">Zbl 0418.90054</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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