Document Zbl 1193.90105

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Math. Modelling</a> <a href="/?q=in%3A259021" title="Articles in this Issue">34, No. 6, 1498-1510 (2010)</a>. </div> <div class="abstract">Summary: This paper studies the parallel machines bi-criteria scheduling problem (PMBSP) in a deteriorating system. Sequencing and scheduling problems (SSP) have seldom considered the two phenomena concurrently. This paper discusses the parallel machines scheduling problem with the effects of machine and job deterioration. By the machine deterioration effect, we mean that each machine deteriorates at a different rate. This deterioration is considered in terms of cost which depends on the production rate, the machine’s operating characteristics and the kind of work done by each machine. Moreover, job processing times are increasing functions of their starting times and follow a simple linear deterioration. The objective functions are minimizing total tardiness and machine deteriorating cost. The problem of total tardiness on identical parallel machines is NP-hard, thus the problem with machine deteriorating cost as an additional term is also NP-hard. We propose the LP-metric method to show the importance of our proposed multi-objective problem. A metaheuristic algorithm is developed to locate optimal or near optimal solutions based on a Tabu search mechanism. Numerical examples are presented to show the efficiency of this model.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5775127">Cited in <strong>19</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><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C11" title="MSC2020">90C11</a> </td> <td class="space"> Mixed integer programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C29" title="MSC2020">90C29</a> </td> <td class="space"> Multi-objective and goal programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ascheduling+and+sequencing">scheduling and sequencing</a>; <a href="/?q=ut%3Aparallel+machines">parallel machines</a>; <a href="/?q=ut%3Amachine+deterioration">machine deterioration</a>; <a href="/?q=ut%3Ajob+deterioration">job deterioration</a>; <a href="/?q=ut%3Amulti-objectives+integer+programming">multi-objectives integer programming</a></div> <div class="software"> <h3>Software:</h3><a href="/software/8556">Tabu search</a>; <a href="/software/4942">LINGO</a>; <a href="/software/4448">LINDO</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 1193.90105" data-ciurl="/ci/05775127" data-biburl="/bibtex/05775127.bib" data-amsurl="/amsrefs/05775127.bib" data-xmlurl="/xml/05775127.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05775127.pdf" title="Zbl 1193.90105 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.apm.2009.08.023" aria-label="DOI for “Parallel machines scheduling to minimize job tardiness and machine deteriorating cost with deteriorating jobs”" title="10.1016/j.apm.2009.08.023">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">Browne, S.; Yechiali, U., Scheduling deteriorating jobs on a single processor, Oper. Res., 38, 495-498 (1990) · <a href="/0703.90051" class="nowrap">Zbl 0703.90051</a></td> </tr><tr> <td>[2]</td> <td class="space">Ruat, S.; Swami, S.; Gupta, N. D., Scheduling a capacitated single machine with time deteriorating job values, Product. Econ., 114, 769-780 (2008)</td> </tr><tr> <td>[3]</td> <td class="space">Gawiejnowicz, S.; Kurc, W.; Pankowska, L., Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences, Discrete Appl. Math., 154, 2150-2166 (2006) · <a href="/1113.90059" class="nowrap">Zbl 1113.90059</a></td> </tr><tr> <td>[4]</td> <td class="space">Wang, J., Single-machine scheduling problems with the effects of learning and deterioration, Omega, 35, 397-402 (2007)</td> </tr><tr> <td>[5]</td> <td class="space">Xu, D.; Sun, K.; Li, H., Parallel machine scheduling with almost periodic maintenance and non-preemptive jobs to minimize makespan, Comput. Oper. Res., 35, 1344-1349 (2008) · <a href="/1171.90411" class="nowrap">Zbl 1171.90411</a></td> </tr><tr> <td>[6]</td> <td class="space">Oron, D., Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times, Comput. Oper. Res., 35, 2071-2078 (2008) · <a href="/1139.90012" class="nowrap">Zbl 1139.90012</a></td> </tr><tr> <td>[7]</td> <td class="space">Wang, J.; Xia, Z., Scheduling jobs under decreasing linear deterioration, Inform. Pro. Lett., 94, 63-69 (2005) · <a href="/1182.68359" class="nowrap">Zbl 1182.68359</a></td> </tr><tr> <td>[8]</td> <td class="space">Jeng, A.; Lin, B., Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs, Comput. Oper. Res., 32, 521-536 (2005) · <a href="/1077.90025" class="nowrap">Zbl 1077.90025</a></td> </tr><tr> <td>[9]</td> <td class="space">Chakravarty, A. K.; Balakrislman, N., Job sequencing rules for minimizing the expected makespan in flexible machines, Eur. J. Oper. Res., 96, 274-288 (1996) · <a href="/0917.90186" class="nowrap">Zbl 0917.90186</a></td> </tr><tr> <td>[10]</td> <td class="space">Lam, C. T.; Yeh, R. H., Optimal maintenance policies for systems under various maintenance strategies, IEEE Trans. Reliab., 31-92 (1993)</td> </tr><tr> <td>[11]</td> <td class="space">Grall, A.; Berenguer, C.; Dieulle, L., A condition-based maintenance policy for stochastically deteriorating systems, Reliab. Eng. Syst. Safe., 76, 167-180 (2002)</td> </tr><tr> <td>[12]</td> <td class="space">Bilge, U.; Kirac, F.; Kurtulan, M.; Pekgun, P., A Tabu search algorithm for parallel machine total tardiness problem, Comput. Oper. Res., 31, 397-414 (2004) · <a href="/1057.90516" class="nowrap">Zbl 1057.90516</a></td> </tr><tr> <td>[13]</td> <td class="space">YI, Y.; Wang, D. W., Soft computing for scheduling with batch set up times earliness-tardiness penalties on parallel machine, J. Int. Man., 14, 311-322 (2003)</td> </tr><tr> <td>[14]</td> <td class="space">Radhakrishnan, S.; Ventura, J., Simulated annealing for parallel machine scheduling with earliness-tardiness penalties and sequence-dependent set-up times, Int. J. Prod. Res., 38, 2233-2252 (2000) · <a href="/0973.90512" class="nowrap">Zbl 0973.90512</a></td> </tr><tr> <td>[15]</td> <td class="space">Lee, C. Y.; Uzsoy, R.; Martin-Vega, L., Efficient algorithms for scheduling semiconductor burn in operations, Oper. Res., 40, 764-775 (1992) · <a href="/0759.90046" class="nowrap">Zbl 0759.90046</a></td> </tr><tr> <td>[16]</td> <td class="space">Park, Y.; Kim, S.; Lee, Y., Scheduling jobs on parallel machines applying neural network heuristic rules, Comput. Ind. Eng., 38, 189-202 (2000)</td> </tr><tr> <td>[17]</td> <td class="space">Cao, D.; Chen, M.; Wan, G., Parallel machine selection and job scheduling to minimize machine cost and job tardiness, Comput. Oper. Res., 32, 1995-2012 (2005) · <a href="/1068.90054" class="nowrap">Zbl 1068.90054</a></td> </tr><tr> <td>[18]</td> <td class="space">Pfund, M.; Fowler J, W.; Gadkari, A.; Chen, Y., Scheduling jobs on parallel machines with setup times and ready times, Comput. Ind. Eng., 54, 764-782 (2008)</td> </tr><tr> <td>[20]</td> <td class="space">Glover, F.; Laguna, M., Tabu Search (1997), Kluwer Academic Publishers: Kluwer Academic Publishers Boston · <a href="/0930.90083" class="nowrap">Zbl 0930.90083</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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