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J. Syst. Sci.</a> <a href="/?q=in%3A186487" title="Articles in this Issue">37, No. 12, 827-833 (2006)</a>. </div> <div class="abstract">Summary: We consider the machine scheduling problems with the effects of deterioration and learning. In this model, job processing times are defined by functions of their starting times and positions in the sequence. The scheduling objectives are makespan (weighted) sum of completion times and maximum lateness. It is shown that even with the introduction of deterioration and learning effect to job processing times, several single machine problems and several flow shop problems remain polynomially solvable, respectively.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5210900">Cited in <strong>49</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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AScheduling">Scheduling</a>; <a href="/?q=ut%3Asingle+machine">single machine</a>; <a href="/?q=ut%3Aflow+shop">flow shop</a>; <a href="/?q=ut%3Alearning+effect">learning effect</a>; <a href="/?q=ut%3Adeteriorating+jobs">deteriorating jobs</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1126.90347" data-ciurl="/ci/05210900" data-biburl="/bibtex/05210900.bib" data-amsurl="/amsrefs/05210900.bib" data-xmlurl="/xml/05210900.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05210900.pdf" title="Zbl 1126.90347 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/10.1080/00207720600879260" aria-label="DOI for “A note on scheduling problems with learning effect and deteriorating jobs”" title="10.1080/00207720600879260">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">Alidaee B, J. Oper. Res. Soc. 50 pp 711– (1999)</td> </tr><tr> <td>[2]</td> <td class="space">Bachman A, Eur. J. Oper. Res. 126 pp 557– (2000) · <a href="/0976.90039" class="nowrap">Zbl 0976.90039</a> · <a href="https://doi.org/10.1016/S0377-2217(99)00310-0" class="nowrap">doi:10.1016/S0377-2217(99)00310-0</a></td> </tr><tr> <td>[3]</td> <td class="space">Bachman A, J. Oper. Res. Soc. 55 pp 257– (2004) · <a href="/1095.90033" class="nowrap">Zbl 1095.90033</a> · <a href="https://doi.org/10.1057/palgrave.jors.2601689" class="nowrap">doi:10.1057/palgrave.jors.2601689</a></td> </tr><tr> <td>[4]</td> <td class="space">Bachman A, Information Proc. Lett. 81 pp 81– (2002) · <a href="/1032.68019" class="nowrap">Zbl 1032.68019</a> · <a href="https://doi.org/10.1016/S0020-0190(01)00196-X" class="nowrap">doi:10.1016/S0020-0190(01)00196-X</a></td> </tr><tr> <td>[5]</td> <td class="space">Badiru AB, IEEE trans. on Eng. Manage. 39 pp 176– (1992) · <a href="https://doi.org/10.1109/17.141275" class="nowrap">doi:10.1109/17.141275</a></td> </tr><tr> <td>[6]</td> <td class="space">Biskup D, Eur. J. Oper. Res. 115 pp 173– (1999) · <a href="/0946.90025" class="nowrap">Zbl 0946.90025</a> · <a href="https://doi.org/10.1016/S0377-2217(98)00246-X" class="nowrap">doi:10.1016/S0377-2217(98)00246-X</a></td> </tr><tr> <td>[7]</td> <td class="space">Browne S, Oper. Res. 38 pp 495– (1990) · <a href="/0703.90051" class="nowrap">Zbl 0703.90051</a> · <a href="https://doi.org/10.1287/opre.38.3.495" class="nowrap">doi:10.1287/opre.38.3.495</a></td> </tr><tr> <td>[8]</td> <td class="space">Chen Z-L, Discrete Applied Math. 70 pp 81– (1996) · <a href="/0855.68032" class="nowrap">Zbl 0855.68032</a> · <a href="https://doi.org/10.1016/0166-218X(96)00102-3" class="nowrap">doi:10.1016/0166-218X(96)00102-3</a></td> </tr><tr> <td>[9]</td> <td class="space">Cheng TCE, Information Processing Lett. 65 pp 75– (1998) · <a href="/1338.68096" class="nowrap">Zbl 1338.68096</a> · <a href="https://doi.org/10.1016/S0020-0190(97)00195-6" class="nowrap">doi:10.1016/S0020-0190(97)00195-6</a></td> </tr><tr> <td>[10]</td> <td class="space">Cheng TCE, Eur. J. Oper. Res. 152 pp 1– (2004) · <a href="/1030.90023" class="nowrap">Zbl 1030.90023</a> · <a href="https://doi.org/10.1016/S0377-2217(02)00909-8" class="nowrap">doi:10.1016/S0377-2217(02)00909-8</a></td> </tr><tr> <td>[11]</td> <td class="space">Graham RL, Annals of Discrete Math. 5 pp 287– (1979) · <a href="/0411.90044" class="nowrap">Zbl 0411.90044</a> · <a href="https://doi.org/10.1016/S0167-5060(08)70356-X" class="nowrap">doi:10.1016/S0167-5060(08)70356-X</a></td> </tr><tr> <td>[12]</td> <td class="space">Ho JC, Comp., Oper. Res. 22 pp 237– (1995) · <a href="/0826.90064" class="nowrap">Zbl 0826.90064</a> · <a href="https://doi.org/10.1016/0305-0548(94)E0007-T" class="nowrap">doi:10.1016/0305-0548(94)E0007-T</a></td> </tr><tr> <td>[13]</td> <td class="space">Kunnathur AS, Eur. J. Oper. Res. 47 pp 56– (1990) · <a href="/0717.90034" class="nowrap">Zbl 0717.90034</a> · <a href="https://doi.org/10.1016/0377-2217(90)90089-T" class="nowrap">doi:10.1016/0377-2217(90)90089-T</a></td> </tr><tr> <td>[14]</td> <td class="space">Lee W-C, Inter. Business J Economics 3 pp 83– (2004)</td> </tr><tr> <td>[15]</td> <td class="space">Lee W-C, Acta Informatica 40 pp 303– (2004) · <a href="/1137.90500" class="nowrap">Zbl 1137.90500</a> · <a href="https://doi.org/10.1007/s00236-003-0132-9" class="nowrap">doi:10.1007/s00236-003-0132-9</a></td> </tr><tr> <td>[16]</td> <td class="space">Mosheiov G, Oper. Res. 39 pp 979– (1991) · <a href="/0748.90033" class="nowrap">Zbl 0748.90033</a> · <a href="https://doi.org/10.1287/opre.39.6.979" class="nowrap">doi:10.1287/opre.39.6.979</a></td> </tr><tr> <td>[17]</td> <td class="space">Mosheiov G, Computers, Operations Research 21 pp 653– (1994) · <a href="/0810.90074" class="nowrap">Zbl 0810.90074</a> · <a href="https://doi.org/10.1016/0305-0548(94)90080-9" class="nowrap">doi:10.1016/0305-0548(94)90080-9</a></td> </tr><tr> <td>[18]</td> <td class="space">Mosheiov G, Computers, Industrial Eng. 28 pp 869– (1995) · <a href="https://doi.org/10.1016/0360-8352(95)00006-M" class="nowrap">doi:10.1016/0360-8352(95)00006-M</a></td> </tr><tr> <td>[19]</td> <td class="space">Mosheiov G, INFOR 36 pp 205– (1998)</td> </tr><tr> <td>[20]</td> <td class="space">Mosheiov G, Eur. J. Oper. Res. 132 pp 687– (2001) · <a href="/1017.90051" class="nowrap">Zbl 1017.90051</a> · <a href="https://doi.org/10.1016/S0377-2217(00)00175-2" class="nowrap">doi:10.1016/S0377-2217(00)00175-2</a></td> </tr><tr> <td>[21]</td> <td class="space">Mosheiov G, J. Oper. Res. Soc. 52 pp 1165– (2001) · <a href="/1178.90159" class="nowrap">Zbl 1178.90159</a> · <a href="https://doi.org/10.1057/palgrave.jors.2601215" class="nowrap">doi:10.1057/palgrave.jors.2601215</a></td> </tr><tr> <td>[22]</td> <td class="space">Mosheiov G, Discrete Applied Math. 117 pp 195– (2002) · <a href="/1004.68031" class="nowrap">Zbl 1004.68031</a> · <a href="https://doi.org/10.1016/S0166-218X(00)00385-1" class="nowrap">doi:10.1016/S0166-218X(00)00385-1</a></td> </tr><tr> <td>[23]</td> <td class="space">Mosheiov G, Eur. J. Oper. Res. 147 pp 665– (2003) · <a href="/1037.90529" class="nowrap">Zbl 1037.90529</a> · <a href="https://doi.org/10.1016/S0377-2217(02)00358-2" class="nowrap">doi:10.1016/S0377-2217(02)00358-2</a></td> </tr><tr> <td>[24]</td> <td class="space">Nembhard DA, Inter.Industrial J Ergonomics 29 pp 297– (2002) · <a href="https://doi.org/10.1016/S0169-8141(01)00070-1" class="nowrap">doi:10.1016/S0169-8141(01)00070-1</a></td> </tr><tr> <td>[25]</td> <td class="space">Ng CT, Information Processing Letters 81 pp 327– (2002) · <a href="https://doi.org/10.1016/S0020-0190(01)00244-7" class="nowrap">doi:10.1016/S0020-0190(01)00244-7</a></td> </tr><tr> <td>[26]</td> <td class="space">Pinedo M, Scheduling: Theory, Algorithms,, Systems (2002)</td> </tr><tr> <td>[27]</td> <td class="space">Sundararaghavan PS, Eur. J. Oper. Res. 78 pp 394– (1994) · <a href="/0816.90088" class="nowrap">Zbl 0816.90088</a> · <a href="https://doi.org/10.1016/0377-2217(94)90048-5" class="nowrap">doi:10.1016/0377-2217(94)90048-5</a></td> </tr><tr> <td>[28]</td> <td class="space">Xiang S, Int. J. Prod. Economics 66 pp 53– (2000) · <a href="https://doi.org/10.1016/S0925-5273(99)00106-1" class="nowrap">doi:10.1016/S0925-5273(99)00106-1</a></td> </tr><tr> <td>[29]</td> <td class="space">Wang J-B, J. Ope. Res. Soc. 56 pp 1325– (2005) · <a href="/1082.90041" class="nowrap">Zbl 1082.90041</a> · <a href="https://doi.org/10.1057/palgrave.jors.2601856" class="nowrap">doi:10.1057/palgrave.jors.2601856</a></td> </tr><tr> <td>[30]</td> <td class="space">Wang J-B, Omega 34 pp 327– (2006) · <a href="https://doi.org/10.1016/j.omega.2004.10.006" class="nowrap">doi:10.1016/j.omega.2004.10.006</a></td> </tr><tr> <td>[31]</td> <td class="space">Wright TP, J. Aero. Sci. 3 pp 122– (1936) · <a href="https://doi.org/10.2514/8.155" class="nowrap">doi:10.2514/8.155</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. 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