<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0874-5161</journal-id>
<journal-title><![CDATA[Investigação Operacional]]></journal-title>
<abbrev-journal-title><![CDATA[Inv. Op.]]></abbrev-journal-title>
<issn>0874-5161</issn>
<publisher>
<publisher-name><![CDATA[APDIO - Associação Portuguesa de Investigação Operacional]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0874-51612004000100004</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A note on polynomially-solvable cases of common due date early-tardy scheduling with release dates]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Valente]]></surname>
<given-names><![CDATA[Jorge M. S.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Alves]]></surname>
<given-names><![CDATA[Rui A. F. S.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidade do Porto Faculdade de Economia ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2004</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2004</year>
</pub-date>
<volume>24</volume>
<numero>1</numero>
<fpage>63</fpage>
<lpage>71</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_arttext&amp;pid=S0874-51612004000100004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_abstract&amp;pid=S0874-51612004000100004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_pdf&amp;pid=S0874-51612004000100004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this paper we consider the single machine scheduling problem with integer release dates and the objective of minimising the sum of deviations of jobs' completion times from a common integer due date. We present an efficient polynomial algorithm for the unit processing time case. We also show how to calculate in polynomial time the minimum non-restrictive due date for the general case.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[scheduling]]></kwd>
<kwd lng="en"><![CDATA[early-tardy]]></kwd>
<kwd lng="en"><![CDATA[common due date]]></kwd>
<kwd lng="en"><![CDATA[unit processing times]]></kwd>
<kwd lng="en"><![CDATA[release dates]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="center"><b>A note on polynomially-solvable cases of common due date early-tardy scheduling with release dates</b></p>     <p align="center">Jorge M. S. Valente * </p>     <p align="center">Rui A. F. S. Alves * </p>     <p align="center">* Faculdade de Economia, Universidade do Porto </p>     <p align="center"><a href="mailto:%7Bjvalente,%20ralves%7D@fep.up.pt">{jvalente,    ralves}@fep.up.pt</a></p>     <p align="center">&nbsp;</p>     <p align="center"><b>Abstract:</b></p>     <p align="justify">In this paper we consider the single machine scheduling problem    with integer release dates and the objective of minimising the sum of deviations    of jobs' completion times from a common integer due date. We present an efficient    polynomial algorithm for the unit processing time case. We also show how to    calculate in polynomial time the minimum non-restrictive due date for the general    case. </p>     <p><b>Keywords:</b> scheduling, early-tardy, common due date, unit processing    times, release dates </p>     <p>&nbsp;</p>     ]]></body>
<body><![CDATA[<p>Texto completo apenas dispon&iacute;vel em PDF. </p>     <p> Full text only available in PDF format.</p>     <p>&nbsp;</p>     <p><b>Bibliography</b> </p>     <!-- ref --><p align="justify">1. BAGCHI, U., SULLIVAN, R., AND CHANG, Y. Minimizing mean    absolute deviation of completion times about a common due date. <i>Naval Research    Logistics Quarterly 33</i> (1986), 227-240. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326965&pid=S0874-5161200400010000400001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p align="justify">2. BAKER, K.&nbsp;R., AND SCUDDER, G.&nbsp;D. Sequencing with    earliness and tardiness penalties: A review.     <br>   <i>Operations Research 38</i> (1990), 22-36.&nbsp; </p>     <!-- ref --><p align="justify">3. BANK, J., AND WERNER, F. Heuristic algorithms for unrelated    parallel machine scheduling with a common due date, release dates, and linear    earliness and tardiness penalties. <i>Mathematical and Computer Modelling 33</i>    (2001), 363-383.&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326968&pid=S0874-5161200400010000400003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify">4. HALL, N., KUBIAK, W., AND SETHI, S. Earliness-tardiness    scheduling problems, ii: Deviation of completion times about a restrictive common    due date. <i>Operations Research 39</i> (1991), 847-856.&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326969&pid=S0874-5161200400010000400004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify">5. KANET, J. Minimizing the average deviation of job completion    times about a common due date. <i>Naval Research Logistics Quarterly 28</i>    (1981), 643-651.&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326970&pid=S0874-5161200400010000400005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify">6. LAWLER, E.&nbsp;L., LENSTRA, J.&nbsp;K., RINNOOY KAN, A.    H.&nbsp;G., AND SHMOYS, D.&nbsp;B. Sequencing and scheduling: Algorithms and    complexity. In <i>Logistics of Production and Inventory, Handbooks in Operations    Research and Management Science, pp. 445-522</i>, S.&nbsp;C. Graves, A.&nbsp;H.&nbsp;G.    Rinnooy Kan, and P.&nbsp;H. Zipkin, Eds. North-Holland, Amsterdam, 1993.&nbsp;  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326971&pid=S0874-5161200400010000400006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify">7. NANDKEOLYAR, U., AHMED, M.&nbsp;U., AND SUNDARARAGHAVAN,    P.&nbsp;S. Dynamic single-machine-weighted absolute deviation problem: Predictive    heuristics and evaluation. <i>International Journal of Production Research 31</i>    (1993), 1453-1466.&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326972&pid=S0874-5161200400010000400007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify">8. SRIDHARAN, V., AND ZHOU, Z. A decision theory based scheduling    procedure for single machine weighted earliness and tardiness problem. <i>European    Journal of Operational Research 94</i> (1996), 292-301. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=326973&pid=S0874-5161200400010000400008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p align="justify">&nbsp;</p>       ]]></body><back>
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</article>
