Document Zbl 1433.90062

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Math. Comput.</a> <a href="/?q=in%3A444013" title="Articles in this Issue">365, Article ID 124697, 13 p. (2020)</a>. </div> <div class="abstract">Summary: This paper investigates the ND-agent scheduling of linear-deteriorating tasks on a single machine with positional due indices. Under the ND-agent setting, there are two agents $A$ and $B$ and each agent $X \in \{A, B\}$ has its set of tasks $\mathcal{T}^{(X)}$, called $X$-tasks. Moreover, ND-agent means that $\mathcal{T}^{(A)}$ and $\mathcal{T}^{(B)}$ are allowed to be non-disjoint, which is a generalization of the traditional two-agent setting. Each task has a linear-deteriorating processing time and a positional due index. In this paper, we consider two problems: The first problem is to find a feasible schedule which minimizes the total completion time of the $A$-tasks under the condition that the maximum cost of the $B$-tasks is bounded by a threshold value. The second problem is the Pareto scheduling problem to minimize the total completion time of the $A$-tasks and the maximum cost of the $B$-tasks, simultaneously. We show in this paper that the two problems are solvable in $O(n^2)$ time and in $O(n^4)$ time, respectively. If the maximum cost of the tasks of agent $B$ is restricted to some lateness-like criteria, for the version without the positional restriction, the time complexity for solving the above two problems can be reduced to $O(n\log n)$ and $O(n^3\log n)$, respectively. Our research includes a new technique for calculating the number of non-dominated points.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7151011">Cited in <strong>1</strong> Document</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%3A68M20" title="MSC2020">68M20</a> </td> <td class="space"> Performance evaluation, queueing, and scheduling in the context of computer systems </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%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%3AND-agent+scheduling">ND-agent scheduling</a>; <a href="/?q=ut%3Alinear-deteriorating+tasks">linear-deteriorating tasks</a>; <a href="/?q=ut%3Adue+indices">due indices</a>; <a href="/?q=ut%3APareto+scheduling">Pareto scheduling</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 1433.90062" data-ciurl="/ci/07151011" data-biburl="/bibtex/07151011.bib" data-amsurl="/amsrefs/07151011.bib" data-xmlurl="/xml/07151011.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07151011.pdf" title="Zbl 1433.90062 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.amc.2019.124697" aria-label="DOI for “ND-agent scheduling of linear-deteriorating tasks with positional due indices to minimize total completion time and maximum cost”" title="10.1016/j.amc.2019.124697">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">Agnetis, A.; Billaut, J. 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