Document Zbl 0673.90023

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S.</a>; <a href="/authors/sotskov.yuri-n" title="Author Profile">Sotskov, Yu. N.</a>; <a href="/authors/strusevich.vitaly-a" title="Author Profile">Strusevich, V. A.</a></div> <h2 class="title"> <strong>Scheduling theory. Multistage systems. (孝械芯褉懈褟褉邪褋锌懈褋邪薪懈泄. 袦薪芯谐芯褋褌邪写懈泄薪褘械褋懈褋褌械屑褘.)</strong> <i>(Russian)</i> <a class="label nowrap" href="/0673.90023">Zbl 0673.90023</a> </h2> <div class="source"> 脠konomiko-Matematicheskaya Biblioteka. Moskva: Nauka. 328 p. R. 5.40 (1989). </div> <div class="abstract">The book is devoted to deterministic scheduling theory problems, their computational complexity, solution and approximation algorithms. The book deals with multistage systems and may be considered as a natural continuation of “Scheduling theory. Single-stage systems” (Russian) by <span class="zbmathjax-textit">V. S. Tanaev</span>, <span class="zbmathjax-textit">V. S. Gordon</span> and <span class="zbmathjax-textit">Ya. M. Shafranski沫</span> (1984; <a href="/0553.90030">Zbl 0553.90030</a>). <br class="zbmathjax-paragraph">The contents: Introduction. Chapter 1. Flow shop. Chapter 2. Job shop. Chapter 3. Open shop. Chapter 4. Mixed graph approach to scheduling problems. <br class="zbmathjax-paragraph">The introduction contains the basic concepts, definitions and three tables which can be regarded as a guide for the reader. Table B.1 presents the list of polynomially solvable problems with time complexity measures of the corresponding algorithms and the book sections where they are discussed. Table B.2 contains the list of NP-hard problems. Table B.3 gives the characteristics of approximate algorithms for solving some NP-hard problems. <br class="zbmathjax-paragraph">Chapter 1 discusses the flow shop scheduling problems. Some properties of flow shop schedules are established, polynomial-time algorithms to minimize the makespan for the two-machine case are described, including those case generalizations with time lags and with no wait in process. The proofs of NP-hardness (in the strong sense, as a rule) of various flow shop problems are presented, both preemptive and nonpreemptive cases being dealt with. Two sections are devoted to polynomially solvable special cases. The last section of this chapter describes polynomial-time approximate algorithms with a priori performance guarantees. <br class="zbmathjax-paragraph">Chapter 2 considers the job shop scheduling problems. It starts with polynomial-time algorithms for constructing both preemptive and nonpreemptive schedules for two jobs to minimize an arbitrary penalty function. Further problems with unit and arbitrary processing times are considered to minimize the makespan and the maximum lateness. Proofs of NP-hardness of several problems are given while for the rest of the problems polynomial-time algorithms are described. The problem with non- waiting process restriction finishes the chapter. <br class="zbmathjax-paragraph">Chapter 3 for the first time in the monograph literature investigates open shop problems. Four first sections deal with the problems of minimizing the makespan. Polynomial-time algorithms are described for two-machine open shop and two-machine heterogeneous systems which generalizes flow, job and open shop situations. Some special cases of multi-machine open shop problems are discussed and NP-hardness of the three machine case is proved. Two approaches to preemptive open shop problems are given, parallel machine open shop problems are discussed. Problems with various types of precedence constraints are also investigated. The rest of the chapter deals with open shop problems with other objectives such as maximum lateness, the number of tardy jobs and mean flow time. <br class="zbmathjax-paragraph">Chapter 4 provides a general approach to a network modelling wide range of scheduling systems based on mixed (disjunctive) graph and multigraph techniques. Some properties of mixed (multi) graphs are established and they are used for representation of a scheduling system with sequential machines and with sequential and parallel machines. In particular, the problem of optimal selecting machines from a given set and distributing operations over selected machines to minimize a fairly general objective is considered. A general scheme of a branch-and-bound method to solve extremal problems on mixed (multi) graphs is described. The developed techniques are used for investigating the stability of the optimal schedules with respect to perturbations of processing times. <br class="zbmathjax-paragraph">Each chapter is accompanied by a bibliographic survey.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A4833">Yakov M. Shafranski沫 (Minsk)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A41713">Cited in <strong>2</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A41713">Cited in <strong>28</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%3A68Q25" title="MSC2020">68Q25</a> </td> <td class="space"> Analysis of algorithms and problem complexity </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B22" title="MSC2020">90B22</a> </td> <td class="space"> Queues and service in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90-01" title="MSC2020">90-01</a> </td> <td class="space"> Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C57" title="MSC2020">90C57</a> </td> <td class="space"> Polyhedral combinatorics, branch-and-bound, branch-and-cut </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acomputational+complexity">computational complexity</a>; <a href="/?q=ut%3Amultistage+systems">multistage systems</a>; <a href="/?q=ut%3Aflow+shop">flow shop</a>; <a href="/?q=ut%3Ajob+shop">job shop</a>; <a href="/?q=ut%3Aopen+shop">open shop</a>; <a href="/?q=ut%3AMixed+graph+approach">Mixed graph approach</a>; <a href="/?q=ut%3Atime+complexity+measures">time complexity measures</a>; <a href="/?q=ut%3Aapproximate+algorithms">approximate algorithms</a>; <a href="/?q=ut%3ANP-hard+problems">NP-hard problems</a>; <a href="/?q=ut%3Apolynomial-time+algorithms">polynomial-time algorithms</a>; <a href="/?q=ut%3Amakespan">makespan</a>; <a href="/?q=ut%3Apreemptive+and+nonpreemptive+schedules">preemptive and nonpreemptive schedules</a>; <a href="/?q=ut%3Abranch-and-bound">branch-and-bound</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0553.90030">Zbl 0553.90030</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 0673.90023" data-ciurl="/ci/00041713" data-biburl="/bibtex/00041713.bib" data-amsurl="/amsrefs/00041713.bib" data-xmlurl="/xml/00041713.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00041713.pdf" title="Zbl 0673.90023 as PDF">Review PDF</a> </div> <div class="fulltexts"> </div> <div class="sfx" style="float: right;"> </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 = ""; 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