Document Zbl 1458.90238

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Oper. Res.</a> <a href="/?q=in%3A444834" title="Articles in this Issue">116, Article ID 104865, 15 p. (2020)</a>. </div> <div class="abstract">Summary: We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and develop a branch-and-cut algorithm in order to solve the resulting mixed-integer linear program to optimality. This algorithm relies on a new set of tree inequalities obtained by combining valid inequalities previously known for each individual scenario of the scenario tree. These inequalities are used within a cutting-plane generation procedure based on a heuristic resolution of the corresponding separation problem. Computational experiments carried out on randomly generated instances show that the proposed branch-and-cut algorithm performs well as compared to the use of a stand-alone mathematical solver. Finally, rolling horizon simulations are carried out to assess the practical performance of the multi-stage stochastic planning model with respect to a deterministic model and a two-stage stochastic planning model.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7157822">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B30" title="MSC2020">90B30</a> </td> <td class="space"> Production models </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%3A90C15" title="MSC2020">90C15</a> </td> <td class="space"> Stochastic 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%3Astochastic+lot-sizing">stochastic lot-sizing</a>; <a href="/?q=ut%3Aremanufacturing+system">remanufacturing system</a>; <a href="/?q=ut%3Alost+sales">lost sales</a>; <a href="/?q=ut%3Amulti-stage+stochastic+integer+programming">multi-stage stochastic integer programming</a>; <a href="/?q=ut%3Ascenario+tree">scenario tree</a>; <a href="/?q=ut%3Avalid+inequalities">valid inequalities</a>; <a href="/?q=ut%3Abranch-and-cut+algorithm">branch-and-cut algorithm</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 1458.90238" data-ciurl="/ci/07157822" data-biburl="/bibtex/07157822.bib" data-amsurl="/amsrefs/07157822.bib" data-xmlurl="/xml/07157822.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07157822.pdf" title="Zbl 1458.90238 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.cor.2019.104865" aria-label="DOI for “A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales”" title="10.1016/j.cor.2019.104865">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://hal.science/hal-02470310" title="Open Access at HAL">HAL </a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ahn, H.-D.; Lee, D.-H.; Kim, H.-J., Solution algorithms for dynamic lot-sizing in remanufacturing systems, Int. 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Manuf., 15, 3, 221-230 (1999)</td> </tr><tr> <td>[10]</td> <td class="space">Hilger, T.; Sahling, F.; Tempelmeier, H., Capacitated dynamic production and remanufacturing planning under demand and return uncertainty, OR spectrum, 38, 4, 849-876 (2016) · <a href="/1352.90004" class="nowrap">Zbl 1352.90004</a></td> </tr><tr> <td>[11]</td> <td class="space">Ilgin, M. A.; Gupta, S. M., Environmentally conscious manufacturing and product recovery (ECMPRO): a review of the state of the art, J. Environ. Manage., 91, 3, 563-591 (2010)</td> </tr><tr> <td>[12]</td> <td class="space">Jayaraman, V., Production planning for closed-loop supply chains with product recovery and reuse: an analytical approach, Int. J. Prod. 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L.; Moreno, A., Hybrid manufacturing and remanufacturing lot-sizing problem with stochastic demand, return, and setup costs, Int. J. Adv. Manuf. Technol., 82, 5-8, 1241-1257 (2016)</td> </tr><tr> <td>[21]</td> <td class="space">Naeem, M. A.; Dias, D. J.; Tibrewal, R.; Chang, P.-C.; Tiwari, M. K., Production planning optimization for manufacturing and remanufacturing system in stochastic environment, J. Intell. Manuf., 1-12 (2013)</td> </tr><tr> <td>[22]</td> <td class="space">Pochet, Y.; Wolsey, L. A., Production Planning by Mixed Integer Programming (2006), Springer Science & Business Media · <a href="/1102.90039" class="nowrap">Zbl 1102.90039</a></td> </tr><tr> <td>[23]</td> <td class="space">Wang, H.-F.; Huang, Y.-S., A two-stage robust programming approach to demand-driven disassembly planning for a closed-loop supply chain system, Int. J. Prod. Res., 51, 8, 2414-2432 (2013)</td> </tr><tr> <td>[24]</td> <td class="space">Zhang, M.; Küçükyavuz, S.; Goel, S., A branch-and-cut method for dynamic decision making under joint chance constraints, Manage. Sci., 60, 5, 1317-1333 (2014)</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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