A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem

<!DOCTYPE html>    <html>  <head> <meta charset="utf-8" /> <title>A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem</title>  <link rel="shortcut icon" type="image/ico" href="./data/ijsom/coversheet/favicon.ico" />  <meta name="viewport" content="width=device-width, maximum-scale=1, initial-scale=1, user-scalable=0" />   <meta name="keywords" content="Periodic routing problem,Multi-Depot,Hybrid algorithm,auction algorithm,Genetic Algorithm,Simulated annealing algorithm" /> <meta name="description" content="In this paper, an integer linear programming formulation is developed for a novel fuzzy multi-period multi-depot vehicle routing problem. The novelty belongs to both the model and the solution methodology. In the proposed model, vehicles are not forced to return to their starting depots. The fuzzy problem is transformed into a mixed-integer programming problem by applying credibility measure whose optimal solution is an (伪,尾)-credibility optimal solution to the fuzzy problem. To solve the problem, a hybrid genetic-simulated annealing-auction algorithm (HGSA), empowered by a modern simulated annealing cooling schedule function, is developed. Finally, the efficiency of the algorithm is illustrated by employing a variety of test problems and benchmark examples. The obtained results showed that the algorithm provides satisfactory results in terms of different performance criteria." /> <meta name="title" content="A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem" /> <meta name="googlebot" content="NOODP" /> <meta name="citation_title" content="A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem" /> <meta name="citation_author" content="Saffarian, Mohsen" /> <meta name="citation_author_institution" content="Birjand University of Technology, Birjand, Iran" /> <meta name="citation_author" content="Niksirat, Malihe" /> <meta name="citation_author_institution" content="Birjand University of Technology, Birjand, Iran" /> <meta name="citation_author" content="Kazemi, Seyed Mahmood" /> <meta name="citation_author_institution" content="Birjand University of Technology, Birjand, Iran" /> <meta name="citation_abstract" content="In this paper, an integer linear programming formulation is developed for a novel fuzzy multi-period multi-depot vehicle routing problem. The novelty belongs to both the model and the solution methodology. In the proposed model, vehicles are not forced to return to their starting depots. The fuzzy problem is transformed into a mixed-integer programming problem by applying credibility measure whose optimal solution is an (伪,尾)-credibility optimal solution to the fuzzy problem. To solve the problem, a hybrid genetic-simulated annealing-auction algorithm (HGSA), empowered by a modern simulated annealing cooling schedule function, is developed. Finally, the efficiency of the algorithm is illustrated by employing a variety of test problems and benchmark examples. The obtained results showed that the algorithm provides satisfactory results in terms of different performance criteria." /> <meta name="citation_id" content="2837" /> <meta name="citation_publication_date" content="2021/05/01" /> <meta name="citation_date" content="2021-05-01" /> <meta name="citation_journal_title" content="International Journal of Supply and Operations Management" /> <meta name="citation_issn" content="23831359" /> <meta name="citation_volume" content="8" /> <meta name="citation_issue" content="2" /> <meta name="citation_firstpage" content="96" /> <meta name="citation_lastpage" content="113" /> <meta name="citation_publisher" content="Kharazmi University" /> <meta name="citation_doi" content="10.22034/ijsom.2021.2.1" /> <meta name="DC.Identifier" content="10.22034/ijsom.2021.2.1" /> <meta name="citation_abstract_html_url" content="http://www.ijsom.com/article_2837.html" /> <meta name="citation_pdf_url" content="http://www.ijsom.com/article_2837_e10519a62bba9f9383271502e6154e0c.pdf" /> <meta name="DC.Title" content="A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem" /> <meta name="DC.Source" content="International Journal of Supply and Operations Management" /> <meta name="DC.Date" content="01/05/2021" /> <meta name="DC.Date.issued" content="2021-05-01" /> <meta name="DC.Format" content="application/pdf" /> <meta name="DC.Contributor" content="Saffarian, Mohsen" /> <meta name="DC.Contributor" content="Niksirat, Malihe" /> <meta name="DC.Contributor" content="Kazemi, Seyed Mahmood" /> <meta name="og:title" content="A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem" /> <meta name="og:description" content="In this paper, an integer linear programming formulation is developed for a novel fuzzy multi-period multi-depot vehicle routing problem. The novelty belongs to both the model and the solution methodology. In the proposed model, vehicles are not forced to return to their starting depots. The fuzzy problem is transformed into a mixed-integer programming problem by applying credibility measure whose optimal solution is an (伪,尾)-credibility optimal solution to the fuzzy problem. To solve the problem, a hybrid genetic-simulated annealing-auction algorithm (HGSA), empowered by a modern simulated annealing cooling schedule function, is developed. Finally, the efficiency of the algorithm is illustrated by employing a variety of test problems and benchmark examples. The obtained results showed that the algorithm provides satisfactory results in terms of different performance criteria." /> <meta name="og:url" content="http://www.ijsom.com/article_2837.html" />  <link href="./themes/base/front/assets/css/social-icon-font.css" rel="stylesheet" type="text/css" />  <link href="./themes/base/front/assets/plugins/bootstrap/css/bootstrap.min.css?v=0.02" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/header.css?v=0.05" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/footer.css" rel="stylesheet" type="text/css" /> <link href="./inc/css/essentials.css?v=0.2" rel="stylesheet" type="text/css" /> <link href="./inc/css/cookieconsent.min.css" rel="stylesheet" type="text/css" /> <link href="./inc/css/print.css" rel="stylesheet" type="text/css" media="print"/>  <link href="./themes/base/front/assets/plugins/bootstrap/css/bootstrap-ltr.min.css" rel="stylesheet" type="text/css" /> <link href=" ./themes/base/front/assets/css/gfonts-OpenSans.css" rel="stylesheet" type="text/css" /> <link href="./themes/old/front/assets/css/accordian.css" rel="stylesheet" type="text/css" /> <link href="./themes/base/front/assets/css/academicons.min.css" rel="stylesheet" type="text/css" />  <meta name="google-site-verification" content="UlbWpwabckk_wTgRmzoJCVPEYKnomtCLcftujpXdou4" /> <link href="./data/ijsom/coversheet/stl_front.css?v=0.59" rel="stylesheet" type="text/css" /> <link href="./data/ijsom/coversheet/stl.css" rel="stylesheet" type="text/css" />  <link rel="alternate" type="application/rss+xml" title="RSS feed" href="ju.rss" /> <script type="text/javascript" src="./themes/base/front/assets/plugins/jquery/jquery.min.js?v=0.5"></script> <script type="text/javascript" src="./inc/js/common.js?v=0.1"></script> <script type="text/javascript" src="./inc/js/jquery/cookieconsent.min.js"></script>   <script src="inc/js/article.js?v=0.31" type="text/javascript" ></script> </head> <body class="ltr len"> <div class="container" id="header"> <div class="row"> <div class="col-xs-12 text-center"> <img src="./data/ijsom/coversheet/head_en.jpg" class="img-responsive text-center" style="display:-webkit-inline-box; width: 100%;" > </div> </div> </div> <div class="container"> <div class="row"> <div class="col-xs-12 col-lg-12 col-md-12 text-center"> <nav class="navbar navbar-default noborder nomargin noradius" role="navigation"> <div class="container-fluid nopadding" > <div class="navbar-header" style="background: #FFFFFF;"> <button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#bs-example-navbar-collapse-1"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button>  </div>  <div class="collapse navbar-collapse nopadding" id="bs-example-navbar-collapse-1"> <ul class="nav navbar-nav"> <li><a href="././"> Home</a></li> <li class="dropdown"> <a href="" class="dropdown-toggle" data-toggle="dropdown">Browse <b class="caret"></b></a> <ul class="dropdown-menu"> <li><a href="./?_action=current">Current Issue</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./browse?_action=issue">By Issue</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./browse?_action=author">By Author</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./browse?_action=subject">By Subject</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./author.index">Author Index</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./keyword.index">Keyword Index</a></li> </ul> </li> <li class="dropdown"> <a href="" class="dropdown-toggle" data-toggle="dropdown">Journal Info <b class="caret"></b></a> <ul class="dropdown-menu"> <li><a href="./journal/about">About Journal</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/aim_scope">Aims and Scope</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/editorial.board">Editorial Board</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/process?ethics">Publication Ethics</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/indexing">Indexing and Abstracting</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/links">Related Links</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/faq">FAQ</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/process">Peer Review Process</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./journal/metrics">Journal Metrics</a></li> <li class="divider margin-bottom-6 margin-top-6"></li> <li><a href="./news">News</a></li> </ul> </li> <li><a href="./journal/authors.note"> Guide for Authors</a></li> <li><a href="./author"> Submit Manuscript</a></li> <li><a href="./reviewer?_action=info"> Reviewers</a></li> <li><a href="./journal/contact.us"> Contact Us</a></li> </ul> <ul class="nav navbar-nav navbar-right nomargin"> <li><a href="./contacts">Login</a></li> <li><a href="./contacts?_action=signup">Register</a></li> </ul> </div>  </div>  </nav> </div> </div> </div>  <div class="container" > <div id="dv_main_cnt"> <section class="no-cover-box"> <div class="row">  <div class="col-lg-9 col-md-9 col-sm-8" id="dv_artcl">  <div> <h1 class="margin-bottom-20 size-18 ltr"><span class="article_title bold"> A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem</span></h1> <div> <div class="margin-bottom-3"> </div> <p class="margin-bottom-3">Document Type : Research Paper</p> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Authors</strong></p> <ul class="list-inline list-inline-seprator margin-bottom-6 ltr"> <li class="padding-3"> <a href="./?_action=article&au=109985&_au=Mohsen++Saffarian">Mohsen Saffarian</a> <sup><a href="mailto:saffarian@birjandut.ac.ir" data-toggle="tooltip" data-placement="bottom" title="Email to Corresponding Author"><i class="fa fa-envelope-o" ></i></a></sup> </li> <li class="padding-3"> <a href="./?_action=article&au=119756&_au=Malihe++Niksirat">Malihe Niksirat</a> </li> <li class="padding-3"> <a href="./?_action=article&au=117524&_au=Seyed+Mahmood++Kazemi">Seyed Mahmood Kazemi</a> </li> </ul> <p class="margin-bottom-3 ltr" id="aff1"> Birjand University of Technology, Birjand, Iran </p> <div class="margin-bottom-3 ltr" id="ar_doi" title="DOI"><i class="ai ai-doi size-25 text-orange"></i> <span dir="ltr"><a href="https://dx.doi.org/10.22034/ijsom.2021.2.1">10.22034/ijsom.2021.2.1</a></span></div> <p style="margin:12px -2px 0 -2px"><strong>Abstract</strong></p> <div class="padding_abstract justify ltr">In this paper, an integer linear programming formulation is developed for a novel fuzzy multi-period multi-depot vehicle routing problem. The novelty belongs to both the model and the solution methodology. In the proposed model, vehicles are not forced to return to their starting depots. The fuzzy problem is transformed into a mixed-integer programming problem by applying credibility measure whose optimal solution is an (α,β)-credibility optimal solution to the fuzzy problem. To solve the problem, a hybrid genetic-simulated annealing-auction algorithm (HGSA), empowered by a modern simulated annealing cooling schedule function, is developed. Finally, the efficiency of the algorithm is illustrated by employing a variety of test problems and benchmark examples. The obtained results showed that the algorithm provides satisfactory results in terms of different performance criteria.</div> <p class="padding-0" style="margin:12px -2px 0 -2px"><strong>Keywords</strong></p> <ul class="block list-inline list-inline-seprator margin-bottom-6 ltr"> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=106154&_kw=Periodic+routing+problem" >Periodic routing problem</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105693&_kw=multi-depot" >multi-depot</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105828&_kw=hybrid+algorithm" >hybrid algorithm</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=106155&_kw=auction+algorithm" >auction algorithm</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=102135&_kw=Genetic+algorithm" >Genetic algorithm</a> </li> <li class="padding-3"> <a class="tag_a" href="./?_action=article&kw=105807&_kw=Simulated+annealing+Algorithm" >Simulated annealing Algorithm</a> </li> </ul> </div> <hr> <div class="page_break"></div> <div class="panel"> <div class="panel-heading card-header"> <h4 class="panel-title "> <a data-toggle="collapse" data-parent="#accordions" href="#collapsesRef"><i class="fa fa-plus"></i> References</a> </h4> </div> <div id="collapsesRef" class="panel-collapse collapse"> <div class="panel-body justify"> <div class="padding-3 margin-top-3 ltr justify">Alonso F., Alvarez M.J. and Beasley J.E. (2008). A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions. Journal of the Operational Research Society, Vol. 59, pp.963-976. </div> <div class="padding-3 margin-top-3 ltr justify"><br />Angelelli E. and Speranza M.G. (2002). The periodic vehicle routing problem with intermediate facilities. European journal of Operational research, Vol. 137, pp. 233-247. </div> <div class="padding-3 margin-top-3 ltr justify"><br />Beltrami E.J. and Bodin L.D. (1974). Networks and vehicle routing for municipal waste collection. Networks, Vol.4, pp.65-94. </div> <div class="padding-3 margin-top-3 ltr justify"><br />Blakeley F., Argüello B., Cao B., Hall W. and Knolmajer J. (2003). Optimizing periodic maintenance operations for Schindler Elevator Corporation Interfaces. Interfaces, Vol. 33, pp. 67-79. </div> <div class="padding-3 margin-top-3 ltr justify"><br />Brunelli M. and Mezei J. (2013). How different are ranking methods for fuzzy numbers? A numerical study. International Journal of Approximate Reasoning, Vol. 54, pp. 627-639. </div> <div class="padding-3 margin-top-3 ltr justify">Claassen G., Hendriks T.H. (2007). An application of special ordered sets to a periodic milk collection problem. European Journal of Operational Research, Vol. 180, pp. 754-769. </div> <div class="padding-3 margin-top-3 ltr justify">Crevier B., Cordeau J.-F. and Laporte G. (2007). The multi-depot vehicle routing problem with inter-depot routes. European Journal of Operational Research, Vol. 176, pp.756-773. </div> <div class="padding-3 margin-top-3 ltr justify">Das S.K., Roy S.K. and Weber G.W. (2020). Application of type-2 fuzzy logic to a multi-objective green solid transportation-location problem with dwell time under carbon tax, cap and offset policy: Fuzzy vs. Non-fuzzy techniques. IEEE Transactions on Fuzzy Systems, 10.1109/TFUZZ.2020.3011745. </div> <div class="padding-3 margin-top-3 ltr justify">Das S.K., Roy S.K. and Weber G.W. (2020). Heuristic approaches for solid transportation-p-facility location problem. Central European Journal of Operations Research, Vol. 28, pp. 939-961. </div> <div class="padding-3 margin-top-3 ltr justify">Dondo R.G. and Cerdá J. (2009). A hybrid local improvement algorithm for large-scale multi-depot vehicle routing problems with time windows. Computers & Chemical Engineering, Vol. 33, pp.513-530. </div> <div class="padding-3 margin-top-3 ltr justify">Drummond L.M., Ochi L.S. and Vianna D.S. (2001). An asynchronous parallel metaheuristic for the period vehicle routing problem. Future Generation Computer Systems, Vol. 17, pp. 379-386. </div> <div class="padding-3 margin-top-3 ltr justify">Eydi A. and Abdorahimi H. (2012). Model and Solution Approach for Multi-Period and Multi-Depot Vehicle Routing Problem with Flexibility in Specifying the Last Depot of Each Route. International Journal of Industrial Engineering, Vol. 23, pp.333-349. </div> <div class="padding-3 margin-top-3 ltr justify">Freling R., Wagelmans A.P. and Paixão J.M.P. (2001). Models and algorithms for single-depot vehicle scheduling, Transportation Science, Vol. 35, pp. 165-180. </div> <div class="padding-3 margin-top-3 ltr justify">Geman S. and Geman D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on pattern analysis and machine intelligence, Vol. 6, pp.721-741. </div> <div class="padding-3 margin-top-3 ltr justify">Ghatee M. and Niksirat M. (2013). A Hopfield neural network applied to the fuzzy maximum cut problem under credibility measure. Information Sciences, Vol. 229, 77-93. </div> <div class="padding-3 margin-top-3 ltr justify">Giosa I., Tansini I. and Viera, I. (2002). New assignment algorithms for the multi-depot vehicle routing problem. Journal of the Operational Research Society, Vol. 53, pp. 977-984. </div> <div class="padding-3 margin-top-3 ltr justify">Hasan M.R. and Mashud A.H.M. (2019). An Economic Order Quantity model for decaying products with the frequency of advertisement, selling price and continuous time-dependent demand under partially backlogged shortage. International Journal of Supply and Operations Management (IJSOM), Vol. 6, pp. 296-314. </div> <div class="padding-3 margin-top-3 ltr justify">Hemmelmayr V.C., Doerner K.F., Hartl R.F. (2009). A variable neighborhood search heuristic for periodic routing problems. European Journal of Operational Research, Vol. 195, 791-802. </div> <div class="padding-3 margin-top-3 ltr justify">Ho W., Ho G.T., Ji P. and Lau H.C. (2008). A hybrid genetic algorithm for the multi-depot vehicle routing problem. Engineering Applications of Artificial Intelligence, Vol. 21, pp. 548-557. </div> <div class="padding-3 margin-top-3 ltr justify">Jalali S. and Boyce J.F. (1995). Determination of optimal general edge detectors by global minimization of a cost function. Image and Vision Computing, Vol. 13, pp. 683-693. </div> <div class="padding-3 margin-top-3 ltr justify">Kang K.H., Lee Y.H. and Lee B.K. (2005). An exact algorithm for multi depot and multi period vehicle scheduling problem. International Conference on Computational Science and Its Applications, Vol. 4, pp. 350-359. </div> <div class="padding-3 margin-top-3 ltr justify">Ke L. and Feng Z. (2013). A two-phase metaheuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research, Vol. 40, pp.633-638. </div> <div class="padding-3 margin-top-3 ltr justify">Kek A.G., Cheu R.L. and Meng Q. (2008). Distance-constrained capacitated vehicle routing problems with flexible assignment of start and end depots. Mathematical and Computer Modelling, Vol. 47, pp. 140-152. </div> <div class="padding-3 margin-top-3 ltr justify">Lin J.-S., Liu M. and Huang N.-F. (2000). The shortest path computation in MOSPF protocol using an annealed Hopfield neural network with a new cooling schedule. Information Sciences, Vol. 129, pp.17-30. </div> <div class="padding-3 margin-top-3 ltr justify">Maity G., Mardanya D., Roy S.K. and Weber G.W. (2019). A new approach for solving dual-hesitant fuzzy transportation problem with restrictions. S膩dhan膩, Vol. 44, pp. 1-11. </div> <div class="padding-3 margin-top-3 ltr justify">Majumder S., Kundu P., Kar S. and Pal T. (2019). Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint. Soft Computing, Vol. 23, pp. 3279-3301. </div> <div class="padding-3 margin-top-3 ltr justify">Mashud A.H.M., Hasan M.R., Wee H.M. and Daryanto Y. (2019). Non-instantaneous deteriorating inventory model under the joined effect of trade-credit, preservation technology and advertisement policy. Kybernetes, Vol. 49 (6), pp. 1645-1674. </div> <div class="padding-3 margin-top-3 ltr justify">Mashud A.H.M., Uddin M.S. and Sana S.S. (2019). A Two-Level Trade-Credit Approach to an Integrated Price-Sensitive Inventory Model with Shortages. International Journal of Applied and Computational Mathematics, Vol. 5(4), pp. 1-28. </div> <div class="padding-3 margin-top-3 ltr justify">Midya S., Roy S.K. and Vincent F.Y. (2020). Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain. International Journal of Machine Learning and Cybernetics, Vol. 49, pp. 1-19. </div> <div class="padding-3 margin-top-3 ltr justify">Mohamadi A., Yaghoubi S. and Derikvand H. (2015). A credibility-based chance-constrained transfer point location model for the relief logistics design (Case Study: earthquake disaster on region 1 of Tehran city). International Journal of Supply and Operations Management, 1(4), 466-488. </div> <div class="padding-3 margin-top-3 ltr justify">Nagy G. and Salhi S.D. (2005). Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. European journal of operational research, Vol. 162, pp. 126-141. </div> <div class="padding-3 margin-top-3 ltr justify">Ngueveu S.U., Prins C. and Calvo R.W. (2010). An effective memetic algorithm for the cumulative capacitated vehicle routing problem. Computers & Operations Research, Vol. 37, pp.1877-1885. </div> <div class="padding-3 margin-top-3 ltr justify">Niksirat M., Hashemi S.M. and Ghatee M. (2016). Branch-and-price algorithm for fuzzy integer programming problems with block angular structure. Fuzzy Sets and Systems, Vol. 296, pp.70-96. </div> <div class="padding-3 margin-top-3 ltr justify">Niksirat M. (2016). Multi-depot vehicle scheduling under fuzzy conditions, Amirkabir Univercity of Thecnology. </div> <div class="padding-3 margin-top-3 ltr justify">Rabbani M., Mokhtarzadeh M. and Farrokhi-Asl, H. (2018). A new mathematical model for designing a municipal solid waste system considering environmentally issues. International Journal of Supply and Operations Management, Vol. 5, pp . 234-255. </div> <div class="padding-3 margin-top-3 ltr justify">Ribeiro G.M. and Laporte G. (2012). An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Computers & Operations Research, Vol.39, pp.728-735. </div> <div class="padding-3 margin-top-3 ltr justify">Roy S.K. and Midya S. (2019). Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment. Applied Intelligence, 49, 3524-3538. </div> <div class="padding-3 margin-top-3 ltr justify">Saffarian M., Barzinpour F. and Eghbali M.A. (2015). A robust programming approach to bi-objective optimization model in the disaster relief logistics response phase. International Journal of Supply and Operations Management, Vol. 2, pp. 595-616. </div> <div class="padding-3 margin-top-3 ltr justify">Saffarian M., Barzinpour F. and Kazemi S.M. (2017). A Multi-period Multi-objective Location-routing Model for Relief Chain Management under Uncertainty. International Journal of Supply and Operations Management, Vol. 4(4), pp. 298-317. </div> <div class="padding-3 margin-top-3 ltr justify">Sumichras R.T. and Markham I.S. (1995). A heuristic and lower bound for a multi-depot routing problem. Computers & Operations Research, Vol. 22, pp. 1047-1056. </div> <div class="padding-3 margin-top-3 ltr justify">Thangiah S.R. and Salhi S. (2001). Genetic clustering: an adaptive heuristic for the multidepot vehicle routing problem. Applied Artificial Intelligence, Vol. 15, pp. 361-383. </div> <div class="padding-3 margin-top-3 ltr justify">Thomas A.S. and Kopczak L.R. (2005). From logistics to supply chain management: the path forward in the humanitarian sector Fritz Institute. Vol. 15, pp. 1-15. </div> <div class="padding-3 margin-top-3 ltr justify">Van Wassenhove L.N. (2006). Humanitarian aid logistics: supply chain management in high gear. Journal of the Operational Research Society, Vol. 57, pp. 475-489. </div> <div class="padding-3 margin-top-3 ltr justify">Van Wassenhove L.N. and Pedraza Martinez A.J. (2012). Using OR to adapt supply chain management best practices to humanitarian logistics. International Transactions in Operational Research, Vol. 19, pp. 307-322. </div> <div class="padding-3 margin-top-3 ltr justify">Wu T.-H., Low C. and Bai J.-W. (2002). Heuristic solutions to multi-depot location-routing problems. Computers & Operations Research, Vol. 29, pp.1393-1415.</div> </div> </div> </div> </div> </div>   <div class="col-lg-3 col-md-3 col-sm-4"> <div class="panel panel-default my_panel-default margin-bottom-10"> <div class="panel-body ar_info_pnl" id="ar_info_pnl_cover"> <div id="pnl_cover"> <div class="row" > <div class="col-xs-6 col-md-6 nomargin-bottom"> <a href="javascript:loadModal('International Journal of Supply and Operations Management', './data/ijsom/coversheet/cover_en.jpg')"> <img src="data/ijsom/coversheet/cover_en.jpg" alt="International Journal of Supply and Operations Management" style="width: 100%;"> </a> </div> <div class="col-xs-6 col-md-6 nomargin-bottom"> <h6><a href="./issue_526_528.html">Volume 8, Issue 2</a><br/>May 2021<div id="sp_ar_pages">Pages <span dir="ltr">96-113</span></div></h6> </div> </div> </div> </div> </div>  <div class="panel panel-default my_panel-default margin-bottom-10 panel-lists"> <div class="panel-heading"> <h3 class="panel-title"><a data-toggle="collapse" data-parent="#accordion" href="#ar_info_pnl_fl"><i class="fa fa-files-o"></i> Files</a></h3> </div> <div id="ar_info_pnl_fl" class="panel-collapse collapse in"> <div class="panel-body ar_info_pnl padding-6"> <ul class="list-group list-group-bordered list-group-noicon nomargin"> <li class="list-group-item"><a href="./?_action=xml&article=2837" target="_blank" class="tag_a pdf_link"><i class="fa fa-file-code-o text-orange" ></i> XML</a></li> <li class="list-group-item"><a href="./article_2837_e10519a62bba9f9383271502e6154e0c.pdf" target="_blank" class="tag_a pdf_link"><i class="fa fa-file-pdf-o text-red" ></i> PDF 1.16 MB</a></li>  </ul> </div> </div> </div> <div class="panel panel-default my_panel-default margin-bottom-10"> <div class="panel-heading"> <h3 class="panel-title"><a data-toggle="collapse" data-parent="#accordion" href="#ar_info_pnl_share"><i class="fa fa-share-square-o" aria-hidden="true"></i> Share</a></h3> </div> <div id="ar_info_pnl_share" class="panel-collapse collapse"> <div class="panel-body ar_info_pnl padding-10 text-center"> <a id="share_facebook" href="https://www.facebook.com/sharer.php?u=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-facebook" data-toggle="tooltip" data-placement="top" title="Facebook"> <i class="icon-facebook"></i> <i class="icon-facebook"></i> </a> <a id="share_linkedin" href="https://www.linkedin.com/shareArticle?mini=true&url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-linkedin" data-toggle="tooltip" data-placement="top" title="Linkedin"> <i class="icon-linkedin"></i> <i class="icon-linkedin"></i> </a> <a id="share_mendeley" href="https://www.mendeley.com/import/?url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-youtube" data-toggle="tooltip" data-placement="top" title="Mendeley"> <i class="icon-mendeley"></i> <i class="icon-mendeley"></i> </a> <a id="share_refworks" href="https://www.refworks.com/express/ExpressImport.asp?url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-disqus" data-toggle="tooltip" data-placement="top" title="Refworks"> <i class="icon-refworks"><span class="path1"></span><span class="path2"></span><span class="path3"></span><span class="path4"></span><span class="path5"></span><span class="path6"></span><span class="path7"></span><span class="path8"></span><span class="path9"></span><span class="path10"></span></i> <i class="icon-refworks"><span class="path1"></span><span class="path2"></span><span class="path3"></span><span class="path4"></span><span class="path5"></span><span class="path6"></span><span class="path7"></span><span class="path8"></span><span class="path9"></span><span class="path10"></span></i> </a> <a id="share_instagram" href="https://www.instagram.com/?url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-instagram" data-toggle="tooltip" data-placement="top" title="Instagram"> <i class="icon-instagram"></i> <i class="icon-instagram"></i> </a> <a id="share_twitter" href="https://twitter.com/share?url=http://www.ijsom.com/article_2837.html&text=A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem" target="_blank" class="social-icon social-icon-sm social-twitter" data-toggle="tooltip" data-placement="top" title="Twitter"> <i class="icon-twitter"></i> <i class="icon-twitter"></i> </a> <a id="share_email" href="javascript:act('email')" class="social-icon social-icon-sm social-email3 " data-toggle="tooltip" data-placement="top" title="Email"> <i class="icon-email3"></i> <i class="icon-email3"></i> </a> <a id="share_print" href="javascript:printDiv('dv_artcl')" class="social-icon social-icon-sm social-print" data-toggle="tooltip" data-placement="top" title="Print"> <i class="icon-print"></i> <i class="icon-print"></i> </a> <a id="share_stumble" href="https://mix.com/mixit?su=submit&url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-stumbleupon" data-toggle="tooltip" data-placement="top" title="StumbleUpon"> <i class="icon-stumbleupon"></i> <i class="icon-stumbleupon"></i> </a> <a id="share_acedemia" href="https://www.academia.edu/" target="_blank" class="social-icon social-icon-sm social-academia" data-toggle="tooltip" data-placement="top" title="Academia"> <i class="ai ai-academia"></i> <i class="ai ai-academia"></i> </a> <a id="share_sems" href="https://www.semanticscholar.org/" target="_blank" class="social-icon social-icon-sm social-forrst" data-toggle="tooltip" data-placement="top" title="Semantic scholar"> <i class="ai ai-semantic-scholar"></i> <i class="ai ai-semantic-scholar"></i> </a> <a id="share_reddit" href="https://www.reddit.com/submit?url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-dwolla" data-toggle="tooltip" data-placement="top" title="Reddit"> <i class="icon-reddit"></i> <i class="icon-reddit"></i> </a> <a id="share_rg" href="https://www.researchgate.net/" target="_blank" class="social-icon social-icon-sm social-researchgate" data-toggle="tooltip" data-placement="top" title="Research Gate"> <i class="ai ai-researchgate"></i> <i class="ai ai-researchgate"></i> </a> <a id="share_blogger" href="https://www.blogger.com/blog-this.g?u=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-blogger" data-toggle="tooltip" data-placement="top" title="Blogger"> <i class="icon-blogger"></i> <i class="icon-blogger"></i> </a> <a id="share_pinterest" href="https://pinterest.com/pin/create/bookmarklet/?media=&url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-pinterest" data-toggle="tooltip" data-placement="top" title="Pinterest"> <i class="icon-pinterest"></i> <i class="icon-pinterest"></i> </a> <a id="share_digg" href="https://www.digg.com/submit?http://www.ijsom.com/article_2837.html&title=A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem" target="_blank" class="social-icon social-icon-sm social-digg" data-toggle="tooltip" data-placement="top" title="Digg"> <i class="icon-digg"></i> <i class="icon-digg"></i> </a> <a id="share_delicious" href="https://del.icio.us/post?url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-delicious" data-toggle="tooltip" data-placement="top" title="Delicious"> <i class="icon-delicious"></i> <i class="icon-delicious"></i> </a> <a id="share_skype" href="https://web.skype.com/share?url=http://www.ijsom.com/article_2837.html" target="_blank" class="social-icon social-icon-sm social-skype" data-toggle="tooltip" data-placement="top" title="Skype"> <i class="icon-skype"></i> <i class="icon-skype"></i> </a> </div> </div> </div>  <div class="panel panel-default my_panel-default margin-bottom-10 panel-lists"> <div class="panel-heading"> <h3 class="panel-title"><a data-toggle="collapse" data-parent="#accordion" href="#ar_info_pnl_cite"><i class=" fa fa-external-link"></i> How to cite</a></h3> </div> <div id="ar_info_pnl_cite" class="panel-collapse collapse "> <div class="panel-body ar_info_pnl"> <ul class="list-group list-group-bordered list-group-noicon" style="display:block !important;max-height:9999px"> <li class="list-group-item ltr"><a class="tag_a" href="./?_action=export&rf=ris&rc=2837">RIS</a></li> <li class="list-group-item ltr"><a class="tag_a" href="./?_action=export&rf=enw&rc=2837">EndNote</a></li> <li class="list-group-item ltr"><a class="tag_a" href="./?_action=export&rf=ris&rc=2837">Mendeley</a></li> <li class="list-group-item ltr"><a class="tag_a" href="./?_action=export&rf=bibtex&rc=2837">BibTeX</a></li> <li class="list-group-item ltr"><a class="tag_a" href="javascript:void(0)" data-toggle="modal" data-target="#cite-apa">APA</a></li> <li class="list-group-item ltr"><a class="tag_a" href="javascript:void(0)" data-toggle="modal" data-target="#cite-mla">MLA</a></li> <li class="list-group-item ltr"><a class="tag_a" href="javascript:void(0)" data-toggle="modal" data-target="#cite-harvard">HARVARD</a></li> <li class="list-group-item ltr"><a class="tag_a" href="javascript:void(0)" data-toggle="modal" data-target="#cite-vancouver">VANCOUVER</a></li> </ul> </div> </div> </div>  <div class="panel panel-default my_panel-default panel-lists"> <div class="panel-heading"> <h3 class="panel-title"><a data-toggle="collapse" data-parent="#accordion" href="#ar_info_pnl_st"><i class="fa fa-bar-chart" aria-hidden="true"></i> Statistics</a></h3> </div> <div id="ar_info_pnl_st" class="panel-collapse collapse in"> <div class="panel-body ar_info_pnl"> <ul class="list-group list-group-bordered list-group-noicon" style="display:block !important;max-height:9999px"> <li class="list-group-item"><a class="tag_a">Article View: <i>895</i></a></li> <li class="list-group-item"><a class="tag_a">PDF Download: <i>684</i></a></li> </ul> </div> </div> </div> </div>  </div> </section> <div id="cite-apa" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">APA</h4> </div>  <div class="modal-body"> <p>Saffarian, M., Niksirat, M., & Kazemi, S. (2021). A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem. <em>International Journal of Supply and Operations Management</em>, 8(2), 96-113. doi: 10.22034/ijsom.2021.2.1</p> </div> </div> </div> </div> <div id="cite-mla" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">MLA</h4> </div>  <div class="modal-body"> <p>Mohsen Saffarian; Malihe Niksirat; Seyed Mahmood Kazemi. "A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem". <em>International Journal of Supply and Operations Management</em>, 8, 2, 2021, 96-113. doi: 10.22034/ijsom.2021.2.1</p> </div> </div> </div> </div> <div id="cite-harvard" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">HARVARD</h4> </div>  <div class="modal-body"> <p>Saffarian, M., Niksirat, M., Kazemi, S. (2021). 'A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem', <em>International Journal of Supply and Operations Management</em>, 8(2), pp. 96-113. doi: 10.22034/ijsom.2021.2.1</p> </div> </div> </div> </div> <div id="cite-vancouver" class="modal fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true"> <div class="modal-dialog"> <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">VANCOUVER</h4> </div>  <div class="modal-body"> <p>Saffarian, M., Niksirat, M., Kazemi, S. A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem. <em>International Journal of Supply and Operations Management</em>, 2021; 8(2): 96-113. doi: 10.22034/ijsom.2021.2.1</p> </div> </div> </div> </div> </div> </div>   <section class="alternate padding-xxs"> </section>   <div class="container"> <footer id="footer"> <div class="scrollup" id="scroll" href="#"><span></span></div> <div class="row"> <div class="col-md-2">  <h4 class="">Explore Journal</h4> <ul class="footer-links list-unstyled"> <li id="fli_home"><a href="./">Home</a></li> <li id="fli_about"><a href="./journal/about">About Journal</a></li> <li id="fli_Edb"><a href="./journal/editorial.board">Editorial Board</a></li> <li id="fli_submit"><a href="./author">Submit Manuscript</a></li> <li id="fli_contactus"><a href="./journal/contact.us">Contact Us</a></li> <li id="fli_glossary"><a href="./journal/glossary">Glossary</a></li> <li id="fli_order_hrdj"><a href="./journal/subscription.form">Hard Copy Subscription</a></li> <li id="fli_sitemap"><a href="./sitemap.xml?usr">Sitemap</a></li> </ul>  </div> <div class="col-md-3">  <h4 class="">Latest News</h4> <ul class="footer-posts list-unstyled"> <li> <a href="./news?newsCode=173">SD of ISC: Sustainable Development of Intelligent Supply Chains based on Trends and Future Directions: Application of Novel Solution Techniques</a> <small class="ltr">2023-03-05</small> </li> </ul>  </div> <div class="col-md-3">  <div><p><a title="Linkedin" href="http://www.linkedin.com/company/ijsom?trk=eml-cp_mktg-btn-welcome-20120607%2F"><img src="images/linkedin.jpg" alt="linkedin" /></a></p></div>  </div> <div class="col-md-4">  <h4 class="">Newsletter Subscription</h4> <p>Subscribe to the journal newsletter and receive the latest news and updates</p> <form class="validate" action="" method="post" data-success="Subscription saved successfully." data-toastr-position="bottom-right"> <input type="hidden" name="_token" value="85de2483a4e05f9b09acd7ab0d786ff1ba1fd522ccb645fe"/> <div class="input-group"> <span class="input-group-addon"><i class="fa fa-envelope"></i></span> <input type="email" id="email" name="email" required="required" class="form-control required sbs_email" placeholder="Enter your Email" oninvalid="this.setCustomValidity('Enter a valid email address.')" oninput="this.setCustomValidity('')"> <span class="input-group-btn"> <button class="btn btn-primary mybtn" type="submit">Subscribe</button> </span> </div> </form>   <div class="margin-top-20"> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Facebook"> <i class="fa fa-facebook-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Twitter"> <i class="fa fa-twitter-square" aria-hidden="true"></i> </a> <a class="noborder" href="" target="_blank" class="social-icon social-icon-border social-facebook pull-left block" data-toggle="tooltip" data-placement="top" title="Linkedin"> <i class="fa fa-linkedin-square" aria-hidden="true"></i> </a> <a class="noborder" href="./ju.rss" class="social-icon social-icon-border social-rss pull-left block" data-toggle="tooltip" data-placement="top" title="Rss"><i class="fa fa-rss-square" aria-hidden="true"></i></a> </div> </div> </div> <div class="copyright" style="position: relative"> <ul class="nomargin list-inline mobile-block"> <li>© Journal Management System. <span id='sp_crt'>Powered by <a target='_blank' href='https://www.sinaweb.net/'>Sinaweb</a></span></li> </ul> </div> </footer> </div>  </div>   <a href="#" id="toTop_old"></a>  <div id="preloader"> <div class="inner"> <span class="loader"></span> </div> </div>  <script type="text/javascript">var plugin_path = './themes/base/front/assets/plugins/';</script> <script type="text/javascript" src="./themes/base/front/assets/js/scripts.js?v=0.02"></script>   <script type="text/javascript"> $('ul.nav li.dropdown').hover(function() { if (window.matchMedia('(max-width: 767px)').matches) return; $(this).find('.dropdown-menu').stop(true, true).delay(200).fadeIn(500); }, function() { if (window.matchMedia('(max-width: 767px)').matches) return; $(this).find('.dropdown-menu').stop(true, true).delay(200).fadeOut(500); }); var btn = $('#toTop_old'); $(window).scroll(function() { if ($(window).scrollTop() > 300) { btn.addClass('show'); } else { btn.removeClass('show'); } }); btn.on('click', function(e) { e.preventDefault(); $('html, body').animate({scrollTop:0}, '300'); }); window.cookieconsent.initialise({ "palette": { "popup": { "background": "#222" }, "button": { "background": "#f1d600" } }, "content": { "message": "This website uses cookies to ensure you get the best experience on our website.", "dismiss": "Got it!", "link": "" } }); </script> </body> </html><div id="actn_modal" class="modal fade" tabindex="-1"> <div id="" class="modal-dialog modal-dialog madal-aw"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close pull-right" data-dismiss="modal" aria-hidden="true" href="#lost">×</button> <h5 class="modal-title"></h5> </div> <div class="modal-body"></div> <div class="modal-footer"></div> </div> </div> </div>

CINXE.COM

A Hybrid Genetic-Simulated Annealing-Auction Algorithm for a Fully Fuzzy Multi-Period Multi-Depot Vehicle Routing Problem