{"id":6137,"date":"2026-05-10T06:18:10","date_gmt":"2026-05-09T22:18:10","guid":{"rendered":"\/jase\/?post_type=tkuisotope&#038;p=6137"},"modified":"2026-07-02T02:07:28","modified_gmt":"2026-07-01T18:07:28","slug":"vrp-model-with-time-window-multiproduct-and-multidepot","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=vrp-model-with-time-window-multiproduct-and-multidepot","title":{"rendered":"VRP Model with time window, multiproduct and multidepot"},"content":{"rendered":"\n<div class=\"wp-block-tkuwpbs5-bs5-row row article-info\">\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-3 align-self-start\">\n<p><i class=\"fa fa-folder\" aria-hidden=\"true\"><\/i>&nbsp;<a href=\"\/jase\/?page_id=6099\" data-type=\"page\" data-id=\"807\">2020<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-3 align-self-start\">\n<p><i class=\"fa fa-folder-open\" aria-hidden=\"true\"><\/i>&nbsp;<a href=\"\/jase\/?page_id=6128\" data-type=\"page\" data-id=\"4630\">Volume 23, Issue 2<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-6 align-self-start\">\n<div class=\"wp-block-tkuwpbs5-bs5-div dv_publish\" data-aos=\"normal\"><div class=\"wp-block-post-date\"><time datetime=\"2026-05-10T06:18:10+08:00\">2026-05-10<\/time><\/div><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-row row\">\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-5 align-self-start\">\n<div class=\"wp-block-tkuwpbs5-bs5-div au-ol\" data-aos=\"normal\">\n<p>Jos\u00e9 Ruiz-Meza<sup>1,2<\/sup><a href=\"mailto:jose.ruizm@cecar.edu.co\"><i class=\"fa fa-envelope\"><\/i><\/a>, Isaid Montes<sup>1<\/sup>, Arnoldo P\u00e9rez<sup>1<\/sup>, and Mar\u00eda Ramos-M\u00e1rquez<sup>3<\/sup><\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>1<\/sup>Industrial Engineering Program, Corporaci\u00f3n Universitaria del Caribe, Sincelejo, Colombia <\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>2<\/sup>Faculty of Engineering, Universidad de La Sabana, Ch\u00eda, Colombia <\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>3<\/sup>Faculty of Engineering, Universidad Tecnol\u00f3gica de Bol\u00edvar, Cartagena, Colombia<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-div\" style=\"margin-top:var(--wp--preset--spacing--40)\" data-aos=\"normal\">\n<p>Received:\u00a0July 30, 2019<br>Accepted:\u00a0February 15, 2020<br>Publication Date:\u00a0May 10, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-7 align-self-start clk=\u5716\u7247\"><img decoding=\"async\" src=\"\/jase\/wp-content\/uploads\/2026\/05\/23_2_8.jpg\" class=\"img-fluid img-fluid mx-auto d-block\" alt=\"\u4e0a\u50b3\u5716\u7247\">\n\n\n<p class=\"has-text-align-center img_caption\">Graphic representation of multiproduct and multidepot VRP<\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><i class=\"fab fa-creative-commons\"><\/i>&nbsp;<strong>Copyright&nbsp;<\/strong>The Author(s). This is an open access article distributed under the terms of the&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\">Creative Commons Attribution&nbsp;License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n<p>Download Citation:&nbsp; <a href=\"\/jase\/wp-content\/uploads\/2026\/05\/V232.0008.bib\" data-type=\"attachment\" data-id=\"6280\" target=\"_blank\" rel=\"noreferrer noopener\">BibTeX <\/a>| <a href=\"http:\/\/dx.doi.org\/10.6180\/jase.202006_23(2).0008\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/dx.doi.org\/10.6180\/jase.202006_23(2).0008<\/a>&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"btn btn-primary article-btn\"><a href=\"\/jase\/wp-content\/uploads\/2026\/05\/08-2019-0222_V23i2.pdf\" data-type=\"attachment\" data-id=\"6295\" target=\"_blank\" rel=\"noreferrer noopener\">Download PDF<\/a><\/p>\n\n\n\n<div style=\"height:24px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>With the increase in the transfer of products in supply chains, the organization of routes requires a complex allocation insofar as different environmental variables are considered, and VRP models are an efficient tool for the solution of routing systems of low, medium and high complexity. In this paper, we developed a vehicle routing model with hard time window, multidepot, multiproduct and heterogeneous fleet for the minimization of the distance travelled. We applied the model to a case study of a company that distributes water bottles and bales in which we made a new distribution of delivery schedules by order applied Pareto analysis. We obtained optimal computational results using exact methods in a very short computational time and minimizing the distance to 35.08 % of the current route.<\/p>\n\n\n\n<p><em>Keywords:\u00a0Pareto analysis; mathematical model; vehicle routing; optimization<\/em><\/p>\n\n\n\n<div style=\"height:2rem\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-div ref_ol\" data-aos=\"normal\">\n<ol>\n<li>[1] Richard R. Young and Paul Esqueda. Vulnerabilidades de la cadena de suministros: consideraciones para el caso de Am\u00e9rica Latina. Academia : Revista Latinoamericana <span class=\"citation-2127 citation-2128 citation-2129 citation-end-2129\">de Administraci\u00f3n, (34):63\u201378, 2005.<\/span><\/li>\n<li><span class=\"citation-2124 citation-2125 citation-2126 citation-end-2126\">[2] Ricardo P\u00e9rez-Rodr\u00edguez and Arturo Hern\u00e1ndez-Aguirre. A hybrid estimation of distribution algorithm for the vehicle routing problem with time windows. Computers and Industrial Engineer<\/span><span class=\"citation-2124 citation-2125 citation-end-2125\">ing, 130:75\u201396, apr 2019.<\/span><\/li>\n<li><span class=\"citation-2122 citation-2123 citation-end-2123\">[3] On<\/span><span class=\"citation-2122 citation-end-2122\">der Belgin, Ismail Karaoglan, and Fulya Altiparmak. Two-echelon vehicle routing problem with simulta<\/span>neous pickup and delivery: Mathematical model and heuristic approach. Computers and Industrial Engineering, 115:1\u201316, 2018.<\/li>\n<li>[4] Pandhapon Sombuntham and Voratas Kachitvichyanukul. Multi-depot vehicle routing problem with pickup and delivery requests. In AIP Conference Proceedings, volume 1285, pages 71\u201385, 2010.<\/li>\n<li>[5] Efrain Ruiz, Valeria Soto-Mendoza, Alvaro Ernesto Ruiz Barbosa, and Ricardo Reyes. Solving the open vehicle routing problem with capacity <span class=\"citation-2121 citation-end-2121\">and distance constraints with a biased random key genetic algorithm. Computers and Industrial Engineering, 133:207\u2013219, 2019.<\/span><\/li>\n<li><span class=\"citation-2120 citation-end-2120\">[6] Martin Gr\u00f6tschel and Olaf Holland. Solution of large-scale symmetric travelling salesman problems. Mat<\/span>hematical Programming, 51(1-3):141\u2013202, jul 1991.<\/li>\n<li>[7] B. L. Golden, T. L. Magnanti, and H. Q. Nguyen. Implementing vehicle routing algorithms. Networks, 7(2):113148, 1977.<\/li>\n<li>[8] G. Clarke and <span class=\"citation-2119 citation-end-2119\">J. W. Wright. Scheduling of Vehicles from a Central Depot to a Number of Delivery Points. Operations Research, 12(4):568\u2013581, aug 1964.<\/span><\/li>\n<li><span class=\"citation-2118\">[9] Ang\u00e9lica Sarmiento Lepesqueur. Estudio del problema de ruteo <\/span><span class=\"citation-2116 citation-2117 citation-2118 citation-end-2118\">de veh\u00edculos con balance de carga : Aplicaci\u00f3n de la meta-heur\u00edstica B\u00fasq<\/span><span class=\"citation-2116 citation-2117 citation-end-2117\">ueda Tab\u00fa. Universidad de La Sabana, 2014.<\/span><\/li>\n<li><span class=\"citation-2114 citation-2115\">[10] Jairo <\/span><span class=\"citation-2112 citation-2113 citation-2114 citation-2115 citation-end-2115\">R. Montoya-Torres, Juli\u00e1n L\u00f3pez Franco, Santiago Nieto Isaza, Heriberto Felizzola Jim\u00e9nez, and Nil<\/span><span class=\"citation-2112 citation-2113 citation-2114 citation-end-2114\">son Herazo-P<\/span><span class=\"citation-2112 citation-2113 citation-end-2113\">adilla. A literature review on the vehicle routing problem with multiple depots, 2015.<\/span><\/li>\n<li><span class=\"citation-2110 citation-2111 citation-end-2111\">[11] Alfredo Olivera. Heur\u00edsticas para problemas de ruteo de veh\u00edculos. Instit<\/span><span class=\"citation-2110 citation-end-2110\">uto de Computacion- Facultad de Ingenieria., page 63, 200<\/span>4.<\/li>\n<li>[12] Linda Bibiana Rocha Medina, Elsa Cristina Gonz\u00e1lez LaRota, and Javier Arturo Orjuela Castro. Una revisi\u00f3n al estado del arte del proble- ma de ruteo de veh\u00edculos : Evoluci\u00f3n hist\u00f3- rica y m<span class=\"citation-2109 citation-end-2109\">\u00e9todos de soluci\u00f3n State of the art review of the vehicle routing problem : A historic account with solving methods Resumen. Ingenier\u00eda. Universidad Francisco Jos\u00e9 de Caldas, 16(2):35\u201355, 2011.<\/span><\/li>\n<li><span class=\"citation-2108 citation-end-2108\">[13] Roberto Baldacci, Paolo Toth, and Daniele Vigo. Recent advances in vehicle routing exact algorith<\/span>ms. 4OR, <span class=\"citation-2106 citation-2107 citation-end-2107\">5(4):269\u2013298, nov 2007.<\/span><\/li>\n<li><span class=\"citation-2104 citation-2105 citation-end-2105\">[14] Marius M. Solomon and Jacques Derosiers. Time window constrained routing and scheduling problems. Transportation Science, 22(1):1\u201313, 1988.<\/span><\/li>\n<li><span class=\"citation-2102 citation-2103 citation-end-2103\">[15] Jacques Renaud, Gilbert Laporte, and Fayez F. Boctor. A tabu search heuris<\/span><span class=\"citation-2102 citation-end-2102\">tic for the multi-depot vehicle routing problem.<\/span> Computers and Operations Research, 23(3):229\u2013235, 1996.<\/li>\n<li>[16] G. Laporte, Y. Nobert, and D. Arpin. An exact algorithm for solving a capacitated location-routing problem. <span class=\"citation-2100 citation-2101 citation-end-2101\">Annals of Operations Research, 6(9):291\u2013310, sep 1986.<\/span><\/li>\n<li><span class=\"citation-2098 citation-2099 citation-end-2099\">[17] Gilbert Laporte, Fran\u00e7ois V. Louveaux, and H\u00e9l\u00e8ne Mercure. A Priori Optimization of the Probabilistic Traveling Salesman Problem. Operations Research, 42(3):543\u2013549, <\/span><span class=\"citation-2098 citation-end-2098\">1994.<\/span><\/li>\n<li><span class=\"citation-2097 citation-end-2097\">[18] N. Wilson H., J. Sussm<\/span>an M., H. K. Wong, and T. Higonnet. Scheduling algorithms for a dial-a-ride system. Technical report, Massachusetts Institute of Technology, Urban <span class=\"citation-2096 citation-end-2096\">Systems Laboratory, 1971.<\/span><\/li>\n<li><span class=\"citation-2095\">[19] Imdat Kara, Bahar Y. Kara, and M. Kadri Yetis. Energy minimizing vehicle routing problem. In Lecture Notes in Computer <\/span><span class=\"citation-2094 citation-2095 citation-end-2095\">Science (including subseries Lecture Notes in Artificial Intelligence and Le<\/span><span class=\"citation-2094 citation-end-2094\">cture Notes in Bioinformatics), volume 4616 LNCS, pages 62\u201371, 2007.<\/span><\/li>\n<li><span class=\"citation-2093 citation-end-2093\">[20] Tolga Bekta\u015f and Gilbert Laporte. The PollutionRouting Problem. Transportation Research Part B: Method<\/span>ological, 45(8):1232\u20131250, 2011.<\/li>\n<li>[21] Gilbert Laporte. The vehicle routing <span class=\"citation-2091 citation-2092 citation-end-2092\">problem: An overview of exact and approximate algorithms. European Journal of Operational Research, 59(3):345\u2013358, jun 1992.<\/span><\/li>\n<li><span class=\"citation-2089 citation-2090 citation-end-2090\">[22] Jean Fran\u00e7ois Cordeau, Gilbert Laporte, Martin W. P. Savelsbergh, and Daniele Vigo. Vehicle Routing<\/span><span class=\"citation-2089 citation-end-2089\">, 2007.<\/span><\/li>\n<li><span class=\"citation-2088 citation-end-2088\">[23] <\/span>\u00c7. <span class=\"citation-2086 citation-2087 citation-end-2087\">Ko\u00e7, Tolga Bekta\u015f, Ola Jabali, and Gilbert Laporte. Thirty years of heterogeneous vehicle routing, feb 2016.<\/span><\/li>\n<li><span class=\"citation-2084 citation-2085\">[24] Santiago Nieto Isaza. Desarrollo y Codificaci\u00f3<\/span><span class=\"citation-2083 citation-2084 citation-2085 citation-end-2085\">n de un Modelo Matem\u00e1tico para la Optimizaci\u00f3n de un Prob<\/span><span class=\"citation-2083 citation-2084 citation-end-2084\">lema de Ruteo de Veh\u00edculo<\/span><span class=\"citation-2083 citation-end-2083\">s con M\u00faltiples Dep\u00f3sitos. 2012.<\/span><\/li>\n<li><span class=\"citation-2082 citation-end-2082\">[25] Sumaiya Iqbal, M. Kaykobad, and M. Sohel Rahman. Solving the multi-objective Vehicle Routing Problem with Soft Time Windows with the help of bees. Swarm and <\/span>Evolutionary Computation, 24:50\u201364, oct 2015.<\/li>\n<li>[26] Suresh Nanda Kumar and Ramasamy Panneerselvam. A Survey <span class=\"citation-2081 citation-end-2081\">on the Vehicle Routing Problem and Its Variants. Intelligent Information Management, 04(03):66\u201374, 2012.<\/span><\/li>\n<li><span class=\"citation-2080 citation-end-2080\">[27] Mariana Puente Riofrio and Francisco Andrade Dominguez. Relaci\u00f3n entre la diversificaci\u00f3n de productos y la rentabilidad empresarial \/ Relationship between <\/span>product diversification and corporate profitability. Ciencia Unemi, 9(18):73, 2016.<\/li>\n<li>[28] P. Parthanadee. A Multi-Product. Multi-Depot Periodic <span class=\"citation-2077 citation-2078 citation-2079 citation-end-2079\">Distribution Problem. Technical report, 2002.<\/span><\/li>\n<li><span class=\"citation-2074 citation-2075 citation-2076 citation-end-2076\">[29] S. Reza Sajjadi, S. Hossein Cheraghi, Morteza Assadi, and Krishna Krishnan. Meta-heuristic approach for multi-product multi-depot vehicle routing problem. In IIE Annual Conference and Expo 2010 Proceedi<\/span><span class=\"citation-2074 citation-2075 citation-end-2075\">ngs, 2010.<\/span><\/li>\n<li><span class=\"citation-2072 citation-2073 citation-end-2073\">[30] Can B. Kalayci and Can Kaya. An ant colony system empowered variable neighborhood search<\/span><span class=\"citation-2072 citation-end-2072\"> algorithm for the vehicle routing problem with simu<\/span>ltaneous pickup and delivery. Expert Systems with Applications, 66:163\u2013175, dec 2016.<\/li>\n<li>[31] Armin L\u00fc<span class=\"citation-2070 citation-2071 citation-end-2071\">er, Magdalena Benavente, Jaime Bustos, and B\u00e1rbara Venegas. In CEUR Workshop Proceedings.<\/span><\/li>\n<li><span class=\"citation-2068 citation-2069\">[32] Christian Blum. Hybrid metaheuristics in combinatorial optimization: A tutorial. In Lecture Notes in Computer <\/span><span class=\"citation-2064 citation-2065 citation-2066 citation-2067 citation-2068 citation-2069 citation-end-2069\">Science (including subseries Lecture<\/span><span class=\"citation-2064 citation-2065 citation-2066 citation-2067 citation-2068 citation-end-2068\"> Notes in Artificial Intelligence and Lecture N<\/span><span class=\"citation-2064 citation-2065 citation-2066 citation-2067 citation-end-2067\">otes in Bioinformatics), volume 7505 LNCS, pages 1\u201310, 2012.<\/span><\/li>\n<li><span class=\"citation-2060 citation-2061 citation-2062 citation-2063 citation-end-2063\">[33] Ilhem Boussa\u00efd, Julien Lepagnot, and Patrick Siarry. A survey on optimization metaheuristics. In Information Sciences, volume 237<\/span><span class=\"citation-2060 citation-2061 citation-2062 citation-end-2062\">, pages 82\u2013117, jul 2013.<\/span><\/li>\n<li><span class=\"citation-2057 citation-2058 citation-2059 citation-end-2059\">[34] L<\/span><span class=\"citation-2057 citation-2058 citation-end-2058\">. Jourdan, M. Basseur, and E. G. Talbi. Hybridizing exact methods and metaheurist<\/span><span class=\"citation-2057 citation-end-2057\">ics: A taxonomy. European Journal of Operati<\/span>onal Research, 199(3):620\u2013629, dec 2009.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"author":3,"template":"wp-custom-template-detail-4-aricles","meta":{"_uag_custom_page_level_css":""},"categories":[1200,6,1202],"tags":[1228],"acf":[],"uagb_featured_image_src":[],"uagb_author_info":{"display_name":"\u6797\u923a\u6db5","author_link":"\/jase\/?author=3"},"uagb_comment_info":0,"uagb_excerpt":"&nbsp;Copyright&nbsp;The Author(s). This is an open access article distributed under the terms of the&nbsp;Creative Commons Attribution&nbsp;License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited. Download Citation:&nbsp; BibTeX | http:\/\/dx.doi.org\/10.6180\/jase.202006_23(2).0008&nbsp;&nbsp; Download PDF With the increase in the transfer of products in supply chains,&hellip;","_links":{"self":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope\/6137"}],"collection":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope"}],"about":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/types\/tkuisotope"}],"author":[{"embeddable":true,"href":"\/jase\/index.php?rest_route=\/wp\/v2\/users\/3"}],"wp:attachment":[{"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6137"},{"taxonomy":"post_tag","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}