{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T10:32:20Z","timestamp":1780050740511,"version":"3.53.1"},"reference-count":65,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T00:00:00Z","timestamp":1600473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Advances in information and communication technologies have made possible the emergence of new shopping channels. The so-called \u2018omnichannel\u2019 retailing mode allows customers to shop for products online and receive them at home. This paper focuses on the omnichannel delivery concept for the retailing industry, which addresses the replenishment of a set of retail stores and the direct shipment of the products to customers within an integrated vehicle routing formulation. Due to its NP-Hardness, a constructive heuristic, which is extended into a biased-randomized heuristic and which is embedded into a multi-start procedure, is introduced for solving the large-sized instances of the problem. Next, the problem is enriched by considering a more realistic scenario in which travel times are modeled as random variables. For dealing with the stochastic version of the problem, a simheuristic algorithm is proposed. A series of computational experiments contribute to illustrate how our simheuristic can provide reliable and low-cost solutions under uncertain conditions.<\/jats:p>","DOI":"10.3390\/a13090237","type":"journal-article","created":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T07:06:09Z","timestamp":1600499169000},"page":"237","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A Simheuristic Algorithm for Solving the Stochastic Omnichannel Vehicle Routing Problem with Pick-up and Delivery"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6529-0270","authenticated-orcid":false,"given":"Leandro do C.","family":"Martins","sequence":"first","affiliation":[{"name":"Internet Interdisciplinary Institute (IN3)\u2013Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0031-5937","authenticated-orcid":false,"given":"Christopher","family":"Bayliss","sequence":"additional","affiliation":[{"name":"Internet Interdisciplinary Institute (IN3)\u2013Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4219-5056","authenticated-orcid":false,"given":"Pedro J.","family":"Copado-M\u00e9ndez","sequence":"additional","affiliation":[{"name":"Internet Interdisciplinary Institute (IN3)\u2013Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javier","family":"Panadero","sequence":"additional","affiliation":[{"name":"Internet Interdisciplinary Institute (IN3)\u2013Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1392-1776","authenticated-orcid":false,"given":"Angel A.","family":"Juan","sequence":"additional","affiliation":[{"name":"Internet Interdisciplinary Institute (IN3)\u2013Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ijpe.2017.11.011","article-title":"Vehicle routing problem in omni-channel retailing distribution systems","volume":"196","author":"Abdulkader","year":"2018","journal-title":"Int. J. Prod. Econ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1287\/mnsc.2014.1951","article-title":"Integration of online and offline channels in retail: The impact of sharing reliable inventory availability information","volume":"60","author":"Gallino","year":"2014","journal-title":"Manag. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/s40685-016-0034-7","article-title":"Distribution systems in omni-channel retailing","volume":"9","author":"Holzapfel","year":"2016","journal-title":"Bus. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1111\/itor.12479","article-title":"Using horizontal cooperation concepts in integrated routing and facility-location decisions","volume":"26","author":"Gruler","year":"2019","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_5","unstructured":"Crainic, T.G., and Laporte, G. (2012). Fleet Management and Logistics, Springer Science & Business Media."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.cie.2015.02.017","article-title":"Integrated scheduling of production and distribution to minimize total cost using an improved ant colony optimization method","volume":"83","author":"Cheng","year":"2015","journal-title":"Comput. Ind. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1002\/net.3230110211","article-title":"Complexity of vehicle routing and scheduling problems","volume":"11","author":"Lenstra","year":"1981","journal-title":"Networks"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1287\/trsc.29.1.17","article-title":"The general pickup and delivery problem","volume":"29","author":"Savelsbergh","year":"1995","journal-title":"Transp. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.trpro.2020.03.082","article-title":"A savings-based heuristic for solving the omnichannel vehicle routing problem with pick-up and delivery","volume":"47","author":"Martins","year":"2020","journal-title":"Transp. Res. Procedia"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1111\/itor.12322","article-title":"A biased-randomized metaheuristic for the capacitated location routing problem","volume":"24","author":"Juan","year":"2017","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Juan, A.A., Kelton, W.D., Currie, C.S., and Faulin, J. (2018, January 9\u201312). Simheuristics applications: Dealing with uncertainty in logistics, transportation, and other supply chain areas. Proceedings of the 2018 Winter Simulation Conference, Gothenburg, Sweden.","DOI":"10.1109\/WSC.2018.8632464"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1057\/jos.2016.11","article-title":"A simheuristic algorithm for solving the arc routing problem with stochastic demands","volume":"12","author":"Juan","year":"2018","journal-title":"J. Simul."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1057\/s41273-016-0002-4","article-title":"Supporting multi-depot and stochastic waste collection management in clustered urban areas via simulation\u2013optimization","volume":"11","author":"Gruler","year":"2017","journal-title":"J. Simul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5","DOI":"10.7195\/ri14.v15i2.1070","article-title":"Understanding the customer experience in the age of omni-channel shopping","volume":"15","author":"Mosquera","year":"2017","journal-title":"Icono14"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jretai.2015.02.005","article-title":"From multi-channel retailing to omni-channel retailing: Introduction to the special issue on multi-channel retailing","volume":"91","author":"Verhoef","year":"2015","journal-title":"J. Retail."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1108\/IJPDLM-08-2015-0179","article-title":"Retail logistics in the transition from multi-channel to omni-channel","volume":"46","author":"Wollenburg","year":"2016","journal-title":"Int. J. Phys. Distrib. Logist. Manag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.jretconser.2013.07.006","article-title":"Cross-channel free-riding consumer behavior in a multichannel environment: An investigation of shopping motives, sociodemographics and product categories","volume":"20","year":"2013","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.jretconser.2015.08.001","article-title":"Categorization of multiple channel retailing in Multi-, Cross-, and Omni-Channel Retailing for retailers and retailing","volume":"27","author":"Beck","year":"2015","journal-title":"J. Retail. Consum. Serv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1287\/mnsc.6.1.80","article-title":"The truck dispatching problem","volume":"6","author":"Dantzig","year":"1959","journal-title":"Manag. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/net.3230160104","article-title":"An exact algorithm for the asymmetrical capacitated vehicle routing problem","volume":"16","author":"Laporte","year":"1986","journal-title":"Networks"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s10107-005-0644-x","article-title":"Robust branch-and-cut-and-price for the capacitated vehicle routing problem","volume":"106","author":"Fukasawa","year":"2006","journal-title":"Math. Program."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0305-0548(98)00047-1","article-title":"A tabu search algorithm for the vehicle routing problem","volume":"26","author":"Barbarosoglu","year":"1999","journal-title":"Comput. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2110","DOI":"10.1016\/j.apm.2011.08.010","article-title":"Optimised crossover genetic algorithm for capacitated vehicle routing problem","volume":"36","author":"Nazif","year":"2012","journal-title":"Appl. Math. Model."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"14","DOI":"10.5772\/9698","article-title":"A algorithm for the Vehicle Problem","volume":"7","author":"Ezzatneshan","year":"2010","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1016\/j.eswa.2007.11.060","article-title":"Applying hybrid meta-heuristics for capacitated vehicle routing problem","volume":"36","author":"Lin","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1287\/trsc.1030.0040","article-title":"An exact algorithm for the multiple vehicle pickup and delivery problem","volume":"38","author":"Lu","year":"2004","journal-title":"Transp. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1287\/trsc.1090.0272","article-title":"Branch and cut and price for the pickup and delivery problem with time windows","volume":"43","author":"Ropke","year":"2009","journal-title":"Transp. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/S0191-2615(99)00016-8","article-title":"Solving the pickup and delivery problem with time windows using reactive tabu search","volume":"34","author":"Nanry","year":"2000","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s00291-004-0173-7","article-title":"A grouping genetic algorithm for the pickup and delivery problem with time windows","volume":"27","author":"Pankratz","year":"2005","journal-title":"OR Spectr."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1287\/trsc.1050.0135","article-title":"An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows","volume":"40","author":"Ropke","year":"2006","journal-title":"Transp. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.ejor.2015.12.032","article-title":"Adaptive large neighborhood search for the pickup and delivery problem with time windows, profits, and reserved requests","volume":"252","author":"Li","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.cor.2016.01.018","article-title":"An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows and scheduled lines","volume":"72","author":"Ghilas","year":"2016","journal-title":"Comput. Oper. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1016\/j.cor.2008.04.003","article-title":"A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery","volume":"36","author":"Ai","year":"2009","journal-title":"Comput. Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/19427867.2016.1270798","article-title":"Fuzzy capacitated location-routing problem with simultaneous pickup and delivery demands","volume":"11","author":"Nadizadeh","year":"2019","journal-title":"Transp. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11750-007-0009-0","article-title":"Static pickup and delivery problems: A classification scheme and survey","volume":"15","author":"Berbeglia","year":"2007","journal-title":"Top"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1287\/opre.12.4.568","article-title":"Scheduling of vehicles from a central depot to a number of delivery points","volume":"12","author":"Clarke","year":"1964","journal-title":"Oper. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"106695","DOI":"10.1016\/j.cie.2020.106695","article-title":"A Two-phase Local Search with a Discrete-event Heuristic for the Omnichannel Vehicle Routing Problem","volume":"148","author":"Bayliss","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1111\/itor.12796","article-title":"Agile optimization of a two-echelon vehicle routing problem with pickup and delivery","volume":"28","author":"Martins","year":"2020","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Estrada-Moreno, A., Ferrer, A., Juan, A.A., Bagirov, A., and Panadero, J. (2019). A biased-randomised algorithm for the capacitated facility location problem with soft constraints. J. Oper. Res. Soc., 1\u201317.","DOI":"10.1080\/01605682.2019.1639478"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.ejor.2016.05.002","article-title":"A biased-randomised large neighbourhood search for the two-dimensional vehicle routing problem with backhauls","volume":"255","author":"Dominguez","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/itor.12379","article-title":"An iterative biased-randomized heuristic for the fleet size and mix vehicle-routing problem with backhauls","volume":"26","author":"Belloso","year":"2019","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1057\/jors.2015.48","article-title":"An ILS-biased randomization algorithm for the two-dimensional loading HFVRP with sequential loading and items rotation","volume":"67","author":"Dominguez","year":"2016","journal-title":"J. Oper. Res. Soc."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Al-Behadili, M., Ouelhadj, D., and Jones, D. (2019). Multi-objective biased randomised iterated greedy for robust permutation flow shop scheduling problem under disturbances. J. Oper. Res. Soc., 1\u201313.","DOI":"10.1080\/01605682.2019.1630330"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1368","DOI":"10.1111\/itor.12719","article-title":"A biased-randomized iterated local search for the distributed assembly permutation flow-shop problem","volume":"27","author":"Ferone","year":"2020","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1111\/itor.12433","article-title":"Designing e-commerce supply chains: A stochastic facility\u2013location approach","volume":"26","author":"Ramalhinho","year":"2019","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"102089","DOI":"10.1016\/j.simpat.2020.102089","article-title":"Speeding up computational times in simheuristics combining genetic algorithms with discrete-Event simulation","volume":"103","author":"Rabe","year":"2020","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.simpat.2018.04.005","article-title":"A simheuristic algorithm to set up starting times in the stochastic parallel flowshop problem","volume":"86","author":"Hatami","year":"2018","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1111\/itor.12540","article-title":"A variable neighborhood search simheuristic for the multiperiod inventory routing problem with stochastic demands","volume":"27","author":"Gruler","year":"2020","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.cie.2018.06.036","article-title":"Combining variable neighborhood search with simulation for the inventory routing problem with stochastic demands and stock-outs","volume":"123","author":"Gruler","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"101970","DOI":"10.1016\/j.simpat.2019.101970","article-title":"Agri-food supply chains with stochastic demands: A multi-period inventory routing problem with perishable products","volume":"97","author":"Onggo","year":"2019","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1177\/0037549714531350","article-title":"A simulation-optimization approach to deploy Internet services in large-scale systems with user-provided resources","volume":"90","author":"Cabrera","year":"2014","journal-title":"Simulation"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s10732-018-9367-z","article-title":"A variable neighborhood search simheuristic for project portfolio selection under uncertainty","volume":"26","author":"Panadero","year":"2020","journal-title":"J. Heuristics"},{"key":"ref_53","first-page":"100123","article-title":"A simheuristic approach for evolving agent behaviour in the exploration for novel combat tactics","volume":"6","author":"Lam","year":"2019","journal-title":"Oper. Res. Perspect."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"104863","DOI":"10.1016\/j.cor.2019.104863","article-title":"A simheuristic approach for throughput maximization of asynchronous buffered stochastic mixed-model assembly lines","volume":"115","author":"Lopes","year":"2020","journal-title":"Comput. Oper. Res."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"103789","DOI":"10.1016\/j.engappai.2020.103789","article-title":"Simheuristic-based decision support system for efficiency improvement of an iron ore crusher circuit","volume":"94","author":"Santos","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_56","unstructured":"Glover, F.W., and Kochenberger, G.A. (2006). Handbook of Metaheuristics, Springer Science & Business Media."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"8131","DOI":"10.1109\/ACCESS.2017.2693030","article-title":"Minimizing carbon dioxide emissions due to container handling at marine container terminals via hybrid evolutionary algorithms","volume":"5","author":"Dulebenets","year":"2017","journal-title":"IEEE Access"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Dulebenets, M.A., Kavoosi, M., Abioye, O., and Pasha, J. (2018). A self-adaptive evolutionary algorithm for the berth scheduling problem: Towards efficient parameter control. Algorithms, 11.","DOI":"10.3390\/a11070100"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1016\/j.compeleceng.2017.09.016","article-title":"A bio-inspired swarm intelligence technique for social aware cognitive radio handovers","volume":"71","author":"Anandakumar","year":"2018","journal-title":"Comput. Electr. Eng."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Brezo\u010dnik, L., Fister, I., and Podgorelec, V. (2018). Swarm intelligence algorithms for feature selection: A review. Appl. Sci., 8.","DOI":"10.3390\/app8091521"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1109\/TII.2017.2786782","article-title":"Nature inspired methods and their industry applications\u2014Swarm intelligence algorithms","volume":"14","author":"Slowik","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.renene.2018.11.061","article-title":"Research and application based on the swarm intelligence algorithm and artificial intelligence for wind farm decision system","volume":"134","author":"Zhao","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Talbi, E.G. (2009). Metaheuristics: From Design to Implementation, John Wiley & Sons.","DOI":"10.1002\/9780470496916"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1016\/j.ress.2008.03.022","article-title":"Predicting availability functions in time-dependent complex systems with SAEDES simulation algorithms","volume":"93","author":"Faulin","year":"2008","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_65","first-page":"201","article-title":"A statistical learning based approach for parameter fine-tuning of metaheuristics","volume":"1","author":"Calvet","year":"2016","journal-title":"SORT-Stat. Oper. Res. Trans."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/9\/237\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:11:31Z","timestamp":1760177491000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/9\/237"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,19]]},"references-count":65,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["a13090237"],"URL":"https:\/\/doi.org\/10.3390\/a13090237","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,19]]}}}