{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T04:06:02Z","timestamp":1773806762297,"version":"3.50.1"},"reference-count":64,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T00:00:00Z","timestamp":1663977600000},"content-version":"vor","delay-in-days":266,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>Order picking, which is collecting a set of products from different locations in a warehouse, has repeatedly been described as one of the most laborious and time\u2010consuming internal logistic processes. Each order is issued to pick some products located at given locations in the warehouse. In this paper, we consider an order picking problem, in which a number of orders with different delivery due dates are going to be retrieved by a limited number of order pickers in multiperiods such that the total tardiness is minimized. The aim is to determine a retrieval plan in terms of order batching and order picker multitrip routing as decision variables. Besides, products are arrived and replenished at the predetermined locations at different periods. Therefore, products sitting in those locations should be delivered soon to provide empty rooms for replenishment. A mixed integer linear programming formulation is proposed for this new problem. The model is optimally solved for small\u2010size problems. For larger instances, grouping metaheuristic algorithms are proposed based on particle swarm optimization and the league championship algorithm that use group\u2010based operators to generate reasonable batches of orders. Improvement heuristics are designed as well. The performance of the MILP formulation and metaheuristic algorithms is analyzed for different problem instances whose designs are based on real data gathered from an auto parts warehouse. Results indicate that our algorithms can stably solve large instances of the problem in a reasonable time.<\/jats:p>","DOI":"10.1155\/2022\/1382558","type":"journal-article","created":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T12:35:14Z","timestamp":1664022914000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Mixed Integer Linear Formulation and a Grouping League Championship Algorithm for a Multiperiod\u2010Multitrip Order Picking System with Product Replenishment to Minimize Total Tardiness"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0241-8123","authenticated-orcid":false,"given":"Morteza","family":"Farhadi Sartangi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6004-6882","authenticated-orcid":false,"given":"Ali","family":"Husseinzadeh Kashan","sequence":"additional","affiliation":[]},{"given":"Hassan","family":"Haleh","sequence":"additional","affiliation":[]},{"given":"Abolfazl","family":"Kazemi","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2022,9,24]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jksues.2019.02.004"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1093\/jcde\/qwab009"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2017.04.002"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10845-016-1248-4"},{"key":"e_1_2_10_5_2","first-page":"481","volume-title":"Design and Control of Warehouse Order Picking: A Literature Review, ERIM Report Series Reference Number","author":"De Koster R.","year":"2006"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2015.03.021"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2017.09.002"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10696-012-9164-1"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2019.107564"},{"key":"e_1_2_10_10_2","doi-asserted-by":"crossref","unstructured":"Husseinzadeh KashanA. League championship algorithm: a new algorithm for numerical function optimization Proceedings of the In SoCPaR 2009 - Soft Computing and Pattern Recognition December 2009 Malacca Malaysia 43\u201348.","DOI":"10.1109\/SoCPaR.2009.21"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2011.07.003"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2013.12.005"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2018.03.051"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105657"},{"key":"e_1_2_10_15_2","doi-asserted-by":"crossref","unstructured":"Husseinzadeh KashanA. KarimiyanS. KarimiyanM. andHusseinzadeh KashanH. A modified League Championship Algorithm for numerical function optimization via artificial modeling of the \u201cbetween two halves analysis\u201d Proceedings of the 6th International Conference on Soft Computing and Intelligent Systems and the 13th International Symposium on Advanced Intelligent Systems 1944-1949 2012 Kube Jappan.","DOI":"10.1109\/SCIS-ISIS.2012.6505146"},{"key":"e_1_2_10_16_2","first-page":"253","article-title":"Optimum structural design with discrete variables using league championship algorithm","volume":"51","author":"Husseinzadeh Kashan A.","year":"2018","journal-title":"Civil Engineering Infrastructures Journal"},{"key":"e_1_2_10_17_2","first-page":"829","article-title":"An effective league championship Algorithm for the stochastic multi-period portfolio optimization problem","volume":"27","author":"Hueesinzadeh Kashan A.","year":"2020","journal-title":"Scientia Iranica"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1061\/(asce)cp.1943-5487.0000617"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2020.01.059"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-017-0467-x"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1080\/13675567.2014.945400"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2016.1252862"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207540701441947"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-008-1571-9"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1108\/01443579710177860"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-5915.1999.tb01619.x"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2003.09.006"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(00)00177-6"},{"key":"e_1_2_10_29_2","unstructured":"ChabotT. CoelhoC. C. RenaudJ. andC\u00f4t\u00e9J. F. Mathematical Models Heuristic and Exact Method for Order Picking in 3D-Narrow Aisles 2015 http:\/\/www.cirrelt.ca."},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24815-6_15"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207540410001733896"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207540600558015"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf03342717"},{"key":"e_1_2_10_34_2","unstructured":"HennS. KochS. andW\u00e4scherG. Order Batching in Order Picking Warehouses: A Survey of Solution Approaches. Working Paper No.01\/2011 2011 http:\/\/www.fww.ovgu.de\/femm."},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10696-011-9101-8"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2011.11.001"},{"key":"e_1_2_10_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2014.11.025"},{"key":"e_1_2_10_38_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2014.09.029"},{"key":"e_1_2_10_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2017.03.069"},{"key":"e_1_2_10_40_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10696-017-9277-7"},{"key":"e_1_2_10_41_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2016.01.020"},{"key":"e_1_2_10_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2017.04.038"},{"key":"e_1_2_10_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2017.06.056"},{"key":"e_1_2_10_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2017.11.021"},{"key":"e_1_2_10_45_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2019.1566668"},{"key":"e_1_2_10_46_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1937-5956.2000.tb00461.x"},{"key":"e_1_2_10_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.01.036"},{"key":"e_1_2_10_48_2","unstructured":"HennS.andSchmidV. Metaheuristics for Order Batching and Sequencing in Manual Order Picking Systems. Working Paper No.11\/2011 2011 http:\/\/www.fww.ovgu.de\/femm."},{"key":"e_1_2_10_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2012.03.045"},{"key":"e_1_2_10_50_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10845-014-0871-1"},{"key":"e_1_2_10_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.promfg.2017.07.323"},{"key":"e_1_2_10_52_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2020.03.075"},{"key":"e_1_2_10_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2014.11.001"},{"key":"e_1_2_10_54_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2017.08.007"},{"key":"e_1_2_10_55_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2789-3"},{"key":"e_1_2_10_56_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11740-018-0836-x"},{"key":"e_1_2_10_57_2","doi-asserted-by":"crossref","unstructured":"Husseinzadeh KashanA. JenabiM. andHusseinzadeh KashanM. A new solution approach for grouping problems based on evolution strategies Proceedings of the SoCPaR 2009 IEEE International Conference of Soft Computing and Pattern Recognition December 2009 Kualalumpur Malaysia 88\u201393.","DOI":"10.1109\/SoCPaR.2009.29"},{"key":"e_1_2_10_58_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.10.036"},{"key":"e_1_2_10_59_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2014.10.011"},{"key":"e_1_2_10_60_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2014.12.007"},{"key":"e_1_2_10_61_2","doi-asserted-by":"publisher","DOI":"10.1002\/tal.1466"},{"key":"e_1_2_10_62_2","doi-asserted-by":"publisher","DOI":"10.1002\/tal.1598"},{"key":"e_1_2_10_63_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2018.12.033"},{"key":"e_1_2_10_64_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2022.102673"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/1382558","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/2022\/1382558","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/1382558","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T21:18:50Z","timestamp":1769116730000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2022\/1382558"}},"subtitle":[],"editor":[{"given":"Reza","family":"Lotfi","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":64,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1155\/2022\/1382558"],"URL":"https:\/\/doi.org\/10.1155\/2022\/1382558","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"2022-07-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-08-17","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-09-24","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"1382558"}}