{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:24:19Z","timestamp":1760239459922,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T00:00:00Z","timestamp":1605657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Put-away operations typically consist of moving products from depots to allocated storage locations using either operators or Material Handling Equipment (MHE), accounting for important operative costs in warehouses and impacting operations efficiency. Therefore, this paper aims to formulate and solve a Put-away Routing Problem (PRP) in distribution centres (DCs). This PRP formulation represents a novel approach due to the consideration of a fleet of homogeneous Material Handling Equipment (MHE), heterogeneous products linked to a put-away list size, depot location and multi-parallel aisles in a distribution centre. It should be noted that the slotting problem, rather than the PRP, has usually been studied in the literature, whereas the PRP is addressed in this paper. The PRP is solved using a discrete particle swarm optimization (PSO) algorithm that is compared to tabu search approaches (Classical Tabu Search (CTS), Tabu Search (TS) 2-Opt) and an empirical rule. As a result, it was found that a discrete PSO generates the best solutions, as the time savings range from 2 to 13% relative to CTS and TS 2-Opt for different combinations of factor levels evaluated in the experimentation.<\/jats:p>","DOI":"10.3390\/computation8040099","type":"journal-article","created":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T22:46:46Z","timestamp":1605653206000},"page":"99","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Discrete Particle Swarm Optimization to Solve the Put-Away Routing Problem in Distribution Centres"],"prefix":"10.3390","volume":"8","author":[{"given":"Rodrigo Andr\u00e9s","family":"G\u00f3mez-Montoya","sequence":"first","affiliation":[{"name":"Facultad de Administraci\u00f3n, Polit\u00e9cnico Colombiano Jaime Isaza Cadavid, Carrera 48 No. 7\u2013151, Medell\u00edn 050022, Colombia"},{"name":"ESACS\u2013Escuela Superior en Administraci\u00f3n de Cadena de Suministro, Calle 4 # 18-55, Medell\u00edn 050021, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2638-5581","authenticated-orcid":false,"given":"Jose Alejandro","family":"Cano","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias Econ\u00f3micas y Administrativas, Universidad de Medell\u00edn, Carrera 87 # 30\u201365, Medell\u00edn 050026, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo","family":"Cort\u00e9s","sequence":"additional","affiliation":[{"name":"Escuela T\u00e9cnica Superior de Ingenier\u00eda, Universidad de Sevilla, Camino de los Descubrimientos s\/n, 41092 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0949-0803","authenticated-orcid":false,"given":"Fernando","family":"Salazar","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias Econ\u00f3micas y Administrativas, Pontificia Universidad Javeriana, Cra. 7 #40, Bogot\u00e1 110231, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,18]]},"reference":[{"key":"ref_1","unstructured":"Bartholdi, J.J., and Hackman, S.T. (2014). Warehouse & Distribution Science, The Supply Chain and Logistics Institute."},{"key":"ref_2","unstructured":"(2016, November 08). CSCMP Supply Chain Management: Terms and Glossary. Available online: https:\/\/bit.ly\/2e3NMGE."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"235","DOI":"10.4067\/S0718-07642018000600235","article-title":"Solving the Order Batching Problem in Warehouses using Genetic Algorithms","volume":"29","author":"Cano","year":"2018","journal-title":"Inf. Tecnol."},{"key":"ref_4","unstructured":"Ceyhun, G.\u00c7. (2020). Order Picking Optimization Based on a Picker Routing Heuristic: Minimizing Total Traveled Distance in Warehouses. Handbook of Research on the Applications of International Transportation and Logistics for World Trade, IGI Global."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2017.09.002","article-title":"Designing Efficient Order Picking Systems by Combining Planning Problems: State-of-the-art Classification and Review","volume":"267","author":"Ramaekers","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_6","first-page":"836","article-title":"Formulations for joint order picking problems in low-level picker-to-part systems","volume":"9","author":"Cano","year":"2020","journal-title":"Bull. Electr. Eng. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/j.tre.2009.05.005","article-title":"Pre-distribution and post-distribution cross-docking operations","volume":"45","author":"Yan","year":"2009","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.ejor.2006.07.009","article-title":"Design and control of warehouse order picking: A literature review","volume":"182","author":"Roodbergen","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1111\/jbl.12135","article-title":"Just-in-Time Retail Distribution: A Systems Perspective on Cross-Docking","volume":"37","author":"Buijs","year":"2016","journal-title":"J. Bus. Logist."},{"key":"ref_10","unstructured":"Frazelle, E.H. (2016). World-Class Warehousing and Material Handling, McGraw-Hill Education. [2nd ed.]."},{"key":"ref_11","first-page":"49","article-title":"Comparative analysis of order batching and routing problem in the picking regarding classical HVRP (heterogeneous vehicle routing problem) [An\u00e1lisis comparativo del problema de conformaci\u00f3n de lotes con ruteo en la preparaci\u00f3n de pedidos respecto al HVRP]","volume":"59","author":"Correa","year":"2016","journal-title":"Dir. Organ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2686","DOI":"10.1016\/j.eswa.2010.08.058","article-title":"Improving the productivity of order picking of a manual-pick and multi-level rack distribution warehouse through the implementation of class-based storage","volume":"38","author":"Chan","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.omega.2007.01.006","article-title":"Efficient formation of storage classes for warehouse storage location assignment: A simulated annealing approach","volume":"36","author":"Muppani","year":"2008","journal-title":"Omega"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.cie.2011.09.016","article-title":"Slotting methodology using correlated improvement for a zone-based carton picking distribution system","volume":"62","author":"Kim","year":"2012","journal-title":"Comput. Ind. Eng."},{"key":"ref_15","unstructured":"Takahama, H., Nishi, T., Konishi, M., and Imai, J. (2002, January 5\u20137). A determination method of product allocation schedule for warehouse management. Proceedings of the 41st SICE Annual Conference, SICE 2002, Osaka, Japan."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/00207540412331285841","article-title":"Mathematical model for warehouse design and product allocation","volume":"43","author":"Heragu","year":"2005","journal-title":"Int. J. Prod. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1080\/09511921003642154","article-title":"A model for storage arrangement and re-allocation for storage management operations","volume":"23","author":"Hou","year":"2010","journal-title":"Int. J. Comput. Integr. Manuf."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kutzelnigg, R. (2011, January 25\u201327). Optimal allocation of goods in a warehouse: Minimizing the order picking costs under real-life constraints. Proceedings of the LINDI 2011\u20143rd IEEE International Symposium on Logistics and Industrial Informatics, Budapest, Hungary.","DOI":"10.1109\/LINDI.2011.6031164"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"53","DOI":"10.4067\/S0718-07642016000600006","article-title":"Conformaci\u00f3n de Lotes M\u00ednimo Tiempo en la Operaci\u00f3n de Acomodo Considerando k Equipos Homog\u00e9neos usando Metaheur\u00edsticos","volume":"27","author":"Giraldo","year":"2016","journal-title":"Inf. Tecnol."},{"key":"ref_20","first-page":"15","article-title":"Modelamiento del ruteo del acomodo de tiempo m\u00ednimo en centros de distribuci\u00f3n (CEDI) usando b\u00fasqueda tab\u00fa","volume":"6","author":"Correa","year":"2014","journal-title":"Rev. Soluc. Postgrado EIA"},{"key":"ref_21","first-page":"180","article-title":"Analysis of particle swarm optimization algorithm","volume":"3","author":"Bai","year":"2010","journal-title":"Comput. Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.cie.2012.01.005","article-title":"A Hybrid Discrete Particle Swarm Optimization for Vehicle Routing Problem with Simultaneous Pickup and Delivery","volume":"65","author":"Goksal","year":"2013","journal-title":"Comput. Ind. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s10845-014-0871-1","article-title":"An ACO-based online routing method for multiple order pickers with congestion consideration in warehouse","volume":"27","author":"Chen","year":"2016","journal-title":"J. Intell. Manuf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"107564","DOI":"10.1016\/j.ijpe.2019.107564","article-title":"Order picker routing in warehouses: A systematic literature review","volume":"224","author":"Masae","year":"2020","journal-title":"Int. J. Prod. Econ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1631\/jzus.2006.A0607","article-title":"Hybrid Discrete Particle Swarm Optimization Algorithm for Capacitated Vehicle Routing Problem","volume":"7","author":"Chen","year":"2006","journal-title":"J. Zhejiang Univ. Sci. A"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1109\/TSMCC.2011.2148712","article-title":"Optimizing the Vehicle Routing Problem with Time Windows: A Discrete Particle Swarm Optimization Approach","volume":"42","author":"Gong","year":"2011","journal-title":"IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.)"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"742","DOI":"10.2507\/IJSIMM15(4)CO19","article-title":"Vehicle routing problem with time windows using multi-objective co-evolutionary approach","volume":"15","author":"Wu","year":"2016","journal-title":"Int. J. Simul. Model."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1007\/s11067-017-9364-z","article-title":"A Novel Model for the Time Dependent Competitive Vehicle Routing Problem: Modified Random Topology Particle Swarm Optimization","volume":"17","author":"Alinaghian","year":"2017","journal-title":"Netw. Spat. Econ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6115","DOI":"10.1080\/00207543.2018.1533260","article-title":"Study on the vehicle routing problem considering congestion and emission factors","volume":"57","author":"Zhu","year":"2019","journal-title":"Int. J. Prod. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4201","DOI":"10.1080\/00207543.2019.1650975","article-title":"Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm","volume":"58","author":"Borne","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Tebaldi, L., Bigliardi, B., and Bottani, E. (2018). Sustainable supply chain and innovation: A review of the recent literature. Sustainability, 10.","DOI":"10.3390\/su10113946"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Di Nardo, M., Clericuzio, M., Murino, T., and Sepe, C. (2020). An economic order quantity stochastic dynamic optimization model in a logistic 4.0 environment. Sustainability, 12.","DOI":"10.3390\/su12104075"},{"key":"ref_33","first-page":"20","article-title":"The evolution of man\u2013machine interaction: The role of human in Industry 4.0 paradigm","volume":"8","author":"Forino","year":"2020","journal-title":"Prod. Manuf. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.ejor.2015.06.074","article-title":"An algorithm for dynamic order-picking in warehouse operations","volume":"248","author":"Lu","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6394","DOI":"10.1080\/00207543.2016.1206982","article-title":"Order picker routing with product returns and interaction delays","volume":"55","author":"Schrotenboer","year":"2017","journal-title":"Int. J. Prod. Res."},{"key":"ref_36","first-page":"219","article-title":"Mathematical programming modeling for joint order batching, sequencing and picker routing problems in manual order picking systems","volume":"32","author":"Cano","year":"2019","journal-title":"J. King Saud Univ. Eng. Sci."},{"key":"ref_37","first-page":"2260","article-title":"Exploring the Role of Picker Personality in Predicting Picking Performance with Pick by Voice, Pick to Light and RF-Terminal Picking","volume":"54","author":"Stam","year":"2015","journal-title":"Int. J. Prod. Res."},{"key":"ref_38","unstructured":"Kennedy, J., and Eberhart, R.C. (1997, January 12\u201315). A discrete binary version of the particle swarm algorithm. Proceedings of the IEEE International Conference on Computational Cybernetics and Simulation, Orlando, FL, USA."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.cor.2015.07.010","article-title":"Genetic based discrete particle swarm optimization for Elderly Day Care Center timetabling","volume":"65","author":"Lin","year":"2016","journal-title":"Comput. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.asoc.2016.12.026","article-title":"A tabu search approach to solving the picking routing problem for large- and medium-size distribution centres considering the availability of inventory and K heterogeneous material handling equipment","volume":"53","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2549","DOI":"10.1016\/j.cor.2011.12.019","article-title":"Algorithms for on-line order batching in an order picking warehouse","volume":"39","author":"Henn","year":"2012","journal-title":"Comput. Oper. Res."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/8\/4\/99\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:34:55Z","timestamp":1760178895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/8\/4\/99"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,18]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["computation8040099"],"URL":"https:\/\/doi.org\/10.3390\/computation8040099","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2020,11,18]]}}}