{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T20:07:48Z","timestamp":1778011668961,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,20]],"date-time":"2025-07-20T00:00:00Z","timestamp":1752969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National University of Science and Technology Politehnica Bucharest","award":["70\/11.10.2023"],"award-info":[{"award-number":["70\/11.10.2023"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Automated parcel lockers (APLs) are transforming urban last-mile delivery by reducing failed distributions, decoupling delivery from recipient availability, optimizing carrier routes, reducing carbon foot-print and mitigating traffic congestion. The paper investigates the optimal design of APLs systems under stochastic demand and operational constraints, formulating the problem as a resource allocation optimization with service-level guarantees. We proposed a data-driven discrete-event simulation (DES) model implemented in ARENA to (i) determine optimal locker configurations that ensure customer satisfaction under stochastic parcel arrivals and dwell times, (ii) examine utilization patterns and spatial allocation to enhance system operational efficiency, and (iii) characterize inventory dynamics of undelivered parcels and evaluate system resilience. The results show that the configuration of locker types significantly influences the system\u2019s ability to maintain high customers service levels. While flexibility in locker allocation helps manage excess demand in some configurations, it may also create resource competition among parcel types. The heterogeneity of locker utilization gradients underscores that optimal APLs configurations must balance locker units with their size-dependent functional interdependencies. The Dickey\u2013Fuller GLS test further validates that postponed parcels exhibit stationary inventory dynamics, ensuring scalability for logistics operators. As a theoretical contribution, the paper demonstrates how DES combined with time-series econometrics can address APLs capacity planning in city logistics. For practitioners, the study provides a decision-support framework for locker sizing, emphasizing cost\u2013service trade-offs.<\/jats:p>","DOI":"10.3390\/systems13070613","type":"journal-article","created":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T09:33:53Z","timestamp":1753090433000},"page":"613","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Automated Parcel Locker Configuration Using Discrete Event Simulation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1080-7321","authenticated-orcid":false,"given":"Eugen","family":"Rosca","sequence":"first","affiliation":[{"name":"Transport, Traffic and Logistics Department, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2602-2534","authenticated-orcid":false,"given":"Floriana Cristina","family":"Oprea","sequence":"additional","affiliation":[{"name":"Transport, Traffic and Logistics Department, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6092-8797","authenticated-orcid":false,"given":"Anamaria","family":"Ilie","sequence":"additional","affiliation":[{"name":"Transport, Traffic and Logistics Department, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9328-1152","authenticated-orcid":false,"given":"Stefan","family":"Burciu","sequence":"additional","affiliation":[{"name":"Transport, Traffic and Logistics Department, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4074-0105","authenticated-orcid":false,"given":"Florin","family":"Rusca","sequence":"additional","affiliation":[{"name":"Transport, Traffic and Logistics Department, National University of Science and Technology Politehnica Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,20]]},"reference":[{"key":"ref_1","unstructured":"World Economic Forum (2021). The Future of the Last-Mile Ecosystem."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ding, Y., Rousseau, R., and Wolfram, D. (2014). Visualizing Bibliometric Networks. Measuring Scholarly Impact: Methods and Practice, Springer.","DOI":"10.1007\/978-3-319-10377-8"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"061","DOI":"10.17352\/aest.000071","article-title":"Collection and delivery points in the last mile of cargo transportation: Sustainability benefits and challenges","volume":"7","author":"Freitas","year":"2023","journal-title":"Ann. Environ. Sci. Toxicol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2090","DOI":"10.1080\/00207543.2020.1856440","article-title":"A parcel network flow approach for joint delivery networks using parcel lockers","volume":"59","author":"Pan","year":"2020","journal-title":"Int. J. Prod. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1007\/s13676-019-00144-7","article-title":"Flexible parcel delivery to automated parcel lockers: Models, solution methods and analysis","volume":"8","author":"Orenstein","year":"2019","journal-title":"EURO J. Transp. Logist."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.trpro.2016.02.018","article-title":"Analysis of Parcel Lockers\u2019 Efficiency as the Last Mile Delivery Solution\u2014The Results of the Research in Poland","volume":"12","author":"Iwan","year":"2016","journal-title":"Transp. Res. Procedia"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1287\/trsc.2016.0675","article-title":"50th Anniversary Invited Article\u2014City Logistics: Challenges and Opportunities","volume":"50","author":"Savelsbergh","year":"2016","journal-title":"Transp. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jtrangeo.2018.06.022","article-title":"Parcel locker systems in a car dominant city: Location, characterisation and potential impacts on city planning and consumer travel access","volume":"71","author":"Lachapelle","year":"2018","journal-title":"J. Transp. Geogr."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1998188","DOI":"10.1155\/2023\/1998188","article-title":"Location Optimization for Community Smart Parcel Lockers Based on Bilevel Programming","volume":"2023","author":"Yang","year":"2023","journal-title":"J. Adv. Transp."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kurowski, M., Sobolewski, M., and Koszorek, M. (2023). Geometrical Parcel Locker Network Design with Consideration of Users\u2019 Preferences as a Solution for Sustainable Last Mile Delivery. Sustainability, 15.","DOI":"10.3390\/su152015114"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s10100-020-00725-2","article-title":"The vehicle routing problem with heterogeneous locker boxes","volume":"29","author":"Grabenschweiger","year":"2021","journal-title":"Cent. Eur. J. Oper. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1108\/09600031011018055","article-title":"Comparative Analysis of the Carbon Footprints of Conventional and Online Retailing: A \u201cLast Mile\u201d Perspective","volume":"40","author":"Edwards","year":"2010","journal-title":"Int. J. Phys. Distrib. Logist. Manag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/00207543.2017.1395490","article-title":"A Parcel Locker Network as a Solution to the Logistics Last Mile Problem","volume":"56","author":"Deutsch","year":"2018","journal-title":"Int. J. Prod. Res."},{"key":"ref_14","first-page":"e20190048","article-title":"Analysis of Accessibility from Collection and Delivery Points: Towards the Sustainability of the E-Commerce Delivery","volume":"11","author":"Caliari","year":"2019","journal-title":"Rev. Bras. Gest."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"101368","DOI":"10.1016\/j.retrec.2023.101368","article-title":"Agent-based model of last-mile parcel deliveries and travel demand incorporating online shopping behavior","volume":"102","author":"Reiffer","year":"2023","journal-title":"Res. Transp. Econ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1080\/14783363.2018.1485484","article-title":"E-Consumer Adoption of Innovative Last-Mile Logistics Services: A Comparison of Behavioural Models","volume":"31","author":"Wang","year":"2018","journal-title":"Total Qual. Manag. Bus. Excell."},{"key":"ref_17","unstructured":"International Transport Forum (2021). ITF Transport Outlook 2021, OECD Publishing."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1108\/IJPDLM-01-2016-0008","article-title":"Research in Urban Logistics: A Systematic Literature Review","volume":"46","author":"Lagorio","year":"2016","journal-title":"Int. J. Phys. Distrib. Logist. Manag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"102443","DOI":"10.1016\/j.trd.2020.102443","article-title":"Carbon Emissions Reductions in Last Mile and Grocery Deliveries Utilizing Air and Ground Autonomous Vehicles","volume":"85","author":"Figliozzi","year":"2020","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1080\/13675560412331298473","article-title":"Use of a Synchronised Vehicle Audit to Determine Opportunities for Improving Transport Efficiency in a Supply Chain","volume":"7","author":"McKinnon","year":"2004","journal-title":"Int. J. Logist. Res. Appl."},{"key":"ref_21","unstructured":"European Environment Agency (2022). Electric Vehicles in Logistics: Lifecycle Assessment, Publications Office of the European Union. EEA Report No 15\/2022."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Silva, V., Amaral, A., and Fontes, T. (2023). Sustainable Urban Last-Mile Logistics: A Systematic Literature Review. Sustainability, 15.","DOI":"10.3390\/su15032285"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"107746","DOI":"10.1016\/j.ijpe.2020.107746","article-title":"Sustainability assessment of last-mile logistics and distribution strategies: The case of local food networks","volume":"228","author":"Melkonyan","year":"2020","journal-title":"Int. J. Prod. Econ."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Che, Z.-H., Chiang, T.-A., and Luo, Y.-J. (2022). Multiobjective Optimization for Planning the Service Areas of Smart Parcel Locker Facilities in Logistics Last Mile Delivery. Mathematics, 10.","DOI":"10.3390\/math10030422"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Serrano-Hernandez, A., Martinez-Abad, S., Ballano, A., Faulin, J., Rabe, M., and Chicaiza-Vaca, J. (2021, January 12\u201315). A Hybrid Modeling Approach for Automated Parcel Lockers as a Last-Mile Delivery Scheme: A Case Study in Pamplona (Spain). Proceedings of the 2021 Winter Simulation Conference (WSC), Phoenix, AZ, USA.","DOI":"10.1109\/WSC52266.2021.9715337"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Sawik, B., Serrano-Hernandez, A., Muro, A., and Faulin, J. (2022). Multi-Criteria Simulation-Optimization Analysis of Usage of Automated Parcel Lockers: A Practical Approach. Mathematics, 10.","DOI":"10.3390\/math10234423"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Rabe, M., Chicaiza-Vaca, J., Tordecilla, R.D., and Juan, A.A. (2020, January 14\u201318). A simulation-optimization approach for locating automated parcel lockers in urban logistics operations. Proceedings of the 2020 Winter Simulation Conference (WSC), Orlando, FL, USA.","DOI":"10.1109\/WSC48552.2020.9384087"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Izco Berastegui, I., Serrano, A., Faulin, J., and Sawik, B. (2023, January 10\u201313). A Dynamic Forecast Demand Scenario Analysis to Design an Automated Parcel Lockers Network in Pamplona (Spain) Using a Simulation-Optimization Model. Proceedings of the 2020 Winter Simulation Conference (WSC), San Antonio, TX, USA.","DOI":"10.1109\/WSC60868.2023.10408738"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Iannaccone, G., Marcucci, E., and Gatta, V. (2021). What Young E-Consumers Want? Forecasting Parcel Lockers Choice in Rome. Logistics, 5.","DOI":"10.3390\/logistics5030057"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Sawik, B. (2024). Optimizing Last-Mile Delivery: A Multi-Criteria Approach with Automated Smart Lockers, Capillary Distribution and Crowdshipping. Logistics, 8.","DOI":"10.3390\/logistics8020052"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.chb.2016.02.051","article-title":"Personal values as determinants of intentions to use self-service technology in retailing","volume":"60","author":"Lee","year":"2016","journal-title":"Comput. Hum. Behav."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.retrec.2017.09.003","article-title":"Analysis of the potential demand of automated delivery stations for e-commerce deliveries in Belo Horizonte, Brazil","volume":"65","author":"Morganti","year":"2017","journal-title":"Res. Transp. Econ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.3390\/smartcities6050120","article-title":"Perceived Importance and Quality Attributes of Automated Parcel Locker Services in Urban Areas","volume":"6","year":"2023","journal-title":"Smart Cities"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ajsl.2021.11.002","article-title":"Determinants of customer satisfaction with parcel locker services in last-mile logistics","volume":"38","author":"Lai","year":"2022","journal-title":"Asian J. Shipp. Logist."},{"key":"ref_35","unstructured":"Adnan, M., Pereira, F., Azevedo, C.L., Basak, K., Lovric, M., Raveau, S., Zhu, Y., Ferreira, J., Zegras, C., and Ben-Akiva, M. (2016). SimMobility: A Multi-Scale Integrated Agent-Based Simulation Platform. Transportation Research Record, Proceedings of the 95th Annual Meeting of the Transportation Research Board, Washington, DC, USA, 10\u201314 January 2016, The National Academies of Sciences, Engineering, and Medicine."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"100083","DOI":"10.1016\/j.martra.2023.100083","article-title":"Cooperation between Vessel Service Providers in Ports: An Impact Analysis Using Simulation for the Port of Rotterdam","volume":"4","author":"Nikghadam","year":"2023","journal-title":"Marit. Transp. Res."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Liang, K., Zhou, L., Yang, J., Liu, H., Li, Y., Jing, F., Shan, M., and Yang, J. (2023). Research on a Dynamic Task Update Assignment Strategy Based on a \u201cParts to Picker\u201d Picking System. Mathematics, 11.","DOI":"10.3390\/math11071684"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Simchi-Levi, D., Kaminsky, P., and Simchi-Levi, E. (2021). Designing and Managing the Supply Chain, McGraw-Hill. [4th ed.].","DOI":"10.1287\/5a6878d6-3b15-474e-b579-c87e86079719"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Vargas-Mu\u00f1oz, J.C., Sanchez-Nitola, F.A., Adarme Jaimes, W., and Rios, R. (2025). Enhancing Logistical Performance in a Colombian Citrus Supply Chain Through Joint Decision Making: A Simulation Study. Logistics, 9.","DOI":"10.3390\/logistics9010030"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Rosca, E., Rusca, F., Rosca, M.A., and Rusca, A. (2024). Performance Analysis of Automated Parcel Lockers in Urban Delivery: Combined Agent-Based\u2013Monte Carlo Simulation Approach. Logistics, 8.","DOI":"10.3390\/logistics8020061"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Wan, J., and Wang, Y. (2024, January 12). Research on Optimization of E-Commerce Automated Storage Layout Simulation Based on Flexsim. Proceedings of the 12th International Conference on Transportation and Traffic Engineering (ICTTE 2023), Wuhan, China.","DOI":"10.1049\/icp.2024.0800"},{"key":"ref_42","first-page":"427","article-title":"Distribution of the Estimators for Autoregressive Time Series with a Unit Root","volume":"74","author":"Dickey","year":"1979","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"813","DOI":"10.2307\/2171846","article-title":"Efficient Tests for an Autoregressive Unit Root","volume":"64","author":"Elliott","year":"1996","journal-title":"Econometrica"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"L\u00fctkepohl, H. (2005). New Introduction to Multiple Time Series Analysis, Springer.","DOI":"10.1007\/978-3-540-27752-1"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/13\/7\/613\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:13:01Z","timestamp":1760033581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/13\/7\/613"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,20]]},"references-count":44,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["systems13070613"],"URL":"https:\/\/doi.org\/10.3390\/systems13070613","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,20]]}}}