{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T09:52:05Z","timestamp":1773309125951,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001655","name":"Deutscher Akademischer Austauschdienst","doi-asserted-by":"publisher","award":["Grants - Doctoral Programmes in Germany, 2017\/18"],"award-info":[{"award-number":["Grants - Doctoral Programmes in Germany, 2017\/18"]}],"id":[{"id":"10.13039\/501100001655","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The introduction of automated parcel locker (APL) systems is one possible approach to improve urban logistics (UL) activities. Based on the city of Dortmund as case study, we propose a simulation-optimization approach integrating a system dynamics simulation model (SDSM) with a multi-period capacitated facility location problem (CFLP). We propose this integrated model as a decision support tool for future APL implementations as a last-mile distribution scheme. First, we built a causal-loop and stock-flow diagram to show main components and interdependencies of the APL systems. Then, we formulated a multi-period CFLP model to determine the optimal number of APLs for each period. Finally, we used a Monte Carlo simulation to estimate the costs and reliability level with random demands. We evaluate three e-shopper rate scenarios with the SDSM, and then analyze ten detailed demand configurations based on the results for the middle-size scenario with our CFLP model. After 36 months, the number of APLs increases from 99 to 165 with the growing demand, and stabilizes in all configurations from month 24. A middle-demand configuration, which has total costs of about 750,000\u20ac, already locates a suitable number of APLs. If the budget is lower, our approach offers alternatives for decision-makers.<\/jats:p>","DOI":"10.3390\/a14020041","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T05:23:05Z","timestamp":1611811385000},"page":"41","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Simulation-Optimization Approach for Multi-Period Facility Location Problems with Forecasted and Random Demands in a Last-Mile Logistics Application"],"prefix":"10.3390","volume":"14","author":[{"given":"Markus","family":"Rabe","sequence":"first","affiliation":[{"name":"IT in Production and Logistics, Faculty of Mechanical Engineering, TU Dortmund, 44227 Dortmund, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0056-7627","authenticated-orcid":false,"given":"Jesus","family":"Gonzalez-Feliu","sequence":"additional","affiliation":[{"name":"Centre de Recherche en Intelligence et Innovation Manag\u00e9riales, Excelia Business School, 17000 La Rochelle, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0184-7484","authenticated-orcid":false,"given":"Jorge","family":"Chicaiza-Vaca","sequence":"additional","affiliation":[{"name":"IT in Production and Logistics, Faculty of Mechanical Engineering, TU Dortmund, 44227 Dortmund, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3028-1686","authenticated-orcid":false,"given":"Rafael D.","family":"Tordecilla","sequence":"additional","affiliation":[{"name":"IN3\u2014Computer Science Department, Universitat Oberta de Catalunya, 08018 Barcelona, Spain"},{"name":"School of Engineering, Universidad de La Sabana, 53753 Chia, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gonzalez-Feliu, J. 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