{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:28:23Z","timestamp":1760232503807,"version":"build-2065373602"},"reference-count":74,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T00:00:00Z","timestamp":1668038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Callaghan Innovation New Zealand","award":["MAIN1901\/PROP-69059-FELLOW-MAIN"],"award-info":[{"award-number":["MAIN1901\/PROP-69059-FELLOW-MAIN"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Modelling freight logistics is challenging due to the variable consignments and diverse customers. Discrete-event Simulation (DES) is an approach that can model freight logistics and incorporate stochastic events. However, the flexible delivery routes of Pickup and Delivery (PUD) are still problematic to simulate. This research aims to develop last-mile delivery architecture in DES and evaluate the credibility of the model. A two-tier architecture was proposed and integrated with a DES model to simulate freight operations. The geographic foundation of the model was determined using Geographic Information Systems (GIS), including identifying customer locations, finding cluster centres, and implementing Travelling Salesman Problem (TSP) simulation. This complex model was simplified to the two-tier architecture with stochastic distances, which is more amenable to DES models. The model was validated with truck GPS data. The originality of the work is the development of a novel and simple methodology for developing a logistics model for highly variable last-mile delivery.<\/jats:p>","DOI":"10.3390\/systems10060214","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T19:18:29Z","timestamp":1668107909000},"page":"214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Developing a Stochastic Two-Tier Architecture for Modelling Last-Mile Delivery and Implementing in Discrete-Event Simulation"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5494-8129","authenticated-orcid":false,"given":"Zichong","family":"Lyu","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Canterbury, Kirkwood Ave, Christchurch 8140, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7141-0291","authenticated-orcid":false,"given":"Dirk","family":"Pons","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Canterbury, Kirkwood Ave, Christchurch 8140, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiasen","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Canterbury, Kirkwood Ave, Christchurch 8140, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5694-8699","authenticated-orcid":false,"given":"Yilei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Canterbury, Kirkwood Ave, Christchurch 8140, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ghiani, G., Laporte, G., and Musmanno, R. (2004). Introduction to Logistics Systems Planning and Control, J. Wiley.","DOI":"10.1002\/0470014040"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Taylor, G.D. (2007). Logistics Engineering Handbook, CRC Press.","DOI":"10.1201\/9780849330537"},{"key":"ref_3","unstructured":"Asuncion, J., Rendall, S., Murray, R., and Krumdieck, S. (2012, January 18\u201321). New Zealand intermodal freight network and the potential for mode shifting. Proceedings of the New Zealand: IPENZ Transportation Group Conference, Rotorua, New Zealand. Available online: https:\/\/ir.canterbury.ac.nz\/bitstream\/handle\/10092\/8825\/12642890_Asuncion_IPENZposter_Mar2012.pdf?sequence=1&isAllowed=y."},{"key":"ref_4","first-page":"93","article-title":"Logistics Future Trends","volume":"6","author":"Zakery","year":"2011","journal-title":"Logist. Oper. Manag."},{"key":"ref_5","first-page":"915","article-title":"Successful Simulation: A Practical Approach to Simulation Projects","volume":"46","author":"Hlupic","year":"1995","journal-title":"J. Oper. Res. Soc."},{"key":"ref_6","first-page":"687","article-title":"Improving picking performance at a large retailer warehouse by combining probabilistic simulation, optimization, and discrete-event simulation","volume":"28","author":"Alves","year":"2020","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.simpat.2010.08.009","article-title":"A mesoscopic simulation modelling methodology for analyzing and evaluating freight train operations in a rail network","volume":"19","author":"Marinov","year":"2011","journal-title":"Simul. Model. Pr. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.trd.2018.02.003","article-title":"Evaluating the impact of off-hour deliveries: An application of the TRansport Agent-BAsed model","volume":"62","author":"Mommens","year":"2018","journal-title":"Transp. Res. Part D: Transp. Environ."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lu, S., Xin, B., Zhang, H., and Chen, J. (2020, January 14\u201318). Agent-based Self-organized Constructive Heuristics for Travelling Salesman Problem. Proceedings of the 2020 59th IEEE Conference on Decision and Control (CDC), Jeju, Korea.","DOI":"10.1109\/CDC42340.2020.9303775"},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.geoforum.2016.06.006","article-title":"Change trends in urban freight delivery: A qualitative inquiry","volume":"74","author":"Hopkins","year":"2016","journal-title":"Geoforum"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lyu, Z., Pons, D., Zhang, Y., and Ji, Z. (2022). Minimum Viable Model (MVM) Methodology for Integration of Agile Methods into Operational Simulation of Logistics. Logistics, 6.","DOI":"10.3390\/logistics6020037"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lyu, Z., Pons, D., Zhang, Y., and Ji, Z. (2021). Freight Operations Modelling for Urban Delivery and Pickup with Flexible Routing: Cluster Transport Modelling Incorporating Discrete-Event Simulation and GIS. Infrastructures, 6.","DOI":"10.3390\/infrastructures6120180"},{"key":"ref_14","first-page":"279","article-title":"A fuzzy optimization approach to the capacitated node-routing problem for municipal solid waste collection with multiple tours: A case study","volume":"38","author":"Aliahmadi","year":"2019","journal-title":"Waste Manag. Res. J. a Sustain. Circ. Econ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1016\/j.cor.2013.01.007","article-title":"The synchronized arc and node routing problem: Application to road marking","volume":"40","author":"Langevin","year":"2013","journal-title":"Comput. Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kumar, A. (2020, January 13\u201315). Improved Genetic Algorithm to Solve Small Scale Travelling Salesman Problem. Proceedings of the 2020 4th International Conference on Intelligent Computing and Control Systems, Madurai, India.","DOI":"10.1109\/ICICCS48265.2020.9120880"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Agrawal, M., and Jain, V. (2020, January 15\u201317). Applying Improved Genetic Algorithm to Solve Travelling Salesman Problem. Proceedings of the 2020 Second International Conference on Inventive Research in Computing Applications, Coimbatore, India.","DOI":"10.1109\/ICIRCA48905.2020.9182884"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104950","DOI":"10.1016\/j.cor.2020.104950","article-title":"Quota travelling salesman problem with passengers, incomplete ride and collection time optimization by ant-based algorithms","volume":"120","author":"Silva","year":"2020","journal-title":"Comput. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104994","DOI":"10.1016\/j.cor.2020.104994","article-title":"The commodity-split multi-compartment capacitated arc routing problem","volume":"122","author":"Zbib","year":"2020","journal-title":"Comput. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1080\/19427867.2019.1679405","article-title":"A bi-objective transportation-location arc routing problem","volume":"12","author":"Amini","year":"2019","journal-title":"Transp. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1002\/net.21990","article-title":"Effects of update frequencies in a dynamic capacitated arc routing problem","volume":"76","author":"Padungwech","year":"2020","journal-title":"Networks"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.ejor.2020.10.035","article-title":"Solving the length constrained K-drones rural postman problem","volume":"292","author":"Campbell","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1016\/j.ejor.2019.01.056","article-title":"The periodic rural postman problem with irregular services on mixed graphs","volume":"276","author":"Benavent","year":"2019","journal-title":"Eur. J. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.orl.2021.01.017","article-title":"The Hierarchical Chinese Postman Problem: The slightest disorder makes it hard, yet disconnectedness is manageable","volume":"49","author":"Afanasev","year":"2021","journal-title":"Oper. Res. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42484-020-00031-9","article-title":"Investigating the Chinese postman problem on a quantum annealer","volume":"3","author":"Siloi","year":"2021","journal-title":"Quantum Mach. Intell."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"11557","DOI":"10.1007\/s00500-018-03697-3","article-title":"Uncertain multi-objective Chinese postman problem","volume":"23","author":"Majumder","year":"2018","journal-title":"Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12544-021-00491-5","article-title":"Assesment of the potential of cargo bikes and electrification for last-mile parcel delivery by means of simulation of urban freight flows","volume":"13","author":"Llorca","year":"2021","journal-title":"Eur. Transp. Res. Rev."},{"key":"ref_28","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_29","doi-asserted-by":"crossref","first-page":"146050","DOI":"10.1109\/ACCESS.2021.3121607","article-title":"Evaluating Sustainable Last-Mile Delivery (LMD) in B2C E-Commerce Using Two-Stage Fuzzy MCDM Approach: A Case Study From Vietnam","volume":"9","author":"Wang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1007\/s00170-013-5349-3","article-title":"Hierarchical modelling of Last Mile logistic distribution system","volume":"70","author":"Aized","year":"2013","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"103552","DOI":"10.1016\/j.scs.2021.103552","article-title":"An integrated crowdshipping framework for green last mile delivery","volume":"78","author":"Ghaderi","year":"2021","journal-title":"Sustain. Cities Soc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"115894","DOI":"10.1016\/j.eswa.2021.115894","article-title":"Scheduling the covering delivery problem in last mile delivery","volume":"187","author":"Jiang","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/s11750-017-0456-1","article-title":"Continuous approximation models in freight distribution management","volume":"25","author":"Franceschetti","year":"2017","journal-title":"TOP"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1007\/s11116-019-10028-4","article-title":"Potential last-mile impacts of crowdshipping services: A simulation-based evaluation","volume":"47","author":"Simoni","year":"2020","journal-title":"Transportation"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s13676-016-0100-5","article-title":"The stochastic vehicle routing problem, a literature review, part I: Models","volume":"7","author":"Oyola","year":"2016","journal-title":"EURO J. Transp. Logist."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s13676-016-0099-7","article-title":"The stochastic vehicle routing problem, a literature review, Part II: Solution methods","volume":"6","author":"Oyola","year":"2016","journal-title":"EURO J. Transp. Logist."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Altiok, T., and Melamed, B. (2007). Simulation Modeling and Analysis with ARENA, Academic Press.","DOI":"10.1016\/B978-012370523-5\/50008-0"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2009.06.004","article-title":"Simulation in manufacturing and business: A review","volume":"203","author":"Jahangirian","year":"2010","journal-title":"Eur. J. Oper. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.simpat.2012.02.009","article-title":"Analysis of urban freight by rail using event based simulation","volume":"25","author":"Motraghi","year":"2012","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2657","DOI":"10.1109\/TITS.2018.2871946","article-title":"Dynamic Multimodal Freight Routing Using a Co-Simulation Optimization Approach","volume":"20","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"04022039","DOI":"10.1061\/(ASCE)PS.1949-1204.0000678","article-title":"Development of a Model to Optimize the Operations of an Intermodal Underground Logistics Transportation","volume":"13","author":"Rezaeifar","year":"2022","journal-title":"J. Pipeline Syst. Eng. Pr."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1061\/41139(387)261","article-title":"Simulation Research on Road Transport in Container Port Based on Arena","volume":"1","author":"Li","year":"2010","journal-title":"ICLEM 2010"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1080\/17477778.2020.1841575","article-title":"Mesoscopic discrete-rate-based simulation models for production and logistics planning","volume":"16","author":"Reggelin","year":"2020","journal-title":"J. Simul."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Hashemi, A.S., and Sattarvand, J. (2015). Application of ARENA Simulation Software for Evaluation of Open Pit Mining Transportation Systems\u2014A Case Study, Springer.","DOI":"10.1007\/978-3-319-12301-1_20"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.simpat.2011.10.003","article-title":"A simulation framework for real-time fleet management in internal transport systems","volume":"21","author":"Jaoua","year":"2012","journal-title":"Simul. Model. Pr. Theory"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.procs.2021.03.028","article-title":"Integrating Urban Last-Mile Package Deliveries into an Agent-Based Travel Demand Model","volume":"184","author":"Reiffer","year":"2021","journal-title":"Procedia Comput. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ejor.2017.04.009","article-title":"Supply chain network design under uncertainty: A comprehensive review and future research directions","volume":"263","author":"Govindan","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_48","unstructured":"Boile, M.P. (2000, January 29\u201331). Intermodal transportation network analysis-a GIS application. Proceedings of the 2000 10th Mediterranean Electrotechnical Conference. Information Technology and Electrotechnology for the Mediterranean Countries, Lemesos, Cyprus."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.3155\/1047-3289.58.8.1004","article-title":"Assessing Energy, Environmental, and Economic Tradeoffs in Intermodal Freight Transportation","volume":"58","author":"Winebrake","year":"2008","journal-title":"J. Air Waste Manag. Assoc."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1007\/s10661-011-2049-z","article-title":"A GIS-based decision support system for determining the shortest and safest route to forest fires: A case study in Mediterranean Region of Turkey","volume":"184","author":"Akay","year":"2012","journal-title":"Environ. Monit. Assess."},{"key":"ref_51","first-page":"1","article-title":"Application of Cloud Computing and GIS Based on Internet of Things in Oil and Gas Storage and Transportation Production Management and Safety Monitoring and Early Warning System","volume":"2022","author":"Wang","year":"2022","journal-title":"Mob. Inf. Syst."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2022\/4303863","article-title":"The Optimization Model of E-Commerce Logistics Distribution Path Based on GIS Technology","volume":"2022","author":"Jiao","year":"2022","journal-title":"Adv. Multimedia"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/j.wasman.2019.11.028","article-title":"Interactions of residential waste composition and collection truck compartment design on GIS route optimization","volume":"102","author":"Vu","year":"2019","journal-title":"Waste Manag."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1007\/s12649-017-9938-5","article-title":"Evaluation of Key Indicators of Waste Collection Using GIS Techniques as a Planning and Control Tool for Route Optimization","volume":"8","author":"Hemidat","year":"2017","journal-title":"Waste Biomass- Valorization"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Jwad, Z.A., and Hasson, S.T. (2018, January 9\u201311). An Optimization Approach for Waste Collection Routes Based on GIS in Hillah-Iraq. Proceedings of the 2018 International Conference on Advanced Science and Engineering (ICOASE), Duhok, Iraq.","DOI":"10.1109\/ICOASE.2018.8548889"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.wasman.2019.03.037","article-title":"Assessment of waste characteristics and their impact on GIS vehicle collection route optimization using ANN waste forecasts","volume":"88","author":"Vu","year":"2019","journal-title":"Waste Manag."},{"key":"ref_57","first-page":"1","article-title":"A bi-objective optimisation of post-disaster relief distribution and short-term network restoration using hybrid NSGA-II algorithm","volume":"60","author":"Ransikarbum","year":"2021","journal-title":"Int. J. Prod. Res."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"107557","DOI":"10.1016\/j.ijpe.2019.107557","article-title":"A scenario-based robust possibilistic model for a multi-objective electronic reverse logistics network","volume":"224","author":"Tosarkani","year":"2019","journal-title":"Int. J. Prod. Econ."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"107653","DOI":"10.1016\/j.cie.2021.107653","article-title":"A solution framework for the integrated problem of cargo assignment, fleet sizing, and delivery planning in offshore logistics","volume":"161","author":"Chagas","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_60","first-page":"62","article-title":"A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems","volume":"2","author":"Juan","year":"2015","journal-title":"Oper. Res. Perspect."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Hazaymeh, K., Almagbile, A., and Alomari, A.H. (2022). Spatiotemporal Analysis of Traffic Accidents Hotspots Based on Geospatial Techniques. ISPRS Int. J. Geo-Inf., 11.","DOI":"10.3390\/ijgi11040260"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Yu, H., and and Cai, X. (2009, January 13\u201314). A novel k-means algorithm for clustering and outlier detection. Proceedings of the 2009 Second International Conference on Future Information Technology and Management Engineering, Sanya, China.","DOI":"10.1109\/FITME.2009.125"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1007\/s11045-019-00687-y","article-title":"Energy centroid clustering algorithm to enhance the network lifetime of wireless sensor networks","volume":"31","author":"Loganathan","year":"2019","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1751","DOI":"10.18494\/SAM.2019.2263","article-title":"Machine Failure Analysis Using Nearest Centroid Classification for Industrial Internet of Things","volume":"31","author":"Kwon","year":"2019","journal-title":"Sensors Mater."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"e201","DOI":"10.7717\/peerj-cs.201","article-title":"A novel variant of social spider optimization using single centroid representation and enhanced mating for data clustering","volume":"5","author":"Thalamala","year":"2019","journal-title":"PeerJ Comput. Sci."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"108452","DOI":"10.1109\/ACCESS.2021.3101250","article-title":"GNSS Multi-Interference Source Centroid Location Based on Clustering Centroid Convergence","volume":"9","author":"Liu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"He, Q., Chen, Z., Ji, K., Wang, L., Ma, K., Zhao, C., and Shi, Y. (2019). Cluster Center Initialization and Outlier Detection Based on Distance and Density for the K-Means Algorithm, Springer.","DOI":"10.1007\/978-3-030-16657-1_49"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1088\/1742-6596\/1646\/1\/012018","article-title":"K-means Clustering Method Based on Kernel Density Estimation to Analysis Residents Travel Features: A Case Study of Chengdu","volume":"1646","author":"Li","year":"2020","journal-title":"J. Physics Conf. Ser."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.aap.2008.12.014","article-title":"Kernel density estimation and K-means clustering to profile road accident hotspots","volume":"41","author":"Anderson","year":"2009","journal-title":"Accid. Anal. Prev."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.procs.2018.03.035","article-title":"DP-Dip: A skinny method for estimating the number and center of clusters","volume":"129","author":"Xu","year":"2018","journal-title":"Procedia Comput. Sci."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"37746","DOI":"10.1109\/ACCESS.2020.2975449","article-title":"Joint Distribution Center Location Problem for Restaurant Industry Based on Improved K-Means Algorithm With Penalty","volume":"8","author":"Zhou","year":"2020","journal-title":"IEEE Access"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1111\/j.1467-9787.1962.tb00902.x","article-title":"AN EFFICIENT ALGORITHM FOR THE NUMERICAL SOLUTION OF THE GENERALIZED WEBER PROBLEM IN SPATIAL ECONOMICS","volume":"4","author":"Kulin","year":"1962","journal-title":"J. Reg. Sci."},{"key":"ref_73","unstructured":"Burt, J., and Barber, G. (1996). 1996: Elementary Statistics for Geographers, The Guilford Press."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1016\/j.procs.2015.06.090","article-title":"Image Segmentation Using K -means Clustering Algorithm and Subtractive Clustering Algorithm","volume":"54","author":"Dhanachandra","year":"2015","journal-title":"Procedia Comput. Sci."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/10\/6\/214\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:48Z","timestamp":1760145228000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/10\/6\/214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,10]]},"references-count":74,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["systems10060214"],"URL":"https:\/\/doi.org\/10.3390\/systems10060214","relation":{},"ISSN":["2079-8954"],"issn-type":[{"type":"electronic","value":"2079-8954"}],"subject":[],"published":{"date-parts":[[2022,11,10]]}}}