{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T20:53:49Z","timestamp":1777064029869,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T00:00:00Z","timestamp":1638230400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The idea defended in this paper consists in finding, at any time and everywhere, the arrangement of containers within a composite container. The digital image of the real arrangement obtained defines its digital twin. This image evolves at the same time as its real twin. It can be used throughout the logistics chain during loading\/unloading phases in hubs, to check the completeness of a load, to find the particular position of a container, etc. This digital twin is obtained through the collection of neighborhood information from the sensor nodes embedded on each container. This embedded solution allows accessibility to this information everywhere. This proximity information and the instrumentation of the containers define new types of constraints and a new version of a packing problem. We propose here a model integrating them. This model is implemented and tested on different test cases, and numerical results are provided. These show that, under certain conditions that will be presented, it is possible to obtain the digital twin of the real arrangement.<\/jats:p>","DOI":"10.3390\/s21237999","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T01:45:02Z","timestamp":1638323102000},"page":"7999","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Pervasive Digital Twin for PI-Containers: A New Packing Problem"],"prefix":"10.3390","volume":"21","author":[{"given":"Patrick","family":"Charpentier","sequence":"first","affiliation":[{"name":"CRAN UMR 7039, Universit\u00e9 de Lorraine, CNRS, Campus Sciences, Boulevard des Aiguillettes-BP 70239, 54506 Vand\u0153uvre-l\u00e8s-Nancy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Chaxel","sequence":"additional","affiliation":[{"name":"CRAN UMR 7039, Universit\u00e9 de Lorraine, CNRS, Campus Sciences, Boulevard des Aiguillettes-BP 70239, 54506 Vand\u0153uvre-l\u00e8s-Nancy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Krommenacker","sequence":"additional","affiliation":[{"name":"CRAN UMR 7039, Universit\u00e9 de Lorraine, CNRS, Campus Sciences, Boulevard des Aiguillettes-BP 70239, 54506 Vand\u0153uvre-l\u00e8s-Nancy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3482-2008","authenticated-orcid":false,"given":"Vincent","family":"Bombardier","sequence":"additional","affiliation":[{"name":"CRAN UMR 7039, Universit\u00e9 de Lorraine, CNRS, Campus Sciences, Boulevard des Aiguillettes-BP 70239, 54506 Vand\u0153uvre-l\u00e8s-Nancy, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6567-8988","authenticated-orcid":false,"given":"Fabian","family":"Seguel","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad de Santiago de Chile, Avenida Ecuador N\u00b0 3519, Estaci\u00f3n Central, Santiago 8350709, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2012.12.006","article-title":"Constraints in container loading \u2014A state-of-the-art review","volume":"229","author":"Bortfeldt","year":"2013","journal-title":"Eur. J. Oper. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s12159-011-0045-x","article-title":"Toward a Physical Internet: Meeting the global logistics sustainability grand challenge","volume":"3","author":"Montreuil","year":"2011","journal-title":"Logist. Res."},{"key":"ref_3","unstructured":"Ballot, E., Montreuil, B., and Meller, R. (2014). The Physical Internet: The Network of Logistics Networks, Predit, La Documentation Francaise. Technical report."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4711","DOI":"10.1109\/JIOT.2020.2971736","article-title":"Toward the internet of things for physical internet: Perspectives and challenges","volume":"7","author":"Krommenacker","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_5","first-page":"2650","article-title":"Containers monitoring through the Physical Internet: A spatial 3D model based on wireless sensor networks","volume":"55","author":"Krommenacker","year":"2016","journal-title":"Int. J. Prod. Res."},{"key":"ref_6","unstructured":"Grieves, M. (2015). Digital Twin: Manufacturing Excellence through Virtual Factory Replication, Florida Institute of Technology. White paper."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Grieves, M., and Vickers, J. (2017). Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems. Transdiscipl. Perspect. Complex Syst. New Find. Approaches, 85\u2013113.","DOI":"10.1007\/978-3-319-38756-7_4"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Barricelli, B.R., Casiraghi, E., and Fogli, D. (2019). A survey on digital twin: Definitions, characteristics, applications, and design implications. IEEE Access, 7.","DOI":"10.1109\/ACCESS.2019.2953499"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.compag.2013.09.006","article-title":"Virtualisation of floricultural supply chains: A review from an Internet of Things perspective","volume":"99","author":"Verdouw","year":"2013","journal-title":"Comput. Electron. Agric."},{"key":"ref_10","unstructured":"Heutger, M., and Kuechelhaus, M. (2019). Digital Twins in Logistics: A DHL Perspective on the Impact of Digital Twins on the Logistics Industry. DHL."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Pretto, A., Tonello, S., and Menegatti, E. (2013). Flexible 3D localization of planar objects for industrial bin-picking with monocamera vision system. IEEE Int. Conf. Autom. Sci. Eng., 168\u2013175.","DOI":"10.1109\/CoASE.2013.6654067"},{"key":"ref_12","unstructured":"Jacquenot, G., and M\u00e9thode, G.J. (2010). M\u00e9thode G\u00e9n\u00e9rique Pour L\u2019optimisation D\u2019agencement G\u00e9om\u00e9trique et Fonctionnel. [Ph.D. Thesis, Ecole Centrale de Nantes (ECN)]."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/j.ejor.2005.12.047","article-title":"An improved typology of cutting and packing problems","volume":"183","author":"Schumann","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0305-0548(80)90001-5","article-title":"A heuristic for packing boxes into a container","volume":"7","author":"George","year":"1980","journal-title":"Comput. Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1057\/palgrave.jors.2600588","article-title":"A simple and effective recursive procedure for the manufacturer\u2019s pallet loading problem","volume":"49","author":"Morabito","year":"1998","journal-title":"J. Oper. Res. Soc."},{"key":"ref_16","unstructured":"Egeblad, J. (2008). Heuristics for Multidimensional Packing Problems. [Ph.D. Thesis, University of Copenhagen (DIKU)]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1080\/05695558208974601","article-title":"A Combined Approach to the Pallet Loading Problem","volume":"14","author":"Hodgson","year":"1981","journal-title":"IIE Trans."},{"key":"ref_18","first-page":"177","article-title":"Logistic constraints in container loading problems: The impact of complete shipment conditions","volume":"29","author":"Alonso","year":"2020","journal-title":"TOP"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/S0377-2217(99)00263-5","article-title":"An efficient approach for the multi-pallet loading problem","volume":"123","author":"Terno","year":"2000","journal-title":"Eur. J. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/0305-0483(95)00015-G","article-title":"Issues in the development of approaches to container loading","volume":"23","author":"Bischoff","year":"1995","journal-title":"Omega"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1111\/j.1475-3995.2009.00714.x","article-title":"Container loading with multi-drop constraints","volume":"16","author":"Christensen","year":"2009","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s10732-011-9162-6","article-title":"Local search for a multi-drop multi-container loading problem","volume":"19","author":"Ceschia","year":"2011","journal-title":"J. Heuristics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1590\/0101-7438.2015.035.01.0001","article-title":"A grasp algorithm for the container loading problem with multi-drop constraints","volume":"35","year":"2015","journal-title":"Pesqui. Oper."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4660","DOI":"10.1080\/00207543.2014.883468","article-title":"A decomposition-based approach for the selection of standardized modular containers","volume":"52","author":"Lin","year":"2014","journal-title":"Int. J. Prod. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.ejor.2017.11.010","article-title":"A tailored two-phase constructive heuristic for the three-dimensional Multiple Bin Size Bin Packing Problem with transportation constraints","volume":"271","author":"Paquay","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"364","DOI":"10.3182\/20120523-3-RO-2023.00282","article-title":"The Impact of Standardized Metric Physical Internet Containers on the Shipping Volume of Manufacturers","volume":"45","author":"Meller","year":"2012","journal-title":"IFAC Proc. Vol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/23\/7999\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:37:55Z","timestamp":1760168275000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/23\/7999"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,30]]},"references-count":26,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["s21237999"],"URL":"https:\/\/doi.org\/10.3390\/s21237999","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,30]]}}}