{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T03:51:01Z","timestamp":1770522661019,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T00:00:00Z","timestamp":1569974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["2018YFB1201403"],"award-info":[{"award-number":["2018YFB1201403"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the past, most researchers have paid attention to the storage space allocation problem in maritime container terminals, while few have studied this problem in rail\u2013water intermodal container terminals. Therefore, this paper proposes a storage space allocation problem to look for a symmetry point between the efficiency and effectivity of rail\u2013water intermodal container terminals and the unbalanced allocations and reallocation operations of inbound containers in the railway operation area, which are two interactive aspects. In this paper, a two-stage model on the storage space allocation problem is formulated, whose objective is to balance inbound container distribution and minimize overlapping amounts, considering both stacking principles, such as container departure time, weight and stacking height, and containers left in railway container yards from earlier planning periods. In Stage 1, a novel simulated annealing algorithm based on heuristics is introduced and a new heuristic algorithm based on a rolling horizon approach is developed in Stage 2. Computational experiments are implemented to verify that the model and algorithm we introduce can enhance the storage effect feasibly and effectively. Additionally, two comparison experiments are carried out: the results show that the approach in the paper performs better than the regular allocation approach and weight constraint is the most important influence on container storage.<\/jats:p>","DOI":"10.3390\/sym11101229","type":"journal-article","created":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T08:17:54Z","timestamp":1570004274000},"page":"1229","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Novel Two-Stage Heuristic for Solving Storage Space Allocation Problems in Rail\u2013Water Intermodal Container Terminals"],"prefix":"10.3390","volume":"11","author":[{"given":"Yimei","family":"Chang","sequence":"first","affiliation":[{"name":"School of Logistics, Beijing Wuzi University, Beijing 101149, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoning","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chang, Y.M., Zhu, X.N., and Haghani, A. (2019). The outbound container slot allocation based on the stowage plan in rail\u2013water intermodal container terminals. Meas. Control.","DOI":"10.1177\/0020294019842599"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1007\/s10696-013-9178-3","article-title":"Storage Yard Operations in Container Terminals: Literature Overview, Trends, and Research Directions","volume":"27","author":"Carlo","year":"2015","journal-title":"Flex. Serv. Manuf. J."},{"key":"ref_3","unstructured":"Wiese, J., Kliewer, N., and Suhl, L. (2012, May 01). A Survey of Container Terminal Characteristics and Equipment Types. Working Paper. University of Paderborn. Available online: wiwi.unipaderborn.de\/fileadmin\/lehrstuehle\/department-3\/wiwi-dep-3-ls-5\/Forschung\/Publikationen\/wiese_et_al_a_survey_of_container_terminal_characteristics_and_equipment_types_2009.pdf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s00291-010-0203-6","article-title":"Mathematical Models and Solution Methods for Optimal Container Terminal Yard Layouts","volume":"32","author":"Wiese","year":"2010","journal-title":"OR Spectr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1016\/S0191-2615(02)00089-9","article-title":"Storage Space Allocation in Container Terminals","volume":"37","author":"Zhang","year":"2003","journal-title":"Transp. Res. B-Meth."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1057\/jors.2011.113","article-title":"Optimizing Container Storage Processes at Multimodal Terminals","volume":"63","author":"Casey","year":"2012","journal-title":"J. Oper. Res. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1016\/S0360-8352(97)00219-2","article-title":"A Routing Algorithm for A Single Transfer Crane to Load Export Containers onto A Containership","volume":"33","author":"Kim","year":"1997","journal-title":"Comput. Ind. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1287\/trsc.1110.0383","article-title":"Dynamic Space and Time Partitioning for Gantry Crane Workload Management in Container Terminals","volume":"46","author":"Guo","year":"2012","journal-title":"Transp. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1016\/j.cor.2009.10.005","article-title":"A Heuristic for Retrieving Container from A Yard","volume":"37","author":"Lee","year":"2010","journal-title":"Comput. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.cie.2011.08.010","article-title":"Heuristic Algorithms for Container Pre-marshalling Problems","volume":"62","author":"Huang","year":"2012","journal-title":"Comput. Ind. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0377-2217(99)00116-2","article-title":"Deriving Decision Rules to Locate Export Containers in Container Yards","volume":"124","author":"Kim","year":"2000","journal-title":"Eur. J. Oper. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/S0377-2217(02)00333-8","article-title":"A Note on a Dynamic Space-allocation Method for Outbound Containers","volume":"148","author":"Kim","year":"2003","journal-title":"Eur. J. Oper. Res."},{"key":"ref_13","first-page":"197","article-title":"An Intelligent Storage Determining Method for Inbound Containers in Container Terminals","volume":"73","author":"Yan","year":"2005","journal-title":"J. Coast. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s00291-006-0045-4","article-title":"An Optimization Model for Storage Yard Management in Transshipment Hubs","volume":"28","author":"Lee","year":"2006","journal-title":"OR Spectr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1016\/j.cor.2004.08.007","article-title":"A Tabu Search Heuristic for the Dynamic Space Allocation Problem","volume":"33","author":"Mckendall","year":"2006","journal-title":"Comput. Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3347","DOI":"10.1016\/j.cor.2007.03.002","article-title":"Improved Tabu Search Heuristics for the Dynamic Space Allocation Problem","volume":"35","author":"Mckendall","year":"2008","journal-title":"Comput. Oper. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.cie.2008.03.012","article-title":"A Genetic Algorithm to Solve the Storage Space Allocation Problem in A Container Terminal","volume":"56","author":"Bazzazi","year":"2009","journal-title":"Comput. Ind. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10845-009-0273-y","article-title":"Generating A Rehandling-free Intra-block Remarshaling Plan for An Automated Container Yard","volume":"22","author":"Choe","year":"2011","journal-title":"J. Intell. Manuf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.ejor.2012.10.045","article-title":"Storage Space Allocation Models for Inbound Containers in An Automatic Container Terminal","volume":"226","author":"Yu","year":"2013","journal-title":"Eur. J. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1016\/j.eswa.2012.10.032","article-title":"Storage Space Allocation at Marine Container Terminals Using Ant-based Control","volume":"40","author":"Sharif","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1007\/s00291-014-0366-7","article-title":"Short-term Space Allocation for Storage Yard Management in A Transshipment Hub Port","volume":"36","author":"Jiang","year":"2014","journal-title":"OR Spectr."},{"key":"ref_22","first-page":"153","article-title":"Optimization Model on Container Slot Allocation in Container Yard with Mixed Storage Mode","volume":"12","author":"Zheng","year":"2012","journal-title":"J. Transp. Syst. Eng. Inf. Technol."},{"key":"ref_23","first-page":"172","article-title":"Optimization Model of Mixed Storage in Railway Container Terminal Yard","volume":"13","author":"Wang","year":"2013","journal-title":"J. Transp. Syst. Eng. Inf. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, L., Zhu, X.N., and Xie, Z.Y. (2014). Storage Space Allocation of Inbound Container in Railway Container Terminal. Math. Probl. Eng., 2014.","DOI":"10.1155\/2014\/956536"},{"key":"ref_25","first-page":"490","article-title":"Space Allocation Optimization Model and Algorithm for Outbound Containers in the Yard","volume":"30","author":"Liu","year":"2016","journal-title":"J. Jiangsu Univ. Sci. Technol. (Nat. Sci. Ed.)"},{"key":"ref_26","first-page":"1555","article-title":"Container Allocation Optimization of the Center Terminal Yard under Rail-sea Intermodal Transportation","volume":"36","author":"Ji","year":"2016","journal-title":"Syst. Eng. Theory Pract."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, Y.J., Zhu, X.N., Wang, L., and Chen, X. (2017). Stowage Plan Based Slot Optimal Allocation in Rail-Water Container Terminal. J. Control Sci. Eng., 2017.","DOI":"10.1155\/2017\/5489597"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/10\/1229\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:27:03Z","timestamp":1760189223000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/10\/1229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,2]]},"references-count":27,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["sym11101229"],"URL":"https:\/\/doi.org\/10.3390\/sym11101229","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,2]]}}}