{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:58:28Z","timestamp":1760241508197,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T00:00:00Z","timestamp":1524614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Classification yards are crucial nodes of railway freight transportation network, which plays a vital role in car flow reclassification and new train formation. Generally, a modern yard covers an expanse of several square kilometers and costs billions of Chinese Yuan (CNY), i.e., hundreds of millions of dollars. The determination of location and size of classification yards in multiple periods is not only related to yard establishment or improvement cost, but also involved with train connection service (TCS) plan. This paper proposes a bi-level programming model for the multi-period and multi-classification-yard location (MML) problem. The upper-level is intended to find an optimal combinatorial investment strategy for candidate nodes throughout the planning horizon, and the lower-level aims to obtain a railcar reclassification plan with minimum operation cost on the basis of the strategy given by the upper-level. The model is constrained by budget, classification capacity, the number of available tracks, etc. A numerical study is then performed to evaluate the validity and effectiveness of the model.<\/jats:p>","DOI":"10.3390\/sym10050135","type":"journal-article","created":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T11:15:39Z","timestamp":1524654939000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modeling the Multi-Period and Multi-Classification-Yard Location Problem in a Railway Network"],"prefix":"10.3390","volume":"10","author":[{"given":"Siqi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9286-0873","authenticated-orcid":false,"given":"Boliang","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaxi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianping","family":"Wu","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":[[2018,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1287\/opre.11.3.331","article-title":"Location-allocation problems","volume":"11","author":"Cooper","year":"1963","journal-title":"Oper. 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