{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T21:11:23Z","timestamp":1648761083879},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> This note examines the likelihood of packing two identical one dimensional shelves of integer length L by items whose individual lengths are divisors of L, given that their combined length sums-up to 2L. We compute the number of packing failures and packing successes for integer shelve lengths L, 1 \u2264 L \u2264 1000, by implementing a dynamic programming scheme using a problem specific \"boundedness property\". The computational results indicate that the likelihood of a packing failure is very rare. We observe that the existence of packing failures is tied to the number of divisors of L and prove that the number of divisors has to be at least 8 for a packing failure to exist. <\/jats:p>","DOI":"10.1142\/s1793830910000565","type":"journal-article","created":{"date-parts":[[2010,7,5]],"date-time":"2010-07-05T10:31:23Z","timestamp":1278325883000},"page":"189-198","source":"Crossref","is-referenced-by-count":1,"title":["PACKING SHELVES WITH ITEMS THAT DIVIDE THE SHELVES' LENGTH: A CASE OF A UNIVERSAL NUMBER PARTITION PROBLEM"],"prefix":"10.1142","volume":"02","author":[{"given":"MOSHE","family":"DROR","sequence":"first","affiliation":[{"name":"MIS Department, Eller College of Management, University of Arizona, Tucson, Arizona 85721, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JAMES B.","family":"ORLIN","sequence":"additional","affiliation":[{"name":"Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MICHAEL","family":"ZHU","sequence":"additional","affiliation":[{"name":"Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400874651"},{"key":"rf3","volume-title":"Dynamic Programming: Theory and Applications","author":"Denardo E.","year":"1982"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1994.1010"},{"key":"rf5","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"Garey M. R.","year":"1979"},{"key":"rf6","volume-title":"Theory of Linear and Integer Programming","author":"Schrijver A.","year":"1986"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830910000565","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:20:38Z","timestamp":1565140838000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830910000565"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":5,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2010,6]]}},"alternative-id":["10.1142\/S1793830910000565"],"URL":"https:\/\/doi.org\/10.1142\/s1793830910000565","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}