{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:24:14Z","timestamp":1740108254044,"version":"3.37.3"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72022018","71701192"],"award-info":[{"award-number":["72022018","71701192"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004739","name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["2021454"],"award-info":[{"award-number":["2021454"]}],"id":[{"id":"10.13039\/501100004739","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s00186-022-00771-3","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T21:03:20Z","timestamp":1644959000000},"page":"81-99","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lagrangian heuristic for simultaneous subsidization and penalization: implementations on rooted travelling salesman games"],"prefix":"10.1007","volume":"95","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1015-3097","authenticated-orcid":false,"given":"Lindong","family":"Liu","sequence":"first","affiliation":[]},{"given":"Yuqian","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Zikang","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"771_CR1","first-page":"119","volume":"10","author":"ON Bondareva","year":"1963","unstructured":"Bondareva ON (1963) Some applications of linear programming methods to the theory of cooperative games. Problemy Kibernetiki 10:119\u2013139","journal-title":"Problemy Kibernetiki"},{"issue":"1\u20132","key":"771_CR2","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s10107-010-0357-7","volume":"124","author":"A Caprara","year":"2010","unstructured":"Caprara A, Letchford AN (2010) New techniques for cost sharing in combinatorial optimization games. Math Program 124(1\u20132):93\u2013118","journal-title":"Math Program"},{"key":"771_CR3","unstructured":"Curiel I (2013) Cooperative game theory and applications: cooperative games arising from combinatorial optimization problems, vol 16. Springer"},{"issue":"4","key":"771_CR4","first-page":"393","volume":"2","author":"G Dantzig","year":"1954","unstructured":"Dantzig G, Fulkerson R, Johnson S (1954) Solution of a large-scale traveling-salesman problem. J Oper Res Soc Am 2(4):393\u2013410","journal-title":"J Oper Res Soc Am"},{"issue":"3","key":"771_CR5","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1002\/net.3230170309","volume":"17","author":"C Duin","year":"1987","unstructured":"Duin C, Volgenant A (1987) Some generalizations of the steiner problem in graphs. Networks 17(3):353\u2013364","journal-title":"Networks"},{"issue":"2","key":"771_CR6","first-page":"141","volume":"38","author":"U Faigle","year":"1993","unstructured":"Faigle U, Kern W (1993) On some approximately balanced combinatorial cooperative games. Zeitschrift f\u00fcr Oper Res 38(2):141\u2013152","journal-title":"Zeitschrift f\u00fcr Oper Res"},{"issue":"1","key":"771_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1287\/mnsc.27.1.1","volume":"27","author":"ML Fisher","year":"1981","unstructured":"Fisher ML (1981) The lagrangian relaxation method for solving integer programming problems. Manag Sci 27(1):1\u201318","journal-title":"Manag Sci"},{"issue":"2","key":"771_CR8","first-page":"76","volume":"50","author":"MX Goemans","year":"2000","unstructured":"Goemans MX, Skutella M (2000) Cooperative facility location games. J Algorith 50(2):76\u201385","journal-title":"J Algorith"},{"issue":"1","key":"771_CR9","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/BF01584070","volume":"1","author":"M Held","year":"1971","unstructured":"Held M, Karp RM (1971) The traveling-salesman problem and minimum spanning trees: Part ii. Math Program 1(1):6\u201325","journal-title":"Math Program"},{"key":"771_CR10","doi-asserted-by":"crossref","unstructured":"Jain K, Mahdian M (2007) Cost sharing. Nisan N, Roughgarden T, Tardos E, Vazirani V, eds. Algorithmic game theory, New York: Cambridge University Press, 385\u2013410","DOI":"10.1017\/CBO9780511800481.017"},{"issue":"3","key":"771_CR11","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1016\/j.ejor.2015.08.002","volume":"248","author":"A Kimms","year":"2016","unstructured":"Kimms A, Kozeletskyi I (2016) Core-based cost allocation in the cooperative traveling salesman problem. Eur J Oper Res 248(3):910\u2013916","journal-title":"Eur J Oper Res"},{"issue":"5","key":"771_CR12","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1057\/jors.1986.84","volume":"37","author":"JG Klincewicz","year":"1986","unstructured":"Klincewicz JG, Luss H (1986) A lagrangian relaxation heuristic for capacitated facility location with single-source constraints. J Oper Res Soc 37(5):495\u2013500","journal-title":"J Oper Res Soc"},{"issue":"3","key":"771_CR13","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/0377-2217(83)90197-2","volume":"12","author":"A Kolen","year":"1983","unstructured":"Kolen A (1983) Solving covering problems and the uncapacitated plant location problem on trees. Eur J Oper Res 12(3):266\u2013278","journal-title":"Eur J Oper Res"},{"issue":"4","key":"771_CR14","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1287\/ijoc.2016.0707","volume":"28","author":"L Liu","year":"2016","unstructured":"Liu L, Qi X, Xu Z (2016) Computing near-optimal stable cost allocations for cooperative games by Lagrangian relaxation. INFORMS J Comput 28(4):687\u2013702","journal-title":"INFORMS J Comput"},{"issue":"5","key":"771_CR15","doi-asserted-by":"publisher","first-page":"1362","DOI":"10.1287\/opre.2018.1723","volume":"66","author":"L Liu","year":"2018","unstructured":"Liu L, Qi X, Xu Z (2018) Simultaneous penalization and subsidization for stabilizing grand cooperation. Oper Res 66(5):1362\u20131735","journal-title":"Oper Res"},{"issue":"2\u20133","key":"771_CR16","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s10107-005-0660-x","volume":"105","author":"I Ljubi\u0107","year":"2006","unstructured":"Ljubi\u0107 I, Weiskircher R, Pferschy U, Klau GW, Mutzel P, Fischetti M (2006) An algorithmic framework for the exact solution of the prize-collecting steiner tree problem. Math Program 105(2\u20133):427\u2013449","journal-title":"Math Program"},{"issue":"4","key":"771_CR17","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1287\/moor.4.4.303","volume":"4","author":"M Maschler","year":"1979","unstructured":"Maschler M, Peleg B, Shapley LS (1979) Geometric properties of the kernel, nucleolus, and related solution concepts. Math Oper Res 4(4):303\u2013338","journal-title":"Math Oper Res"},{"issue":"1\u20133","key":"771_CR18","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/BF01585702","volume":"53","author":"JA Potters","year":"1992","unstructured":"Potters JA, Curiel IJ, Tijs SH (1992) Traveling salesman games. Math Program 53(1\u20133):199\u2013211","journal-title":"Math Program"},{"issue":"2","key":"771_CR19","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/j.ejor.2011.04.020","volume":"214","author":"J Puerto","year":"2011","unstructured":"Puerto J, Tamir A, Perea F (2011) A cooperative location game based on the 1-center location problem. Eur J Oper Res 214(2):317\u2013330","journal-title":"Eur J Oper Res"},{"issue":"4","key":"771_CR20","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1287\/opre.1100.0841","volume":"58","author":"AS Schulz","year":"2010","unstructured":"Schulz AS, Uhan NA (2010) Sharing supermodular costs. Oper Res 58(4):1051\u20131056","journal-title":"Oper Res"},{"issue":"1","key":"771_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/0022-0531(69)90008-8","volume":"1","author":"LS Shapley","year":"1969","unstructured":"Shapley LS, Shubik M (1969) On market games. J Econ Theory 1(1):9\u201325","journal-title":"J Econ Theory"},{"issue":"1","key":"771_CR22","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/0167-6377(89)90030-8","volume":"8","author":"A Tamir","year":"1989","unstructured":"Tamir A (1989) On the core of a traveling salesman cost allocation game. Oper Res Lett 8(1):31\u201334","journal-title":"Oper Res Lett"},{"key":"771_CR23","doi-asserted-by":"crossref","unstructured":"Woeginger GJ (2003) Exact algorithms for $$np$$-hard problems: a survey. Combinatorial optimization: Eureka, You Shrink! Heidelberg, Berlin: Springer, pp 185\u2013207","DOI":"10.1007\/3-540-36478-1_17"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-022-00771-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00186-022-00771-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-022-00771-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T12:04:10Z","timestamp":1647864250000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00186-022-00771-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["771"],"URL":"https:\/\/doi.org\/10.1007\/s00186-022-00771-3","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"type":"print","value":"1432-2994"},{"type":"electronic","value":"1432-5217"}],"subject":[],"published":{"date-parts":[[2022,2]]},"assertion":[{"value":"23 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 January 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 February 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}