{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T21:17:01Z","timestamp":1777151821125,"version":"3.51.4"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1989,5,1]],"date-time":"1989-05-01T00:00:00Z","timestamp":609984000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1989,5]]},"DOI":"10.1007\/bf01587077","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T05:09:28Z","timestamp":1114664968000},"page":"67-75","source":"Crossref","is-referenced-by-count":10,"title":["Marginal values in mixed integer linear programming"],"prefix":"10.1007","volume":"44","author":[{"given":"A. C.","family":"Williams","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"CR1","volume-title":"Topological Spaces","author":"C. Berge","year":"1963","unstructured":"C. Berge,Topological Spaces (Macmillan, New York, 1963)."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF01583794","volume":"3","author":"C.E. Blair","year":"1982","unstructured":"C.E. Blair and R.G. Jeroslow, \u201cThe value function of an integer program,\u201dMathematical programming 3 (1982) 237\u2013273.","journal-title":"Mathematical programming"},{"key":"CR3","volume-title":"Theory of Value, Cowles Foundation Monograph No. 17","author":"G. Debreu","year":"1959","unstructured":"G. Debreu,Theory of Value, Cowles Foundation Monograph No. 17 (John Wiley, New York, 1959)."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1287\/opre.14.3.361","volume":"14","author":"M.A. Efroymson","year":"1966","unstructured":"M.A. Efroymson and T.L. Ray, \u201cA branch and bound algorithm for plant location,\u201dOperations Research 14 (1966) 361\u2013368.","journal-title":"Operations Research"},{"key":"CR5","doi-asserted-by":"crossref","unstructured":"A.M. Geoffrion and R. Nauss. \u201cParametric and postoptimality analysis in integer linear programming,\u201dManagement Science 23 (1977).","DOI":"10.1287\/mnsc.23.5.453"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1137\/1015073","volume":"15","author":"William W. Hogan","year":"1973","unstructured":"William W. Hogan. \u201cPoint to set maps in mathematical programming,\u201dSIAM Review 15 (1973) 591\u2013603.","journal-title":"SIAM Review"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01588222","volume":"17","author":"R.G. Jeroslow","year":"1979","unstructured":"R.G. Jeroslow, \u201cMinimal inequalities,\u201dMathematical Programming 17 (1979) 1\u201315.","journal-title":"Mathematical Programming"},{"key":"CR8","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BFb0120692","volume":"2","author":"E.L. Johnson","year":"1974","unstructured":"E.L. Johnson \u201cOn the group problem for mixed integer programming,\u201dMathematical Programming Study 2 (1974) 137\u2013179.","journal-title":"Mathematical Programming Study"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1137\/0308003","volume":"8","author":"R. Meyer","year":"1970","unstructured":"R. Meyer. \u201cThe validity of a family of optimization methods,\u201dSIAM Journal of Control 8 (1970) 41\u201354.","journal-title":"SIAM Journal of Control"},{"key":"CR10","first-page":"183","volume-title":"Linear Inequalities and Related Systems","author":"H.D. Mills","year":"1956","unstructured":"H.D. Mills, \u201cMarginal values of matrix games and linear programs,\u201d in: H.W. Kuhn and A.W. Tucker, ed,Linear Inequalities and Related Systems (Princeton University Press, Princeton, N.J., 1956) pp. 183\u2013193."},{"key":"CR11","doi-asserted-by":"crossref","DOI":"10.21236\/ADA006401","volume-title":"Parametric Integer Programming","author":"R.M. Nauss","year":"1975","unstructured":"R.M. Nauss,Parametric Integer Programming, Ph.D. Thesis (University of California, Los Angeles, January 1975)."},{"key":"CR12","volume-title":"Sensitivity Analysis in Discrete Optimization","author":"M.A. Radke","year":"1975","unstructured":"M.A. Radke,Sensitivity Analysis in Discrete Optimization, Ph.D. Thesis (University of California, Los Angeles, September 1975)."},{"key":"CR13","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"R.T. Rockafellar,Convex Analysis (Princeton University Press, Princeton, N.J., 1970)."},{"key":"CR14","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BFb0121219","volume":"21","author":"R.T. Rockafellar","year":"1984","unstructured":"R.T. Rockafellar, \u201cDirectional differentiability of the optimal value function in a non-linear program,\u201dMathematical Programming Study 21 (1984) 213\u2013226.","journal-title":"Mathematical Programming Study"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BFb0121040","volume":"24","author":"Roger J.-B. Wets","year":"1985","unstructured":"Roger J.-B. Wets, \u201cOn the continuity of the value of a linear program and of related polyhedral-valued multifunctions,\u201dMathematical programming Study 24 (1985) 14\u201329.","journal-title":"Mathematical programming Study"},{"key":"CR16","first-page":"82","volume":"11","author":"A.C. Williams","year":"1963","unstructured":"A.C. Williams, \u201cMarginal values in linear programming,\u201dJournal of SIAM 11 (1963) 82\u201394.","journal-title":"Journal of SIAM"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1137\/1012015","volume":"12","author":"A.C. Williams","year":"1970","unstructured":"A.C. Williams, \u201cComplementarity theorems for linear programming,\u201dSIAM Review 12 (1970) 135\u2013137.","journal-title":"SIAM Review"},{"key":"CR18","volume-title":"\u201cSensitivity to data in LP and MIP,\u201d Presented at the8th Symposium on Mathematical Programming","author":"A.C. Williams","year":"1973","unstructured":"A.C. Williams, \u201cSensitivity to data in LP and MIP,\u201d Presented at the8th Symposium on Mathematical Programming (Stanford, Calif., 1973)."},{"key":"CR19","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01589344","volume":"20","author":"Laurence A. Wolsey","year":"1981","unstructured":"Laurence A. Wolsey, \u201cInteger programming duality: Price functions and sensitivity analysis,\u201dMathematical Programming 20 (1981) 173\u2013195.","journal-title":"Mathematical Programming"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01587077.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01587077\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01587077","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T11:31:37Z","timestamp":1556883097000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01587077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,5]]},"references-count":19,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1989,5]]}},"alternative-id":["BF01587077"],"URL":"https:\/\/doi.org\/10.1007\/bf01587077","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,5]]}}}