{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T12:28:46Z","timestamp":1773145726078,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T00:00:00Z","timestamp":1130803200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2005,11]]},"DOI":"10.1007\/s10479-005-3972-6","type":"journal-article","created":{"date-parts":[[2005,11,26]],"date-time":"2005-11-26T07:12:53Z","timestamp":1132989173000},"page":"215-233","source":"Crossref","is-referenced-by-count":10,"title":["Some Classes of Valid Inequalities and Convex Hull Characterizations for Dynamic Fixed-Charge Problems under Nested Constraints"],"prefix":"10.1007","volume":"140","author":[{"given":"Fred","family":"Glover","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanif D.","family":"Sherali","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"3972_CR1","unstructured":"Atamturk, A. and J.C. Munoz. (2003). \u201cA Study of the Lot-Sizing Polytope.\u201d Mathematical Programming (to appear)."},{"key":"3972_CR2","first-page":"94720","volume-title":"Lot-Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation","author":"A. Atamturk","year":"2003","unstructured":"Atamturk, A. and S. Kucukyavuz. (2003). \u201cLot-Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation.\u201d Department of Industrial Engineering and Operations Research, University of California-Berkeley, CA 94720\u20131777."},{"key":"3972_CR3","doi-asserted-by":"crossref","unstructured":"Baharona, F. (1996). \u201cNetwork Design Using Cut Inequalities.\u201d SIAM Journal of Optimization, 823\u2013837.","DOI":"10.1137\/S1052623494279134"},{"key":"3972_CR4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0167-5060(08)70342-X","volume":"5","author":"E. Balas","year":"1979","unstructured":"Balas, E. (1979). \u201cDisjunctive Programming.\u201d Annals of Discrete Mathematics 5, 3\u201351.","journal-title":"Annals of Discrete Mathematics"},{"issue":"1\/2","key":"3972_CR5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0166-218X(98)00136-X","volume":"80","author":"E. Balas","year":"1998","unstructured":"Balas, E. (1998). \u201cDisjunctive Programming: Properties of the Convex Hull of Feasible Points.\u201d Discrete Applied Mathematics 80(1\/2), 3\u201344.","journal-title":"Discrete Applied Mathematics"},{"key":"3972_CR6","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1137\/1018115","volume":"18","author":"E. Balas","year":"1976","unstructured":"Balas, E. and M.W. Padberg. (1976). \u201cSet Partitioning: A Survey.\u201d SIAM Review 18, 710\u2013760.","journal-title":"SIAM Review"},{"key":"3972_CR7","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/BFb0121006","volume":"22","author":"I. Barany","year":"1984a","unstructured":"Barany, I., T.J. van Roy, and L.A. Wolsey. (1984a). \u201cUncapacitated Lot Sizing: The Convex Hull of Solutions.\u201d Mathematical Programming Study 22, 32\u201343.","journal-title":"Mathematical Programming Study"},{"key":"3972_CR8","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1287\/mnsc.30.10.1255","volume":"30","author":"I. Barany","year":"1984b","unstructured":"Barany, I., T.J. van Roy, and L.A. Wolsey. (1984b). \u201cStrong Formulations for Multi-Item Capacitated Lot-Sizing.\u201d Management Science 30, 1255\u20131261.","journal-title":"Management Science"},{"key":"3972_CR9","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1002\/nav.3800310115","volume":"31","author":"A.V. Cabot","year":"1984","unstructured":"Cabot, A.V. and S.S. Erenguc. (1984). \u201cSome Branch-and-Bound Procedures for Fixed-Cost Transportation Problems.\u201d Naval Research Logistics Quarterly 31, 145\u2013154.","journal-title":"Naval Research Logistics Quarterly"},{"key":"3972_CR10","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1287\/mnsc.23.8.789","volume":"23","author":"G. Cornuejols","year":"1977","unstructured":"Cornuejols, G., L. Fisher, and G.L. Nemhauser. (1977). \u201cLocation of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms.\u201d Management Science 23, 789\u2013810.","journal-title":"Management Science"},{"key":"3972_CR11","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0166-218X(00)00310-3","volume":"112","author":"T.G. Crainic","year":"2001","unstructured":"Crainic, T.G., A. Frangioni, and B. Gendron. (2001). \u201cBundle-based Relaxation Methods for Multicommodity Capacitated Fixed Charge Network Design.\u201d Discrete Applied Mathematics 112, 73\u201399.","journal-title":"Discrete Applied Mathematics"},{"issue":"1","key":"3972_CR12","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S0305-0548(98)80010-5","volume":"25","author":"F.R.B. Cruz","year":"1998","unstructured":"Cruz, F.R.B., J. M. Smith, and G.R. Mateus. (1998). \u201cSolving to Optimality the Uncapacitated Fixed-Charge Network Flow Problem.\u201d Computers and Operations Research 25(1), 67\u201381.","journal-title":"Computers and Operations Research"},{"issue":"8","key":"3972_CR13","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/0305-0548(94)90012-4","volume":"21","author":"F. Glover","year":"1994","unstructured":"Glover, F. (1994). \u201cOptimization by Ghost Image Processes in Neural Networks.\u201d Computers and Operations Research 21(8), 801\u2013822.","journal-title":"Computers and Operations Research"},{"key":"3972_CR14","doi-asserted-by":"crossref","DOI":"10.1002\/9781118033173","volume-title":"Network Models in Optimization and their Applications in Practice","author":"F. Glover","year":"1992","unstructured":"Glover, F., D. Klingman, and N. Phillips. (1992). Network Models in Optimization and their Applications in Practice, John Wiley & Sons, New York, NY."},{"key":"3972_CR15","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1002\/net.3230190304","volume":"19","author":"D.S. Hochbaum","year":"1989","unstructured":"Hochbaum, D.S. and A. Segev. (1989). \u201cAnalysis of a Flow Problem with Fixed Charges.\u201d Networks 19, 291\u2013312.","journal-title":"Networks"},{"key":"3972_CR16","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0167-6377(99)00004-8","volume":"24","author":"D. Kim","year":"1999","unstructured":"Kim, D. and P.M. Pardalos. (1999). A Solution Approach to the Fixed-Charge Network Flow Problem Using a Dynamic Slope Scaling Procedure.\u201d Operations Research Letters 24, 195\u2013203.","journal-title":"Operations Research Letters"},{"key":"3972_CR17","doi-asserted-by":"crossref","unstructured":"Loparic, M., H. Marchand, and L.A. Wolsey. (2003). \u201cDynamic Knapsack Sets and Capacitated Lot-Sizing.\u201d Mathematical Programming Series B 95, 53\u201369.","DOI":"10.1007\/s10107-002-0341-y"},{"key":"3972_CR18","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0166-218X(87)90021-7","volume":"18","author":"H.P.L. Luna","year":"1987","unstructured":"Luna, H.P.L., N. Ziviani, and R.M.B. Cabral. (1987). \u201cThe Telephonic Switching Centre Network Problem: Formalization and Computational Experience.\u201d Discrete Applied Mathematics 18, 199\u2013210.","journal-title":"Discrete Applied Mathematics"},{"key":"3972_CR19","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1007\/BFb0121090","volume":"26","author":"T.L. Magnanti","year":"1986","unstructured":"Magnanti, T.L., P. Mireault, and R.T. Wong. (1986). \u201cTailoring Benders Decomposition for Uncapacitated Network Design.\u201d Mathematical Programming Study 26, 112\u2013154.","journal-title":"Mathematical Programming Study"},{"key":"3972_CR20","unstructured":"Marchand, H. (1998). \u201cA Polyhedral Study of the Mixed Knapsack Set and its Use to Solve Mixed Integer Programs.\u201d Ph.D. Thesis, CORE, Belgium."},{"key":"3972_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/net.3230150102","volume":"15","author":"A. Mirzan","year":"1985","unstructured":"Mirzan, A. (1985). \u201cLagrangian Relaxation for the Star-Star Concentrator Location Problem: Approximation Algorithm and Bounds.\u201d Networks 15, 1\u201320.","journal-title":"Networks"},{"key":"3972_CR22","doi-asserted-by":"crossref","DOI":"10.1002\/9781118627372","volume-title":"Integer and Combinatorial Optimization","author":"G.L. Nemhauser","year":"1988","unstructured":"Nemhauser, G.L. and L.A. Wolsey. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, Inc., New York, NY."},{"key":"3972_CR23","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S1366-5545(00)00018-1","volume":"37","author":"L. Nozick","year":"2001","unstructured":"Nozick, L. (2001). \u201cThe Fixed Charge Facility Location Problem with Coverage Restrictions.\u201d Transportation Research E 37, 281\u2013296.","journal-title":"Transportation Research E"},{"key":"3972_CR24","unstructured":"Nozick, L. and M. Turnquist. (1998a). \u201cTwo-Echelon Inventory Allocation and Distribution Center Location Analysis.\u201d In Proceedings of Tristan III (Transportation Science Section of INFORMS), San Juan, Puerto Rico."},{"issue":"3","key":"3972_CR25","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S1366-5545(98)00010-6","volume":"31","author":"L. Nozick","year":"1998b","unstructured":"Nozick, L. and M. Turnquist. (1998b). \u201cIntegrating Inventory Impacts into a Fixed Charge Model for Locating Distribution Centers.\u201d Transportation Research Part E 31(3), 173\u2013186.","journal-title":"Transportation Research Part E"},{"issue":"4","key":"3972_CR26","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1287\/opre.33.4.842","volume":"33","author":"M.W. Padberg","year":"1985","unstructured":"Padberg, M.W., T.J. van Roy, and L.A. Wolsey. (1985). \u201cValid Linear Inequalities for Fixed Charge Problems.\u201d Operations Research 33(4), 842\u2013861.","journal-title":"Operations Research"},{"issue":"3","key":"3972_CR27","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0167-6377(88)90076-4","volume":"7","author":"Y. Pochet","year":"1988","unstructured":"Pochet, Y. (1988). \u201cValid Inequalities and Separation for Capacitated Economic Lot Sizing.\u201d Operations Research Letters 7(3), 109\u2013115.","journal-title":"Operations Research Letters"},{"key":"3972_CR28","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1090\/dimacs\/020\/05","volume":"20","author":"Y. Pochet","year":"1995","unstructured":"Pochet, Y. and L.A. Wolsey. (1995). \u201cAlgorithms and Reformulations for Lot-Sizing Problems.\u201d In DIMACS Series in Discrete Mathematics and Theoretical Computer Science 20, 245\u2013293.","journal-title":"DIMACS Series in Discrete Mathematics and Theoretical Computer Science"},{"key":"3972_CR29","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1287\/opre.18.6.992","volume":"18","author":"B. Rothfarb","year":"1970","unstructured":"Rothfarb, B., H. Frank, D.M. Rosembaun, and K. Steiglitz. (1970). \u201cOptimal Design of Offshore Natural-Gas Pipeline Systems.\u201d Operations Research 18, 992\u20131020.","journal-title":"Operations Research"},{"issue":"3","key":"3972_CR30","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"H.D. Sherali","year":"1990","unstructured":"Sherali, H.D. and W.P. Adams. (1990). \u201cA Hierarchy of Relaxations Between the Continuous and Convex Hull Representations for Zero-One Programming Problems.\u201d SIAM Journal on Discrete Mathematics 3(3), 411\u2013430.","journal-title":"SIAM Journal on Discrete Mathematics"},{"key":"3972_CR31","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0166-218X(92)00190-W","volume":"52","author":"H.D. Sherali","year":"1994","unstructured":"Sherali, H.D. and W.P. Adams. (1994). \u201cA Hierarchy of Relaxations and Convex Hull Characterizations for Mixed-Integer Zero-One Programming Problems.\u201d Discrete Applied Mathematics 52, 83\u2013106.","journal-title":"Discrete Applied Mathematics"},{"issue":"3","key":"3972_CR32","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1287\/opre.46.3.396","volume":"46","author":"H.D. Sherali","year":"1998","unstructured":"Sherali, H.D., W.P. Adams, and P.J. Driscoll. (1998). \u201cExploiting Special Structures in Constructing a Hierarchy of Relaxations for 0-1 Mixed Integer Problems.\u201d Operations Research 46(3), 396\u2013405.","journal-title":"Operations Research"},{"issue":"1","key":"3972_CR33","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0167-6377(94)00065-E","volume":"17","author":"H.D. Sherali","year":"1995","unstructured":"Sherali, H.D., Y. Lee, and W.P. Adams. (1995). \u201cA Simultaneous Lifting Strategy for Identifying New Classes of Facets for the Boolean Quadric Polytope.\u201d Operations Research Letters 17(1), 19\u201326.","journal-title":"Operations Research Letters"},{"key":"3972_CR34","doi-asserted-by":"crossref","unstructured":"Sherali, H.D. and C.M. Shetty. (1980). Optimization with Disjunctive Constraints. Series in Economics and Mathematical Systems, Springer-Verlag, Berlin-Heidelberg-New York Vol. 181.","DOI":"10.1007\/978-3-642-48794-1"},{"key":"3972_CR35","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0166-218X(99)00164-X","volume":"98","author":"J. Stallaert","year":"2000","unstructured":"Stallaert, J. (2000). \u201cValid Inequalities and Separation for Capacitated Fixed Charge Flow Problems.\u201d Discrete Applied Mathematics 98, 265\u2013274.","journal-title":"Discrete Applied Mathematics"},{"key":"3972_CR36","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF01586089","volume":"32","author":"U. Suhl","year":"1985","unstructured":"Suhl, U. (1985). \u201cSolving Large Scale Mixed Integer Programs with Fixed-Charge Variables.\u201d Mathematical Programming 32, 165\u2013182.","journal-title":"Mathematical Programming"},{"key":"3972_CR37","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/S0377-2217(97)00284-1","volume":"106","author":"M. Sun","year":"1998","unstructured":"Sun, M., J.E. Aronson, P.G. McKeown, and D. Drinka. (1998). \u201cA Tabu Search Heuristic Procedure for the Fixed Charge Transportation Problem.\u201d European Journal of Operational Research 106, 441\u2013456.","journal-title":"European Journal of Operational Research"},{"key":"3972_CR38","unstructured":"Van Vyve, M. and F. Ortega. (2003). \u201cLot-sizing with Fixed Charges on Stocks: The Convex Hull.\u201d CORE DP 2003\/14, Universite Catholique de Louvain, Louvainla-Neuve."},{"key":"3972_CR39","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0167-6377(89)90036-9","volume":"8","author":"L.A. Wolsey","year":"1989","unstructured":"Wolsey, L.A. (1989). \u201cSubmodularity and Valid Inequalities in Capacitated Fixed Charge Networks.\u201d Operations Research Letters 8, 119\u2013124.","journal-title":"Operations Research Letters"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-005-3972-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-005-3972-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-005-3972-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T13:59:35Z","timestamp":1559138375000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-005-3972-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,11]]}},"alternative-id":["3972"],"URL":"https:\/\/doi.org\/10.1007\/s10479-005-3972-6","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,11]]}}}