{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:35:25Z","timestamp":1759847725810},"reference-count":86,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1989,8,1]],"date-time":"1989-08-01T00:00:00Z","timestamp":617932800000},"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":[[1989,8]]},"DOI":"10.1007\/bf01589110","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T08:22:34Z","timestamp":1114676554000},"page":"331-359","source":"Crossref","is-referenced-by-count":72,"title":["Facets and algorithms for capacitated lot sizing"],"prefix":"10.1007","volume":"45","author":[{"given":"Janny M. Y.","family":"Leung","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas L.","family":"Magnanti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rita","family":"Vachani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/0377-2217(82)90176-X","volume":"9","author":"S. Axs\u00e4ter","year":"1982","unstructured":"S. Axs\u00e4ter, \u201cWorst case performance for lot sizing heuristics,\u201dEuropean Journal of Operational Research 9 (1982) 339\u2013343.","journal-title":"European Journal of Operational Research"},{"key":"CR2","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1287\/mnsc.31.5.634","volume":"31","author":"S. Axs\u00e4ter","year":"1985","unstructured":"S. Axs\u00e4ter, \u201cPerformance bounds for lot sizing heuristics,\u201dManagement Science 31 (1985) 634\u2013640.","journal-title":"Management Science"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"1710","DOI":"10.1287\/mnsc.24.16.1710","volume":"24","author":"K.R. Baker","year":"1978","unstructured":"K.R. Baker, P. Dixon, M.J. Magazine and E.A. Silver, \u201cAn algorithm for the dynamic lot-size problem with time-varying production capacity constraints,\u201dManagement Science 24 (1978) 1710\u20131720.","journal-title":"Management Science"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF02592077","volume":"39","author":"A. Balakrishnan","year":"1987","unstructured":"A. Balakrishnan, \u201cLP extreme points and cuts for the fixed charge network design problem,\u201dMathematical Programming 39 (1987) 263\u2013284.","journal-title":"Mathematical Programming"},{"key":"CR5","unstructured":"A. Balakrishnan and T.L. Magnanti, \u201cSet packing-based cuts for the fixed charge network design problem,\u201dBulletin 20, ORSA\/TIMS, Atlanta (1985) 51."},{"key":"CR6","unstructured":"E. Balas, \u201cOn the facial structure of scheduling polyhedra, \u201cManagement Science Research Report No. 496(R), Graduate School of Industrial Administration, Carnegie-Mellon University (1984)."},{"key":"CR7","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1137\/1018115","volume":"18","author":"E. Balas","year":"1976","unstructured":"E. Balas and M.W. Padberg, \u201cSet partitioning: A survey,\u201dSIAM Review 18 (1976) 710\u2013760.","journal-title":"SIAM Review"},{"key":"CR8","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1287\/moor.2.1.15","volume":"2","author":"E. Balas","year":"1977","unstructured":"E. Balas and E. Zemel, \u201cCritical cutsets of graphs and canonical facets of set-packing polytopes,\u201dMathematics of Operations Research 2 (1977) 15\u201319.","journal-title":"Mathematics of Operations Research"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1002\/nav.3800080104","volume":"8","author":"M.L. Balinski","year":"1961","unstructured":"M.L. Balinski, \u201cFixed-cost transportation problems,\u201dNaval Research Logistics Quarterly 8 (1961) 41\u201354.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/BFb0121006","volume":"22","author":"I. Barany","year":"1984","unstructured":"I. Barany, T.J. Van Roy and L.A. Wolsey, \u201cUncapacitated lot-sizing: The convex hull of solutions,\u201dMathematical Programming Study 22 (1984a) 32\u201343.","journal-title":"Mathematical Programming Study"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1287\/mnsc.30.10.1255","volume":"30","author":"I. Barany","year":"1984","unstructured":"I. Barany, T.J. Van Roy and L.A. Wolsey, \u201cStrong formulations for multi-item capacitated lot sizing,\u201dManagement Science 30 (1984b) 1255\u20131261.","journal-title":"Management Science"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1287\/mnsc.30.9.1121","volume":"30","author":"G.R. Bitran","year":"1984","unstructured":"G.R. Bitran, T.L. Magnanti and H.H. Yanasse, \u201cApproximation methods for the uncapacitated dynamic lot size problem,\u201dManagement Science 30 (1984) 1121\u20131140.","journal-title":"Management Science"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1287\/opre.34.1.63","volume":"34","author":"G.R. Bitran","year":"1986","unstructured":"G.R. Bitran and H. Matsuo, \u201cApproximation formulations for the single-product capacitated lot size problem,\u201dOperations Research 34 (1986a) 63\u201374.","journal-title":"Operations Research"},{"key":"CR14","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1287\/mnsc.32.3.350","volume":"32","author":"G.R. Bitran","year":"1986","unstructured":"G.R. Bitran and H. Matsuo, \u201cThe multi-item capacitated lot size problem: Error bounds of Manne's formulations,\u201dManagement Science 32 (1986b) 350\u2013359.","journal-title":"Management Science"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1287\/mnsc.28.10.1174","volume":"28","author":"G.R. Bitran","year":"1982","unstructured":"G.R. Bitran and H.H. Yanasse, \u201cComputational complexity of the capacitated lot size problem,\u201dManagement Science 28 (1982) 1174\u20131186.","journal-title":"Management Science"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1287\/moor.8.4.579","volume":"8","author":"D.C. Cho","year":"1983","unstructured":"D.C. Cho, E.L. Johnson, M.W. Padberg and M.R. Rao, \u201cOn the uncapacitated plant location problem I: Valid inequalities and facets,\u201dMathematics of Operations Research 8 (1983a) 579\u2013589.","journal-title":"Mathematics of Operations Research"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1287\/moor.8.4.590","volume":"8","author":"D.C. Cho","year":"1983","unstructured":"D.C. Cho, M.W. Padberg and M.R. Rao, \u201cOn the uncapacitated plant location problem II: Facets and lifting theorems,\u201dMathematics of Operations Research 8 (1983b) 590\u2013612.","journal-title":"Mathematics of Operations Research"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0012-365X(73)90167-2","volume":"4","author":"V. Chv\u00e1tal","year":"1973","unstructured":"V. Chv\u00e1tal, \u201cEdmonds polytopes and a hierarchy of combinatorial problems,\u201dDiscrete Mathematics 4 (1973) 305\u2013337.","journal-title":"Discrete Mathematics"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/0095-8956(75)90041-6","volume":"18","author":"V. Chv\u00e1tal","year":"1975","unstructured":"V. Chv\u00e1tal, \u201cOn certain polytopes associated with graphs,\u201dJournal of Combinatorial Theory B 18 (1975) 138\u2013154.","journal-title":"Journal of Combinatorial Theory B"},{"key":"CR20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1002\/nav.3800140110","volume":"14","author":"L. Cooper","year":"1967","unstructured":"L. Cooper and C. Drebes, \u201cAn approximate solution method for the fixed charge problem,\u201dNaval Research Logistics Quarterly 14 (1967) 101\u2013113.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR21","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/BF01583779","volume":"23","author":"G. Cornuejols","year":"1982","unstructured":"G. Cornuejols and J-M. Thizy, \u201cSome facets of the simple plant location polytope,\u201dMathematical Programming 23 (1982) 50\u201374.","journal-title":"Mathematical Programming"},{"key":"CR22","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1287\/opre.31.5.803","volume":"31","author":"H. Crowder","year":"1983","unstructured":"H. Crowder, E.L. Johnson and M.W. Padberg, \u201cSolving large-scale zero\u2013one linear programming problems,\u201dOperations Research 31 (1983) 803\u2013834.","journal-title":"Operations Research"},{"key":"CR23","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1287\/mnsc.26.5.495","volume":"26","author":"H. Crowder","year":"1980","unstructured":"H. Crowder and M.W. Padberg, \u201cSolving large-scale symmetric travelling salesman problems to optimality,\u201dManagement Science 26 (1980) 495\u2013509.","journal-title":"Management Science"},{"key":"CR24","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/nav.3800160311","volume":"16","author":"D.R. Danzler","year":"1969","unstructured":"D.R. Danzler, \u201cAn approximate algorithm for the fixed charge problem,\u201dNaval Research Logistics Quarterly 16 (1969) 411\u2013416.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0272-6963(81)90033-4","volume":"2","author":"P.S. Dixon","year":"1981","unstructured":"P.S. Dixon and E.A. Silver, \u201cA heuristic solution procedure for the multi-item, single level, limited capacity, log sizing problem,\u201dJournal of Operations Management 2 (1981) 23\u201329.","journal-title":"Journal of Operations Management"},{"key":"CR26","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1080\/05695558108974565","volume":"13","author":"A. Dogramaci","year":"1981","unstructured":"A. Dogramaci, J.E. Panayiotopoulos and N.R. Adam, \u201cThe dynamic lot sizing problem for multiple items under limited capacity,\u201dAIIE Transactions 13 (1981) 294\u2013303.","journal-title":"AIIE Transactions"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1287\/mnsc.9.2.229","volume":"9","author":"B.P. Dzielinski","year":"1963","unstructured":"B.P. Dzielinski, C.T. Baker and A.S. Manne, \u201cSimulation tests of lot size programming,\u201dManagement Science 9 (1963) 229\u2013258.","journal-title":"Management Science"},{"key":"CR28","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1287\/mnsc.11.9.874","volume":"11","author":"B.P. Dzielinski","year":"1965","unstructured":"B.P. Dzielinski and R.E. Gomory, \u201cOptimal programming of lot sizes, inventory and labor allocations,\u201dManagement Science 11 (1965) 874\u2013890.","journal-title":"Management Science"},{"key":"CR29","doi-asserted-by":"crossref","first-page":"125","DOI":"10.6028\/jres.069B.013","volume":"69","author":"J. Edmonds","year":"1965","unstructured":"J. Edmonds, \u201cMaximum matching and a polyhedron with 0, 1-vertices,\u201dJournal of Research of the National Bureau of Standards. Section B 69 (1965) 125\u2013130.","journal-title":"Journal of Research of the National Bureau of Standards. Section B"},{"key":"CR30","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1287\/mnsc.15.5.268","volume":"15","author":"G.D. Eppen","year":"1969","unstructured":"G.D. Eppen, F.J. Gould and B.P. Pashigian, \u201cExtensions of the planning horizon theorem in the dynamic lot size model,\u201dManagement Science 15 (1969) 268\u2013277.","journal-title":"Management Science"},{"key":"CR31","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1287\/opre.35.6.832","volume":"35","author":"G.D. Eppen","year":"1987","unstructured":"G.D. Eppen and R.K. Martin, \u201cSolving multi-item capacitated lot sizing problems using variable redefinition,\u201dOperations Research 35 (1987) 832\u2013848.","journal-title":"Operations Research"},{"key":"CR32","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1287\/mnsc.18.1.12","volume":"18","author":"M. Florian","year":"1971","unstructured":"M. Florian and M. Klein, \u201cDeterministic production planning with concave costs and capacity constraints,\u201dManagement Science 18 (1971) 12\u201320.","journal-title":"Management Science"},{"key":"CR33","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1287\/mnsc.26.7.669","volume":"26","author":"M. Florian","year":"1980","unstructured":"M. Florian, J.K. Lenstra and A.H.G. Rinnooy Kan, \u201cDeterministic production planning: algorithms and complexity,\u201dManagement Science 26 (1980) 669\u2013679.","journal-title":"Management Science"},{"key":"CR34","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"M.R. Garey","year":"1979","unstructured":"M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, CA, 1979)."},{"key":"CR35","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1287\/mnsc.28.3.260","volume":"28","author":"S.C. Graves","year":"1982","unstructured":"S.C. Graves, \u201cUsing Lagrangean techniques to solve hierarchical production planning problems,\u201dManagement Science 28 (1982) 260\u2013275.","journal-title":"Management Science"},{"key":"CR36","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1287\/opre.19.6.1529","volume":"19","author":"P. Gray","year":"1971","unstructured":"P. Gray, \u201cExact solution of the fixed-charge transportation problem,\u201dOperations Research 19 (1971) 1529\u20131538.","journal-title":"Operations Research"},{"key":"CR37","volume-title":"Combinatorial Optimization: Annotated Bibliographies","author":"M. Gr\u00f6tschel","year":"1985","unstructured":"M. Gr\u00f6tschel, \u201cPolyhedral combinatorics,\u201d in: M. O'hEigeartaigh, J.K. Lenstra and A.H.G. Rinnooy Kan, eds.,Combinatorial Optimization: Annotated Bibliographies (Wiley Interscience, New York, 1985)."},{"key":"CR38","volume-title":"\u201cSolving matching problems with linear programming,\u201d Preprint No. 37","author":"M. Gr\u00f6tschel","year":"1984","unstructured":"M. Gr\u00f6tschel and O. Holland, \u201cSolving matching problems with linear programming,\u201d Preprint No. 37, Mathematisches Institut, Universitat Augsburg (Augsburg, FRG, 1984)."},{"key":"CR39","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1287\/opre.32.6.1195","volume":"32","author":"M. Gr\u00f6tschel","year":"1984","unstructured":"M. Gr\u00f6tschel, M. J\u00fcnger and G. Reinelt, \u201cA cutting plane algorithm for the linear ordering problem,\u201dOperations Research 32 (1984) 1195\u20131220.","journal-title":"Operations Research"},{"key":"CR40","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01582010","volume":"33","author":"M. Gr\u00f6tschel","year":"1985","unstructured":"M. Gr\u00f6tschel, M. J\u00fcnger and G. Reinelt, \u201cFacets for the linear ordering problem,\u201dMathematical Programming 33 (1985) 43\u201360.","journal-title":"Mathematical Programming"},{"key":"CR41","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF02579273","volume":"1","author":"M. Gr\u00f6tschel","year":"1981","unstructured":"M. Gr\u00f6tschel, L. Lovasz and A. Schrijver, \u201cThe consequences of the ellipsoid method for combinatorial optimization,\u201dCombinatorica 1 (1981) 169\u2013198.","journal-title":"Combinatorica"},{"key":"CR42","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF01582116","volume":"16","author":"M. Gr\u00f6tschel","year":"1979","unstructured":"M. Gr\u00f6tschel and M.W. Padberg, \u201cOn the symmetric travelling salesman problem I: Inequalities,\u201dMathematical Programming 16 (1979a) 265\u2013280.","journal-title":"Mathematical Programming"},{"key":"CR43","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF01582117","volume":"16","author":"M. Gr\u00f6tschel","year":"1979","unstructured":"M. Gr\u00f6tschel and M.W. Padberg, \u201cOn the symmetric travelling salesman problem II: Lifting theorems and facets, \u201cMathematical Programming 16 (1979b) 281\u2013302.","journal-title":"Mathematical Programming"},{"key":"CR44","volume-title":"Production and Inventory Management","author":"A.C. Hax","year":"1984","unstructured":"A.C. Hax and C. Candea,Production and Inventory Management (Prentice-Hall, Englewood Cliffs, NJ, 1984)."},{"key":"CR45","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF02022040","volume":"4","author":"K. Hoffman","year":"1985","unstructured":"K. Hoffman and M.W. Padberg, \u201cLP-based combinatorial problem solving,\u201dAnnals of Operations Research 4 (1985) 145\u2013194.","journal-title":"Annals of Operations Research"},{"key":"CR46","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1287\/mnsc.19.11.1295","volume":"19","author":"R. Jagannathan","year":"1973","unstructured":"R. Jagannathan and M.R. Rao, \u201cA class of deterministic production planning problems,\u201dManagement Science 19 (1973) 1295\u20131300.","journal-title":"Management Science"},{"key":"CR47","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1287\/opre.33.4.803","volume":"33","author":"E.L. Johnson","year":"1985","unstructured":"E.L. Johnson, M.M. Kostreva and H.H. Suhl, \u201cSolving 0\u20131 integer programming problems arising from large scale planning models,\u201dOperations Research 33 (1985) 803\u2013820.","journal-title":"Operations Research"},{"key":"CR48","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1287\/mnsc.16.1.67","volume":"16","author":"A.P. Jones","year":"1969","unstructured":"A.P. Jones and R.M. Soland, \u201cA branch-and-bound algorithm for multi-level fixed-charge problems,\u201dManagement Science 16 (1969) 67\u201376.","journal-title":"Management Science"},{"key":"CR49","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1287\/opre.20.4.860","volume":"20","author":"B.A. Kalymon","year":"1972","unstructured":"B.A. Kalymon, \u201cA decomposition algorithm for arborescence inventory systems,\u201dOperations Research 20 (1972) 860\u2013874.","journal-title":"Operations Research"},{"key":"CR50","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1137\/0211053","volume":"11","author":"R.M. Karp","year":"1982","unstructured":"R.M. Karp and C.H. Papadimitriou, \u201cOn linear characterization of combinatorial optimization,\u201dSIAM Journal of Computing 11 (1982) 620\u2013632.","journal-title":"SIAM Journal of Computing"},{"key":"CR51","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1287\/opre.23.2.299","volume":"23","author":"P.R. Kleindorfer","year":"1975","unstructured":"P.R. Kleindorfer and E.F.P. Newson, \u201cA lower bounding structure for lot size scheduling problems,\u201dOperations Research 23 (1975) 299\u2013311.","journal-title":"Operations Research"},{"key":"CR52","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1002\/nav.3800150212","volume":"15","author":"K.O. Kortanek","year":"1968","unstructured":"K.O. Kortanek, D. Sodaro and A.L. Soyster, \u201cMulti-product production scheduling via extreme point properties of linear programming,\u201dNaval Research Logistics Quarterly 15 (1968) 287\u2013300.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR53","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/0377-2217(78)90109-1","volume":"2","author":"M. Lambrecht","year":"1978","unstructured":"M. Lambrecht and J. Vander Eecken, \u201cA capacity constrained single-facility dynamic lot-size model,\u201dEuropean Journal of Operational Research 2 (1978) 132\u2013136.","journal-title":"European Journal of Operational Research"},{"key":"CR54","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/05695557908974478","volume":"11","author":"M. Lambrecht","year":"1979","unstructured":"M. Lambrecht and H. Vanderveken, \u201cHeuristic procedure for the single operation multi-item loading problem,\u201dAIIE Transactions 11 (1979) 319\u2013326.","journal-title":"AIIE Transactions"},{"key":"CR55","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1287\/opre.19.4.946","volume":"19","author":"L.S. Lasdon","year":"1971","unstructured":"L.S. Lasdon and R.C. Terjung, \u201cAn efficient algorithm for multi-item scheduling,\u201dOperations Research 19 (1971) 946\u2013969.","journal-title":"Operations Research"},{"key":"CR56","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/BF01587093","volume":"44","author":"J.M.Y. Leung","year":"1989","unstructured":"J.M.Y. Leung and T.L. Magnanti, \u201cValid inequalities and facets of the capacitated plant location problem,\u201dMathematical Programming 44 (1989) 271\u2013292.","journal-title":"Mathematical Programming"},{"key":"CR57","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1287\/mnsc.20.3.313","volume":"20","author":"S.F. Love","year":"1973","unstructured":"S.F. Love \u201cBounded production and inventory models with piecewise concave costs,\u201dManagement Science 20 (1973) 313\u2013318.","journal-title":"Management Science"},{"key":"CR58","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1080\/07408178608975338","volume":"18","author":"J. Maes","year":"1986","unstructured":"J. Maes and L.N. Van Wassenhove, \u201cMulti item single level capacitated dynamic lotsizing heuristics: A computational comparison (Part I: Static case),\u201dIIE Transactions 18 (1986a) 114\u2013123.","journal-title":"IIE Transactions"},{"key":"CR59","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1080\/07408178608975339","volume":"18","author":"J. Maes","year":"1986","unstructured":"J. Maes and L.N. Van Wassenhove, \u201cMulti item single level capacitated dynamic lot sizing heuristics: A computational comparison (Part II: Rolling horizon),\u201dIIE Transactions 18 (1986b) 124\u2013129.","journal-title":"IIE Transactions"},{"key":"CR60","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1287\/mnsc.4.2.115","volume":"4","author":"A.S. Manne","year":"1958","unstructured":"A.S. Manne, \u201cProgramming of economic lot sizes,\u201dManagement Science 4 (1958) 115\u2013135.","journal-title":"Management Science"},{"key":"CR61","volume-title":"Constraint Aggregation and Coefficient Reduction Cuts for Mixed-0\/1 linear Programming","author":"R.K. Martin","year":"1986","unstructured":"R.K. Martin and L. Schrage, \u201cConstraint Aggregation and Coefficient Reduction Cuts for Mixed-0\/1 linear Programming,\u201d Graduate School of Business, University of Chicago (Chicago, IL, 1986)."},{"key":"CR62","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1287\/opre.16.2.268","volume":"16","author":"K.G. Murty","year":"1968","unstructured":"K.G. Murty \u201cSolving the fixed charge problem by ranking the extreme points,\u201dOperations Research 16 (1968) 268\u2013279.","journal-title":"Operations Research"},{"key":"CR63","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/BF01580222","volume":"6","author":"G.L. Nemhauser","year":"1974","unstructured":"G.L. Nemhauser and L.E. Trotter, \u201cProperties of vertex packing and independence system polyhedra,\u201dMathematical Programming 6 (1974) 48\u201361.","journal-title":"Mathematical Programming"},{"key":"CR64","unstructured":"G.L. Nemhauser and L.A. Wolsey, \u201cA recursive procedure for generating all mixed integer cuts,\u201dBulletin 20, ORSA\/TIMS, Atlanta (1985) 137."},{"key":"CR65","doi-asserted-by":"crossref","DOI":"10.1002\/9781118627372","volume-title":"Integer and Combinatorial Optimization","author":"G.L. Nemhauser","year":"1988","unstructured":"G.L. Nemhauser and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley\/Interscience, New York, 1988)."},{"key":"CR66","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1287\/mnsc.21.10.1086","volume":"21","author":"E.F.P. Newson","year":"1975","unstructured":"E.F.P. Newson, \u201cMulti-item lot size scheduling by heuristic. Part I: With fixed resources,\u201dManagement Science 21 (1975) 1186\u20131193.","journal-title":"Management Science"},{"key":"CR67","volume-title":"Material Requirements Planning: The New Way of Life in Production and Inventory Management","author":"J. Orlicky","year":"1974","unstructured":"J. Orlicky,Material Requirements Planning: The New Way of Life in Production and Inventory Management (McGraw-Hill, New York, 1974)."},{"key":"CR68","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF01580121","volume":"5","author":"M.W. Padberg","year":"1973","unstructured":"M.W. Padberg, \u201cOn the facial structure of set packing polyhedra,\u201dMathematical Programming 5 (1973) 199\u2013215.","journal-title":"Mathematical Programming"},{"key":"CR69","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/S0167-5060(08)70831-8","volume":"4","author":"M.W. Padberg","year":"1979","unstructured":"M.W. Padberg, \u201cCovering, packing and knapsack problems,\u201dAnnals of Discrete Mathematics 4 (1979) 265\u2013287.","journal-title":"Annals of Discrete Mathematics"},{"key":"CR70","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/BFb0120888","volume":"12","author":"M.W. Padberg","year":"1980","unstructured":"M.W. Padberg and S. Hong, \u201cOn the symmetric travelling salesman problem: A computational study,\u201dMathematical Programming Study 12 (1980) 78\u2013107.","journal-title":"Mathematical Programming Study"},{"key":"CR71","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1287\/moor.7.1.67","volume":"7","author":"M.W. Padberg","year":"1982","unstructured":"M.W. Padberg and M.R. Rao, \u201cOdd minimum cut-sets andb-matchings,\u201dMathematics of Operations Research 7 (1982) 67\u201380.","journal-title":"Mathematics of Operations Research"},{"key":"CR72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-6377(87)90002-2","volume":"6","author":"M.W. Padberg","year":"1987","unstructured":"M.W. Padberg and G. Rinaldi, \u201cOptimization of a 532-city symmetric traveling salesman problem by branch and cut,\u201dOperations Research Letters 6 (1987) 1\u20138.","journal-title":"Operations Research Letters"},{"key":"CR73","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1287\/opre.33.4.842","volume":"33","author":"M.W. Padberg","year":"1985","unstructured":"M.W. Padberg, T.J. Van Roy and L.A. Wolsey, \u201cValid linear inequalities for fixed charge problems,\u201dOperations Research 33 (1985) 842\u2013861.","journal-title":"Operations Research"},{"key":"CR74","volume-title":"Decision Systems for Inventory Management and Production Planning","author":"R. Peterson","year":"1979","unstructured":"R. Peterson and E.A. Silver,Decision Systems for Inventory Management and Production Planning (Wiley, New York, 1979)."},{"key":"CR75","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0167-6377(88)90076-4","volume":"7","author":"Y. Pochet","year":"1988","unstructured":"Y. Pochet, \u201cValid inequalities and separation for capacitated economic lot sizing,\u201dOperations Research Letters 7 (1988) 109\u2013116.","journal-title":"Operations Research Letters"},{"key":"CR76","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/BF01580738","volume":"40","author":"Y. Pochet","year":"1988","unstructured":"Y. Pochet and L.A. Wolsey, \u201cLot-size models with backlogging: Strong formulations and cutting planes,\u201dMathematical Programming 40 (1988) 317\u2013335.","journal-title":"Mathematical Programming"},{"key":"CR77","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/nav.3800170209","volume":"17","author":"D. I. Steinberg","year":"1970","unstructured":"D. I. Steinberg, \u201cThe fixed charge problem,\u201dNaval Research Logistics Quarterly 17 (1970) 217\u2013235.","journal-title":"Naval Research Logistics Quarterly"},{"key":"CR78","volume-title":"\u201cDecomposition algorithms for the multi-product lot-sizing problem with capacity constraints,\u201d Report 82-15","author":"J.-M. Thizy","year":"1986","unstructured":"J.-M. Thizy and L.N. Van Wassenhove, \u201cDecomposition algorithms for the multi-product lot-sizing problem with capacity constraints,\u201d Report 82-15, Department of Industrial Engineering, Katholieke Universiteit Leuven (Leuvon, Belgium, 1986)."},{"key":"CR79","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/0012-365X(75)90077-1","volume":"12","author":"L.E. Trotter","year":"1975","unstructured":"L.E. Trotter, \u201cA class of facet producing graphs for vertex packing polytopes,\u201dDiscrete Mathematics 12 (1975) 373\u2013388.","journal-title":"Discrete Mathematics"},{"key":"CR80","volume-title":"Analysis of heuristics for the uncapacitated lot size problem","author":"R. Vachani","year":"1984","unstructured":"R. Vachani, \u201cAnalysis of heuristics for the uncapacitated lot size problem,\u201d Unpublished manuscript, Sloan School of Management, MIT (Cambridge, MA, 1984)."},{"key":"CR81","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1287\/opre.17.2.262","volume":"17","author":"A.F. Veinott","year":"1968","unstructured":"A.F. Veinott \u201cMinimum concave-cost solution of Leontief substitution models of multi-facility inventory systems,\u201dOperations Research 17 (1968) 262\u2013291.","journal-title":"Operations Research"},{"key":"CR82","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1287\/mnsc.5.1.89","volume":"5","author":"H.M. Wagner","year":"1958","unstructured":"H.M. Wagner and T.M. Whitin, \u201cDynamic version of the economic lot size model,\u201dManagement Science 5 (1958) 89\u201396.","journal-title":"Management Science"},{"key":"CR83","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1287\/mnsc.22.5.587","volume":"22","author":"W.E. Walker","year":"1976","unstructured":"W.E. Walker, \u201cA heuristic adjacent extreme point algorithm for the fixed charge problem,\u201dManagement Science 22 (1976) 587\u2013596.","journal-title":"Management Science"},{"key":"CR84","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1287\/mnsc.10.3.465","volume":"10","author":"E. Zabel","year":"1964","unstructured":"E. Zabel, \u201cSome generalizations of an inventory planning horizon theorem,\u201dManagement Science 10 (1964) 465\u2013471.","journal-title":"Management Science"},{"key":"CR85","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1287\/mnsc.13.1.105","volume":"13","author":"W.I. Zangwill","year":"1966","unstructured":"W.I. Zangwill, \u201cA deterministic multi-period production scheduling model with backlogging,\u201dManagement Science 13 (1966) 105\u2013119.","journal-title":"Management Science"},{"key":"CR86","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1287\/mnsc.15.9.506","volume":"15","author":"W.I. Zangwill","year":"1969","unstructured":"W.I. Zangwill, \u201cA backlogging model and multi-echelon model of a dynamic economic lot size production system\u2014A network approach,\u201dManagement Science 15 (1969) 506\u2013527.","journal-title":"Management Science"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01589110.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01589110\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01589110","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T11:36:31Z","timestamp":1556883391000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01589110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,8]]},"references-count":86,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1989,8]]}},"alternative-id":["BF01589110"],"URL":"https:\/\/doi.org\/10.1007\/bf01589110","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,8]]}}}