{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T10:27:08Z","timestamp":1777026428232,"version":"3.51.4"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T00:00:00Z","timestamp":1328745600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2012,12]]},"DOI":"10.1007\/s10589-012-9465-z","type":"journal-article","created":{"date-parts":[[2012,2,8]],"date-time":"2012-02-08T16:50:14Z","timestamp":1328719814000},"page":"729-753","source":"Crossref","is-referenced-by-count":21,"title":["A computational analysis of lower bounds for big bucket production planning problems"],"prefix":"10.1007","volume":"53","author":[{"given":"Kerem","family":"Akartunal\u0131","sequence":"first","affiliation":[]},{"given":"Andrew J.","family":"Miller","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,2,9]]},"reference":[{"key":"9465_CR1","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.ejor.2007.11.033","volume":"193","author":"K. Akartunal\u0131","year":"2009","unstructured":"Akartunal\u0131, K., Miller, A.J.: A heuristic approach for big bucket multi-level production planning problems. Eur. J. Oper. Res. 193, 396\u2013411 (2009)","journal-title":"Eur. J. Oper. Res."},{"key":"9465_CR2","unstructured":"Akartunal\u0131, K.: Computational methods for big bucket production planning problems: feasible solutions and strong formulations. Ph.D. thesis, Industrial and Systems Engineering Department, University of Wisconsin-Madison (2007)"},{"issue":"1","key":"9465_CR3","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s10107-007-0202-9","volume":"119","author":"S. Anily","year":"2009","unstructured":"Anily, S., Tzur, M., Wolsey, L.A.: Multi-item lot-sizing with joint set-up costs. Math. Program. 119(1), 79\u201394 (2009)","journal-title":"Math. Program."},{"key":"9465_CR4","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s10107-003-0465-8","volume":"98","author":"A. Atamt\u00fcrk","year":"2004","unstructured":"Atamt\u00fcrk, A., Mu\u00f1oz, J.C.: A study of the lot-sizing polytope. Math. Program. 98, 443\u2013465 (2004)","journal-title":"Math. Program."},{"issue":"10","key":"9465_CR5","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1287\/mnsc.30.10.1255","volume":"30","author":"I. Barany","year":"1984","unstructured":"Barany, I., Van Roy, T.J., Wolsey, L.A.: Strong formulations for multi-item capacitated lot-sizing. Manag. Sci. 30(10), 1255\u20131261 (1984)","journal-title":"Manag. Sci."},{"key":"9465_CR6","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/BFb0121006","volume":"22","author":"I. Barany","year":"1984","unstructured":"Barany, I., Van Roy, T.J., Wolsey, L.A.: Uncapacitated lot sizing: the convex hull of solutions. Math. Program. Stud. 22, 32\u201343 (1984)","journal-title":"Math. Program. Stud."},{"issue":"5","key":"9465_CR7","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1287\/mnsc.46.5.724.12048","volume":"46","author":"G. Belvaux","year":"2000","unstructured":"Belvaux, G., Wolsey, L.A.: bc-prod: A specialized branch-and-cut system for lot-sizing problems. Manag. Sci. 46(5), 724\u2013738 (2000)","journal-title":"Manag. Sci."},{"issue":"7","key":"9465_CR8","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1287\/mnsc.47.7.993.9800","volume":"47","author":"G. Belvaux","year":"2001","unstructured":"Belvaux, G., Wolsey, L.A.: Modelling practical lot-sizing problems as mixed-integer programs. Manag. Sci. 47(7), 993\u20131007 (2001)","journal-title":"Manag. Sci."},{"key":"9465_CR9","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1287\/mnsc.32.8.989","volume":"32","author":"P.J. Billington","year":"1986","unstructured":"Billington, P.J., McClain, J.O., Thomas, L.J.: Heuristics for multilevel lot-sizing with a bottleneck. Manag. Sci. 32, 989\u20131006 (1986)","journal-title":"Manag. Sci."},{"key":"9465_CR10","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1287\/mnsc.32.3.350","volume":"32","author":"G.R. Bitran","year":"1986","unstructured":"Bitran, G.R., Matsuo, H.: The multi-item capacitated lot size problem: error bounds of Manne\u2019s formulations. Manag. Sci. 32, 350\u2013359 (1986)","journal-title":"Manag. Sci."},{"issue":"10","key":"9465_CR11","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1287\/mnsc.28.10.1174","volume":"28","author":"G.R. Bitran","year":"1982","unstructured":"Bitran, G.R., Yanasse, H.H.: Computational complexity of the capacitated lot size problem. Manag. Sci. 28(10), 1174\u20131186 (1982)","journal-title":"Manag. Sci."},{"issue":"2","key":"9465_CR12","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s00291-008-0150-7","volume":"32","author":"L. Buschk\u00fchl","year":"2010","unstructured":"Buschk\u00fchl, L., Sahling, F., Helber, S., Tempelmeier, H.: Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spektrum 32(2), 231\u2013261 (2010)","journal-title":"OR Spektrum"},{"key":"9465_CR13","first-page":"353","volume":"75","author":"M. Constantino","year":"1996","unstructured":"Constantino, M.: A cutting plane approach to capacitated lot-sizing with start-up costs. Math. Program. 75, 353\u2013376 (1996)","journal-title":"Math. Program."},{"issue":"5","key":"9465_CR14","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1287\/opre.1070.0404","volume":"55","author":"Z. Degraeve","year":"2007","unstructured":"Degraeve, Z., Jans, R.: A new Dantzig-Wolfe reformulation and branch-and-price algorithm for the capacitated lot-sizing problem with setup times. Oper. Res. 55(5), 909\u2013920 (2007)","journal-title":"Oper. Res."},{"issue":"6","key":"9465_CR15","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1287\/opre.35.6.832","volume":"35","author":"G.D. Eppen","year":"1987","unstructured":"Eppen, G.D., Martin, R.K.: Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35(6), 832\u2013848 (1987)","journal-title":"Oper. Res."},{"issue":"8","key":"9465_CR16","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1287\/mnsc.37.8.909","volume":"37","author":"A. Federgruen","year":"1991","unstructured":"Federgruen, A., Tzur, M.: A simple forward algorithm to solve general dynamic lot sizing models with n periods in O(nlogn) or O(n) time. Manag. Sci. 37(8), 909\u2013925 (1991)","journal-title":"Manag. Sci."},{"issue":"3","key":"9465_CR17","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1287\/opre.1070.0392","volume":"55","author":"A. Federgruen","year":"2007","unstructured":"Federgruen, A., Meissner, J., Tzur, M.: Progressive interval heuristics for multi-item capacitated lot sizing problem. Oper. Res. 55(3), 490\u2013502 (2007)","journal-title":"Oper. Res."},{"issue":"1","key":"9465_CR18","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1287\/mnsc.18.1.12","volume":"18","author":"M. Florian","year":"1971","unstructured":"Florian, M., Klein, M.: Deterministic production planning with concave costs and capacity constraints. Manag. Sci. 18(1), 12\u201320 (1971)","journal-title":"Manag. Sci."},{"issue":"7","key":"9465_CR19","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1287\/mnsc.26.7.669","volume":"26","author":"M. Florian","year":"1980","unstructured":"Florian, M., Lenstra, J.K., Rinnooy Kan, H.G.: Deterministic production planning: algorithms and complexity. Manag. Sci. 26(7), 669\u2013679 (1980)","journal-title":"Manag. Sci."},{"key":"9465_CR20","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/PL00011430","volume":"90","author":"O. G\u00fcnl\u00fck","year":"2001","unstructured":"G\u00fcnl\u00fck, O., Pochet, Y.: Mixing mixed integer inequalities. Math. Program. 90, 429\u2013457 (2001)","journal-title":"Math. Program."},{"key":"9465_CR21","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.orl.2003.06.001","volume":"32","author":"R. Jans","year":"2004","unstructured":"Jans, R., Degraeve, Z.: Improved lower bounds for the capacitated lot sizing problem with setup times. Oper. Res. Lett. 32, 185\u2013195 (2004)","journal-title":"Oper. Res. Lett."},{"issue":"6","key":"9465_CR22","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1287\/mnsc.44.6.859","volume":"44","author":"E. Katok","year":"1998","unstructured":"Katok, E., Lewis, H.S., Harrison, T.P.: Lot sizing in general assembly systems with setup costs, setup times, and multiple constrained resources. Manag. Sci. 44(6), 859\u2013877 (1998)","journal-title":"Manag. Sci."},{"key":"9465_CR23","first-page":"155","volume-title":"Optimierung bei Graphentheoretischen und Ganzzahligen Probleme","author":"J. Krarup","year":"1977","unstructured":"Krarup, J., Bilde, O.: Plant location, set covering and economic lotsizes: an O(mn) algorithm for structured problems. In: Optimierung bei Graphentheoretischen und Ganzzahligen Probleme, pp. 155\u2013180. Birkhauser, Basel (1977)"},{"issue":"1","key":"9465_CR24","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s10107-007-0186-5","volume":"118","author":"S. K\u00fc\u00e7\u00fckyavuz","year":"2009","unstructured":"K\u00fc\u00e7\u00fckyavuz, S., Pochet, Y.: Uncapacitated lot-sizing with backlogging: the convex hull. Math. Program. 118(1), 151\u2013175 (2009)","journal-title":"Math. Program."},{"issue":"2","key":"9465_CR25","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1287\/moor.1070.0305","volume":"33","author":"R. Levi","year":"2008","unstructured":"Levi, R., Lodi, A., Sviridenko, M.: Approximation algorithms for the capacitated multi-item lot-sizing problem via flow-cover inequalities. Math. Oper. Res. 33(2), 461\u2013474 (2008)","journal-title":"Math. Oper. Res."},{"key":"9465_CR26","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/PL00011411","volume":"89","author":"M. Loparic","year":"2001","unstructured":"Loparic, M., Pochet, Y., Wolsey, L.A.: The uncapacitated lot-sizing problem with sales and safety stocks. Math. Program. 89, 487\u2013504 (2001)","journal-title":"Math. Program."},{"key":"9465_CR27","unstructured":"LOTSIZELIB. Lot-sizing problems: a library of models and matrices (1999). http:\/\/www.core.ucl.ac.be\/wolsey\/lotsizel.htm"},{"issue":"2","key":"9465_CR28","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1287\/mnsc.4.2.115","volume":"4","author":"A.S. Manne","year":"1958","unstructured":"Manne, A.S.: Programming of economic lot sizes. Manag. Sci. 4(2), 115\u2013135 (1958)","journal-title":"Manag. Sci."},{"issue":"1","key":"9465_CR29","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s101070050044","volume":"85","author":"H. Marchand","year":"1999","unstructured":"Marchand, H., Wolsey, L.A.: The 0-1 knapsack problem with a single continuous variable. Math. Program. 85(1), 15\u201333 (1999)","journal-title":"Math. Program."},{"issue":"3","key":"9465_CR30","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1287\/opre.49.3.363.11211","volume":"49","author":"H. Marchand","year":"2001","unstructured":"Marchand, H., Wolsey, L.A.: Aggregation and mixed integer rounding to solve MIPs. Oper. Res. 49(3), 363\u2013371 (2001)","journal-title":"Oper. Res."},{"key":"9465_CR31","unstructured":"Miller, A.J., Nemhauser, G.L., Savelsbergh, M.W.P.: Solving the multi-item capacitated lot-sizing problem with setup times by branch-and-cut. CORE Discussion Paper 2000\/39, CORE, UCL, Belgium (2000)"},{"key":"9465_CR32","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s10107-002-0325-y","volume":"94","author":"A.J. Miller","year":"2003","unstructured":"Miller, A.J., Nemhauser, G.L., Savelsbergh, M.W.P.: On the polyhedral structure of a multi-item production planning model with setup times. Math. Program. 94, 375\u2013405 (2003)","journal-title":"Math. Program."},{"key":"9465_CR33","unstructured":"Multi-LSB: Multi-item lot-sizing problems with backlogging: a library of test instances (2010). Available at http:\/\/personal.strath.ac.uk\/kerem.akartunali\/research\/multi-lsb\/"},{"key":"9465_CR34","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/BF01580738","volume":"40","author":"Y. Pochet","year":"1988","unstructured":"Pochet, Y., Wolsey, L.A.: Lot-size models with backlogging: Strong reformulations and cutting planes. Math. Program. 40, 317\u2013335 (1988)","journal-title":"Math. Program."},{"issue":"1","key":"9465_CR35","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1287\/mnsc.37.1.53","volume":"37","author":"Y. Pochet","year":"1991","unstructured":"Pochet, Y., Wolsey, L.A.: Solving multi-item lot-sizing problems using strong cutting planes. Manag. Sci. 37(1), 53\u201367 (1991)","journal-title":"Manag. Sci."},{"key":"9465_CR36","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01582225","volume":"67","author":"Y. Pochet","year":"1994","unstructured":"Pochet, Y., Wolsey, L.A.: Polyhedra for lot-sizing with Wagner-Whitin costs. Math. Program. 67, 297\u2013323 (1994)","journal-title":"Math. Program."},{"key":"9465_CR37","volume-title":"Production Planning by Mixed Integer Programming","author":"Y. Pochet","year":"2006","unstructured":"Pochet, Y., Wolsey, L.A.: Production Planning by Mixed Integer Programming. Springer, Berlin (2006)"},{"key":"9465_CR38","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0377-2217(93)90263-M","volume":"71","author":"R.L. Rardin","year":"1993","unstructured":"Rardin, R.L., Wolsey, L.A.: Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems. Eur. J. Oper. Res. 71, 95\u2013109 (1993)","journal-title":"Eur. J. Oper. Res."},{"issue":"1\u20133","key":"9465_CR39","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s10107-003-0398-2","volume":"98","author":"J.-P.P. Richard","year":"2003","unstructured":"Richard, J.-P.P., de Farias, I.R., Nemhauser, G.L.: Lifted inequalities for 0-1 mixed integer programming: Basic theory and algorithms. Math. Program. 98(1\u20133), 89\u2013113 (2003)","journal-title":"Math. Program."},{"issue":"1\u20133","key":"9465_CR40","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s10107-003-0399-1","volume":"98","author":"J.-P.P. Richard","year":"2003","unstructured":"Richard, J.-P.P., de Farias, I.R., Nemhauser, G.L.: Lifted inequalities for 0-1 mixed integer programming: Superlinear lifting. Math. Program. 98(1\u20133), 115\u2013143 (2003)","journal-title":"Math. Program."},{"key":"9465_CR41","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1002\/nav.20097","volume":"52","author":"N.C. Simpson","year":"2005","unstructured":"Simpson, N.C., Erenguc, S.S.: Modeling multiple stage manufacturing systems with generalized costs and capacity issues. Nav. Res. Logist. 52, 560\u2013570 (2005)","journal-title":"Nav. Res. Logist."},{"key":"9465_CR42","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1287\/opre.51.3.487.14949","volume":"51","author":"H. Stadtler","year":"2003","unstructured":"Stadtler, H.: Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows. Oper. Res. 51, 487\u2013502 (2003)","journal-title":"Oper. Res."},{"issue":"5","key":"9465_CR43","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1287\/mnsc.42.5.738","volume":"42","author":"H. Tempelmeier","year":"1996","unstructured":"Tempelmeier, H., Derstroff, M.: A lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times. Manag. Sci. 42(5), 738\u2013757 (1996)","journal-title":"Manag. Sci."},{"issue":"4","key":"9465_CR44","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1080\/07408178508975308","volume":"17","author":"J.M. Thizy","year":"1985","unstructured":"Thizy, J.M., Van Wassenhove, L.N.: Lagrangean relaxation for the multi-item capacitated lot-sizing problem: A heuristic implementation. IIE Trans. 17(4), 308\u2013313 (1985)","journal-title":"IIE Trans."},{"key":"9465_CR45","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1287\/mnsc.35.3.353","volume":"35","author":"W.W. Trigeiro","year":"1989","unstructured":"Trigeiro, W.W., Thomas, L.J., McClain, J.O.: Capacitated lot sizing with setup times. Manag. Sci. 35, 353\u2013366 (1989)","journal-title":"Manag. Sci."},{"issue":"3","key":"9465_CR46","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1287\/ijoc.1030.0042","volume":"16","author":"M. Van Vyve","year":"2004","unstructured":"Van Vyve, M., Pochet, Y.: A general heuristic for production planning problems. INFORMS J. Comput. 16(3), 316\u2013327 (2004)","journal-title":"INFORMS J. Comput."},{"key":"9465_CR47","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1287\/mnsc.5.1.89","volume":"5","author":"H.M. Wagner","year":"1958","unstructured":"Wagner, H.M., Whitin, T.M.: Dynamic version of the economic lot size model. Manag. Sci. 5, 89\u201396 (1958)","journal-title":"Manag. Sci."},{"key":"9465_CR48","volume-title":"Integer Programming","author":"L.A. Wolsey","year":"1998","unstructured":"Wolsey, L.A.: Integer Programming. Wiley-Interscience, New York (1998)"},{"issue":"12","key":"9465_CR49","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1287\/mnsc.48.12.1587.442","volume":"48","author":"L.A. Wolsey","year":"2002","unstructured":"Wolsey, L.A.: Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation. Manag. Sci. 48(12), 1587\u20131602 (2002)","journal-title":"Manag. Sci."},{"issue":"9","key":"9465_CR50","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1287\/mnsc.15.9.506","volume":"15","author":"W.I. Zangwill","year":"1969","unstructured":"Zangwill, W.I.: A backlogging model and a multi-echelon model of a dynamic economic lot size production system\u2014a network approach. Manag. Sci. 15(9), 506\u2013527 (1969)","journal-title":"Manag. Sci."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-012-9465-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-012-9465-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-012-9465-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:42Z","timestamp":1559302602000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-012-9465-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,9]]},"references-count":50,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["9465"],"URL":"https:\/\/doi.org\/10.1007\/s10589-012-9465-z","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,9]]}}}