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Dynamic capacitated lot-sizing problems: a classification and review of solution approaches

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Abstract

This paper presents a review of four decades of research on dynamic lot-sizing with capacity constraints. We discuss both different modeling approaches to the optimization problems and different algorithmic solution approaches. The focus is on research that separates the lot-sizing problem from the detailed sequencing and scheduling problem. Our conceptional point of reference is the multi-level capacitated lot-sizing problem (MLCLSP). We show how different streams of research emerged over time. One result is that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice. Our review also shows that currently mathematical programing and the use of metaheuristics are particularly popular among researchers in a vivid and flourishing field of research.

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References

  • Akartunalı K, Miller AJ (2008) A heuristic approach for big bucket multi-level production planning problems. Eur J Oper Res. doi:10.1016/j.ejor.2007.11.033

  • Alfieri A, Brandimarte P, D’Orazio S (2002) LP-based heuristics for the capacitated lot-sizing problem: the interaction of model formulation and solution algorithm. Int J Prod Res 40: 441–458

    Google Scholar 

  • Armentano VA, França PM, de Toledo FMB (1999) A network flow model for the capacitated lot-sizing problem. Omega 27: 275–284

    Google Scholar 

  • Bahl HC (1983) Column generation based heuristic algorithm for multi-item scheduling. IIE Trans 15: 136–141

    Google Scholar 

  • Bahl HC, Ritzman LP, Gupta JND (1987) Determining lot sizes and resource requirements: a review. Oper Res 35: 329–345

    Google Scholar 

  • Barany I, van Roy TJ, Wolsey LA (1984) Strong formulations for multi-item capacitated lot sizing. Manage Sci 30: 1255–1261

    Google Scholar 

  • Barbarosoglu G, Özdamar L (2000) Analysis of solution space-dependent performance of simulated annealing: the case of the multi-level capacitated lot sizing problem. Comput Oper Res 27: 895–903

    Google Scholar 

  • Belvaux G, Wolsey LA (2000) bc-prod: a specialized branch-and-cut system for lot-sizing problems. Manage Sci 46: 724–738

    Google Scholar 

  • Belvaux G, Wolsey LA (2001) Modelling practical lot-sizing problems as mixed-integer programs. Manage Sci 47: 993–1007

    Google Scholar 

  • Berretta R, Rodrigues LF (2004) A memetic algorithm for a multistage capacitated lot-sizing problem. Int J Prod Econ 87: 67–81

    Google Scholar 

  • Berretta R, França PM, Armentano VA (2005) Metaheuristic approaches for the multilevel resource-constrained lot-sizing problem with setup and lead times. Asia Pac J Oper Res 22: 261–286

    Google Scholar 

  • Billington PJ, McClain JO, Thomas LJ (1983) Mathematical programming approaches to capacity-constrained MRP systems: review, formulation and problem reduction. Manage Sci 29: 1126–1141

    Google Scholar 

  • Billington PJ, McClain JO, Thomas LJ (1986) Heuristics for multilevel lot-sizing with a bottleneck. Manage Sci 32: 989–1006

    Google Scholar 

  • Bitran GR, Matsuo H (1986) The multi-item capacitated lot size problem: error bounds of Manne’s formulations. Manage Sci 32: 350–359

    Google Scholar 

  • Bitran GR, Yanasse HH (1982) Computational complexity of the capacitated lot size problem. Manage Sci 28: 1174–1186

    Google Scholar 

  • Blackburn JD, Millen RA (1984) Simultaneous lot-sizing and capacity planning in multi-stage assembly processes. Eur J Oper Res 16: 84–93

    Google Scholar 

  • Boctor FF, Poulin P (2005) Heuristics for N-product, M-stage, economic lot sizing and scheduling problem with dynamic demand. Int J Prod Res 43: 2809–2828

    Google Scholar 

  • Bourjolly J-M, Ding K, Gopalakrishnan M, Gramani MCN, Mohan S (2001) On a tactical/operational production planning problem in supply chain management: balancing inventory and setup costs. In: MIC’2001—4th metaheuristics international conference, pp 569–571

  • Brahimi N, Dauzère-Pérès S, Najid NM (2006a) Capacitated multi-item lot-sizing problems with time windows. Oper Res 54: 951–967

    Google Scholar 

  • Brahimi N, Dauzère-Pérès S, Najid NM, Nordli A (2006b) Single item lot sizing problems. Eur J Oper Res 168: 1–16

    Google Scholar 

  • Campbell GM, Mabert VA (1991) Cyclical schedules for capacitated lot sizing with dynamic demands. Manage Sci 37: 409–427

    Google Scholar 

  • Cattrysse D, Maes J, van Wassenhove LN (1990) Set partitioning and column generation heuristics for capacitated dynamic lotsizing. Eur J Oper Res 46: 38–47

    Google Scholar 

  • Chen H, Chu C (2003) A lagrangian relaxation approach for supply chain planning with order/setup costs and capacity constraints. J Syst Sci Syst Eng 12: 98–110

    Google Scholar 

  • Chen W-H, Thizy J-M (1990) Analysis of relaxations for the multi-item capacitated lot-sizing problem. Ann Oper Res 26: 29–72

    Google Scholar 

  • Clark AR, Armentano VA (1995) A heuristic for a resource-capacitated multi-stage lot-sizing problem with lead times. J Oper Res Soc 46: 1208–1222

    Google Scholar 

  • Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper Res 8: 101–111

    Google Scholar 

  • Degraeve Z, Jans R (2003) A new Dantzig–Wolfe reformulation and branch-and-price algorithm for the capacitated lot sizing problem with set up times. (April 2003, 03). In: ERIM report series reference no. ERS-2003-010-LIS. Available at SSRN: http://ssrn.com/abstract=411647

  • DeMatteis JJ (1968) An economic lot-sizing technique i—the part-period algorithm. IBM Syst J 7: 30–38

    Article  Google Scholar 

  • Denizel M, Altekin FT, Süral H, Stadtler H (2008) Equivalence of the LP relaxations of two strong formulations for the capacitated lot-sizing problem with setup times. OR Spectr 30: 773–785

    Google Scholar 

  • Diaby M, Bahl HC, Karwan MH, Zionts S (1992a) Capacitated lot-sizing and scheduling by Lagrangean relaxation. Eur J Oper Res 59: 444–458

    Google Scholar 

  • Diaby M, Bahl HC, Karwan MH, Zionts S (1992b) A lagrangean relaxation approach for very-large-scale capacitated lot-sizing. Manage Sci 38: 1329–1340

    Google Scholar 

  • Dillenberger C, Escudero LF, Wollensak A, Zhang W (1993) On solving a large-scale resource allocation problem in production planning. In: Fandel G, Gulledge T, Jones A (eds) Operations research in production planning and control. Springer, Heidelberg, pp 105–119

    Google Scholar 

  • Dillenberger C, Escudero LF, Wollensak A, Zhang W (1994) On practical resource allocation for production planning and scheduling with period overlapping setups. Eur J Oper Res 75: 275–286

    Google Scholar 

  • Dixon PS, Silver EA (1981) A heuristic solution procedure for the multi-item, single-level, limited capacity, lot-sizing problem. J Oper Manage 2: 23–39

    Google Scholar 

  • Dogramaci A, Panayiotopoulos JC, Adam NR (1981) The dynamic lot-sizing problem for multiple items under limited capacity. AIIE Trans 13: 294–303

    Google Scholar 

  • Drexl A, Haase K (1995) Proportional lotsizing and scheduling. Int J Prod Econ 40: 73–87

    Google Scholar 

  • Drexl A, Kimms A (1997) Lot sizing and scheduling: survey and extensions. Eur J Oper Res 99: 221–235

    Google Scholar 

  • Dzielinski BP, Gomory RE (1965) Optimal programming of lot sizes, inventory and labor allocations. Manage Sci 11: 874–890

    Google Scholar 

  • Eisenhut PS (1975) A dynamic lot sizing algorithm with capacity constraints. AIIE Trans 7: 170–176

    Google Scholar 

  • Eppen GD, Martin RK (1987) Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper Res 35: 832–848

    Google Scholar 

  • Evans JR (1985) An efficient implementation of the Wagner-Whitin algorithm for dynamic lot-sizing. J Oper Manage 5: 229–235

    Google Scholar 

  • Federgruen A, Tzur M (1991) A simple forward algorithm to solve general dynamic lot sizing models with n periods in o(n log n) or o(n) time. Manage Sci 37: 909–925

    Google Scholar 

  • Federgruen A, Meissner J, Tzur M (2007) Progressive interval heuristics for multi-item capacitated lot-sizing problems. Oper Res 55: 490–502

    Google Scholar 

  • Fleischmann B (1990) The discrete lot-sizing and scheduling problem. Eur J Oper Res 44: 337–348

    Google Scholar 

  • Fleischmann B, Meyr H (1997) The general lotsizing and scheduling problem. OR Spektrum 19: 11–21

    Google Scholar 

  • Florian M, Lenstra J, Kan AR (1980) Deterministic production planning: algorithms and complexity. Manage Sci 26: 669–679

    Google Scholar 

  • França PM, Armentano VA, Berretta RE, Clark AR (1997) A heuristic method for lot-sizing in multi-stage systems. Comput Oper Res 24: 861–874

    Google Scholar 

  • Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York

    Google Scholar 

  • Gelders LF, Maes J, van Wassenhove LN (1986) A branch and bound algorithm for the multi item single level capacitated dynamic lotsizing problem. In: Axsäter S, Schneeweiss C, Silver E (eds) Multi-stage production planning and inventory control. Springer, Berlin, pp 92–108

    Google Scholar 

  • Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13: 533–549

    Google Scholar 

  • Gopalakrishnan M, Ding K, Bourjolly J-M, Mohan S (2001) A tabu-search heuristic for the capacitated lot-sizing problem with set-up carryover. Manage Sci 47: 851–863

    Google Scholar 

  • Groff G (1979) A lot sizing rule for time-phased component demand. Prod Inventory Manage 20: 47–53

    Google Scholar 

  • Günther H-O (1987) Planning lot sizes and capacity requirements in a single stage production sytem. Eur J Oper Res 31: 223–231

    Google Scholar 

  • Gupta YP, Keung Y (1990) A review of multi-stage lot-sizing models. Int J Oper Prod Manage 10: 57–73

    Google Scholar 

  • Gupta D, Magnusson T (2005) The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times. Comput Oper Res 32: 727–747

    Google Scholar 

  • Gutierrez E, Hernández W, Süer GA (2001) Genetic algorithms in capacitated lot sizing decisions. In: Computer research conference

  • Haase K (1994) Lotsizing and scheduling for production planning. Lecture notes in economics and mathematical systems, vol 408. Springer, Berlin

  • Haase K (1998) Capacitated lot-sizing with linked production quantities of adjacent periods. In: Drexl A, Kimms A (eds) Beyond manufacturing resource planning (MRP II)—advanced models and methods for production planning. Springer, Berlin, pp 127–146

    Google Scholar 

  • Haase K (2005) Solving large-scale capacitated lot-sizing problems close to optimality. Working paper, Technische Universität Dresden

  • Haase K, Kohlmorgen U (1995) Parallel genetic algorithm for the capacitated lot-sizing problem. In: Kleinschmidt P, Bachem A, Derigs U, Fischer D, Leopold-Wildburger U, Möhring R (eds) Operations research proceedings. Springer, Berlin, pp 370–375

    Google Scholar 

  • Hansen P, Mlaydenović N (1999) An introduction to variable neighborhood search. In: Voß S, Martello S, Osman I, Roucairol C (eds) Metaheuristics: advances and trends in local search paradigms for optimization. Kluwer, Dordrecht, pp 433–458

    Google Scholar 

  • Hansen P, Mlaydenović N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130: 449–467

    Google Scholar 

  • Harrison TP, Lewis HS (1996) Lot sizing in serial assembly systems with multiple constrained resources. Manage Sci 42: 19–36

    Google Scholar 

  • Helber S (1994) Kapazitätsorientierte Losgröß enplanung in PPS-Sytemen. M&P

  • Helber S (1995) Lot sizing in capacitated production planning and control systems. OR Spektrum 17: 5–18

    Google Scholar 

  • Hindi KS (1995) Computationally efficient solution of the multi-item, capacitated lot-sizing problem. Comput Ind Eng 28: 709–719

    Google Scholar 

  • Hindi KS (1996) Solving the CLSP by a tabu search heuristic. J Oper Res Soc 47: 151–161

    Google Scholar 

  • Hindi KS, Fleszar K, Charalambous C (2003) An effective heuristic for the CLSP with set-up times. J Oper Res Soc 54: 490–498

    Google Scholar 

  • Huisman D, Jans R, Peeters M, Wagelmans APM (2003) Combining column generation and Lagrangian relaxation (1 January 2003). In: ERIM report series reference no. ERS-2003-092-LIS. Available at SSRN: http://ssrn.com/abstract=496704

  • Hung Y-F, Chien KL (2000) A multi-class multi-level capacitated lot sizing model. J Oper Res Soc 51: 1309–1318

    Google Scholar 

  • Hung Y-F, Hu Y-C (1998) Solving mixed integer programming production planning problems with setups by shadow price information. Comput Oper Res 25: 1027–1042

    Google Scholar 

  • Hung Y-F, Shih C-C, Chen C-P (1999) Evolutionary algorithms for production planning problems with setup decisions. J Oper Res Soc 50: 857–866

    Google Scholar 

  • Hung Y-F, Chen C-P, Shih C-C, Hung M-H (2003) Using tabu search with ranking candidate list to solve production planning problems with setups. Comput Ind Eng 45: 615–634

    Google Scholar 

  • Jacobs F, Khumawala B (1982) Multi-level lot sizing in material requirements planning: an empirical investigation. Comput Oper Res 9: 139–144

    Google Scholar 

  • Jans R, Degraeve Z (2007) Meta-heuristics for dynamic lot sizing: a review and comparison of solution approaches. Eur J Oper Res 177: 1855–1875

    Google Scholar 

  • Karimi B, Ghomi SMTF, Wilson JM (2003) The capacitated lot sizing problem: a review of models and algorithms. Omega 31: 365–378

    Google Scholar 

  • Karmarkar US, Schrage L (1985) The deterministic dynamic product cycling problem. Oper Res 66: 326–345

    Google Scholar 

  • Karni R, Roll Y (1982) A heuristic algorithm for the multi-item lot sizing problem with capacity constraints. IIE Trans 14: 249–256

    Google Scholar 

  • Katok E, Lewis HS, Harrison TP (1998) Lot sizing in general assembly systems with setup costs, setup times, and multiple constrained resources. Manage Sci 44: 859–877

    Google Scholar 

  • Kirca Ö (1990) An efficient algorithm for the capacitated single dynamic lot size problem. Eur J Oper Res 45: 15–24

    Google Scholar 

  • Kirca Ö, Kökten M (1994) A new heuristic approach for the multi-item dynamic lot sizing problem. Eur J Oper Res 75: 332–341

    Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220: 671–680

    Google Scholar 

  • Kohlmorgen U, Schmeck H, Haase K (1999) Experiences with fine-grained parallel genetic algorithms. Ann Oper Res 90: 203–219

    Google Scholar 

  • Krarup J, Bilde O (1977) Plant location, set covering and economic lot size: An o(mn)-algorithm for structured problems. In: Collatz L, Meinardus G, Wetterling W (eds) Numerische Methoden bei Optimierungsaufgaben Band 3. Birkhäuser, Basel, pp 155–180

    Google Scholar 

  • Kuik R, Salomon M (1990) Multi-level lot-sizing problem: evaluation of a simulated-annealing heuristic. Eur J Oper Res 45: 25–37

    Google Scholar 

  • Kuik R, Salomon M, van Wassenhove LN, Maes J (1993) Linear programming, simulated annealing and tabu search heuristics for lotsizing in bottleneck assembly systems. IIE Trans 25: 62–72

    Google Scholar 

  • Kuik R, Salomon M, van Wassenhove LN (1994) Batching decisions: structure and models. Eur J Oper Res 75: 243–263

    Google Scholar 

  • Lambrecht MR, Vanderveken H (1979) Heuristic procedures for the single operation, multi-item loading problem. AIIE Trans 11: 319–326

    Google Scholar 

  • Lasdon LS, Terjung RC (1971) An efficient algorithm for multi-item scheduling. Oper Res 19: 946–969

    Google Scholar 

  • Maes J, van Wassenhove LN (1986a) Multi item single level capacitated dynamic lotsizing heuristics: a computational comparison (part I: static case). IIE Trans 18: 114–123

    Google Scholar 

  • Maes J, van Wassenhove LN (1986b) Multi item single level capacitated dynamic lotsizing heuristics: a computational comparison (part II: rolling horizon). IIE Trans 18: 124–129

    Google Scholar 

  • Maes J, van Wassenhove LN (1986c) A simple heuristic for the multi item single level capacitated lotsizing problem. Oper Res Lett 4: 265–273

    Google Scholar 

  • Maes J, van Wassenhove L (1988) Multi-item single-level capacitated dynamic lot-sizing heuristics: a general review. J Oper Res Soc 39: 991–1004

    Google Scholar 

  • Maes J, McClain JO, van Wassenhove LN (1991) Multilevel capacitated lotsizing complexity and LP-based heuristics. Eur J Oper Res 53: 131–148

    Google Scholar 

  • Manne AS (1958) Programming of economic lot sizes. Manage Sci 4: 115–135

    Google Scholar 

  • Mercé C, Fontan G (2003) MIP-based heuristics for capacitated lotsizing problems. Int J Prod Econ 85: 97–111

    Google Scholar 

  • Millar HH, Yang M (1994) Lagrangian heuristics for the capacitated multi-item lot-sizing problem with backordering. Int J Prod Econ 34: 1–15

    Google Scholar 

  • Miller AJ, Nemhauser GL, Savelsbergh MWP (2000) Solving multi-item capacitated lot-sizing problems with setup times by branch-and-cut. Université Catholique de Louvain, Belgium. Core discussion paper 00/39

  • Moorkanat J (2000) Studies in certain resource loading, scheduling and production control problems in multi-stage production control problems in multi-stage production inventory systems. Ph.D. thesis, Indian Institute of Technology, Bombay

  • Newson EFP (1975a) Multi-item lot size scheduling by heuristic, part I: with fixed resources. Manage Sci 21: 1186–1193

    Google Scholar 

  • Newson EFP (1975b) Multi-item lot size scheduling by heuristic, part II: with variable resources. Manage Sci 21: 1194–1203

    Google Scholar 

  • Özdamar L, Barbarosoglu G (1999) Hybrid heuristics for the multi-stage capacitated lot sizing and loading problem. J Oper Res Soc 50: 810–825

    Google Scholar 

  • Özdamar L, Barbarosoglu G (2000) An integrated Lagrangean relaxation-simulated annealing approach to the multi-level multi-item capacitated lot sizing problem. Int J Prod Econ 68: 319–331

    Google Scholar 

  • Özdamar L, Bozyel MA (2000) The capacitated lot sizing problem with overtime decisions and setup times. IIE Trans 32: 1043–1057

    Google Scholar 

  • Özdamar L, Birbil ŞI, Portmann M-C (2002) Technical note: new results for the capacitated lot sizing problem with overtime decisions and setup times. Prod Plann Control 13: 2–10

    Google Scholar 

  • Pitakaso R, Almeder C, Doerner KF, Hartl RF (2006) Combining exact and population-based methods for the constrained multilevel lot sizing problem. Int J Prod Res 44: 4755–4771

    Google Scholar 

  • Pochet Y, Wolsey LA (1991) Solving multi-item lot-sizing problems using strong cutting planes. Manage Sci 37: 53–67

    Google Scholar 

  • Quadt D, Kuhn H (2008) Capacitated lot-sizing with extensions: a review. 4OR Q J Oper Res 6: 61–83

    Google Scholar 

  • Rogers J (1958) A computational approach to the economic lot scheduling problem. Manage Sci 4: 264–291

    Google Scholar 

  • Rosling K (1986) Optimal lot-sizing for dynamic assembly systems. In: Axsäter S, Schneeweiss C, Silver E (eds) Multi-stage production planning and inventory control. Springer, Berlin, pp 119–131

    Google Scholar 

  • Salomon M (1991) Deterministic lotsizing models for production planning. Lecture notes in economics and mathematical systems, vol 355. Springer, Berlin

  • Salomon M, Kroon LG, Kuik R, van Wassenhove LN (1991) Some extensions of the discrete lotsizing and scheduling problem. Manage Sci 37: 801–812

    Google Scholar 

  • Salomon M, Kuik R, van Wassenhove LN (1993) Statistical search methods for lotsizing problems. Ann Oper Res 41: 453–468

    Google Scholar 

  • Sambasivan M, Yahya S (2005) A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers. Comput Oper Res 32: 537–555

    Google Scholar 

  • Sambasivan M, Schmidt CP (2002) A heuristic procedure for solving multi-plant, multi-item, multi-period capacitated lot-sizing problems. Asia Pac J Oper Res 19: 87–105

    Google Scholar 

  • Selen WJ, Heuts RM (1989) A modified priority index for Günther’s lot-sizing heuristic under capacitated single stage production. Eur J Oper Res 41: 181–185

    Google Scholar 

  • Silver EA, Meal HC (1969) A simple modification of the EOQ for the case of a varying demand rate. Prod Inventory Manage 10: 51–55

    Google Scholar 

  • Silver EA, Meal HC (1973) A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment. Prod Inventory Manage 14: 64–74

    Google Scholar 

  • Sox CR, Gao Y (1999) The capacitated lot sizing problem with setup carry-over. IIE Trans 31: 173–181

    Google Scholar 

  • Stadtler H (1996) Mixed integer programming model formulations for dynamic multi-item multi-level capacitated lotsizing. Eur J Oper Res 94: 561–581

    Google Scholar 

  • Stadtler H (1997) Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing. OR Spektrum 19: 87–96

    Google Scholar 

  • Stadtler H (2000) Improved rolling schedules for the dynamic single-level lot-sizing problem. Manage Sci 46: 318–326

    Google Scholar 

  • Stadtler H (2003) Multilevel lot sizing with setup times and multiple constrained resources: internally rolling schedules with lot-sizing windows. Oper Res 51: 487–502

    Google Scholar 

  • Staggemeier AT, Clark AR (2001) A survey of lot-sizing and scheduling models. In: 23rd annual symposium of the Brazilian Operational Research Society (SOBRAPO), Campos do Jordao SP, Brazil, pp 938–947

  • Sürie C, Stadtler H (2003) The capacitated lot-sizing problem with linked lot sizes. Manage Sci 49: 1039–1054

    Google Scholar 

  • Tempelmeier H, Derstroff M (1993) Mehrstufige Mehrprodukt-Losgröß enplanung bei beschränkten Ressourcen und genereller Erzeugnisstruktur. OR Spektrum 15: 63–73

    Google Scholar 

  • Tempelmeier H, Derstroff M (1996) A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times. Manage Sci 42: 738–757

    Google Scholar 

  • Tempelmeier H, Helber S (1994) A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures. Eur J Oper Res 75: 296–311

    Google Scholar 

  • Thizy J-M, van Wassenhove LN (1985) Lagrangean relaxation for the multi-item capacitated lot-sizing problem: A heuristic implementation. IIE Trans 17: 308–313

    Google Scholar 

  • Trigeiro WW (1987) A dual-cost heuristic for the capacitated lot sizing problem. IIE Trans 19: 67–72

    Google Scholar 

  • Trigeiro WW (1989) A simple heuristic for lot sizing with setup times. Decis Sci 20: 294–303

    Google Scholar 

  • Trigeiro WW, Thomas LJ, McClain JO (1989) Capacitated lot sizing with setup times. Manage Sci 35: 353–366

    Google Scholar 

  • van Nunen JAEE, Wessels J (1978) Multi-item lot size determination and scheduling under capacity constraints. Eur J Oper Res 2: 36–41

    Google Scholar 

  • Wagelmans A, van Hoesel S, Kolen A (1992) Economic lot sizing: An o (n log n) algorithm that runs in linear time in the Wagner–Whitin case. Oper Res 40: 145–156

    Google Scholar 

  • Wagner HM, Whitin TM (1958) Dynamic version of the economic lot size model. Manage Sci 5: 89–96

    Google Scholar 

  • Wolsey LA (1995) Progress with single-item lot-sizing. Eur J Oper Res 86: 395–401

    Google Scholar 

  • Xie J, Dong J (2002) Heuristic genetic algorithms for general capacitated lot-sizing problems. Comput Math Appl 44: 263–276

    Google Scholar 

  • Zangwill WI (1966) A deterministic multi-period production scheduling model with backlogging. Manage Sci 13: 105–119

    Google Scholar 

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  1. Seminar für Supply Chain Management und Produktion, Universität zu Köln, Albertus-Magnus-Platz, 50923, Cologne, Germany

    Lisbeth Buschkühl & Horst Tempelmeier

  2. Institut für Produktionswirtschaft, Leibniz Universität Hannover, Königsworther Platz 1, 30167, Hannover, Germany

    Florian Sahling & Stefan Helber

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Buschkühl, L., Sahling, F., Helber, S. et al. Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectrum 32, 231–261 (2010). https://doi.org/10.1007/s00291-008-0150-7

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