Skip to main content
Log in

Simultaneous lotsizing and scheduling problems: a classification and review of models

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

The current paper presents a structured overview over the literature on dynamic simultaneous lotsizing and scheduling problems. We introduce a classification scheme, review the historical development of research in this area and identify recent developments. The main contribution of the present review is the discussion of the historical development of the body of knowledge in the field of simultaneous lotsizing and scheduling and the identification of recent trends. This helps to reveal research opportunities, but it can also be helpful in the selection of appropriate models for industrial applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

Notes

  1. In the tables shown below, a field will be left empty if it is not possible to identify the value of the attribute.

  2. See Buschkühl et al. (2010), pp. 243–244.

  3. Note the erratum Brüggemann and Jahnke (2000b).

  4. The model formulation is incomplete, but an example is mentioned.

  5. Which can be mitigated as, for example, Seeanner (2013), p. 148 has shown.

References

  • Almada-Lobo B, Carravilla MA, Oliveira JF (2008) Production planning and scheduling in the glass container industry: a VNS approach. Int J Prod Econ 114(1):363–375

    Article  Google Scholar 

  • Almada-Lobo B, James RJW (2010) Neighbourhood search meta-heuristics for capacitated lot-sizing with sequence-dependent setups. Int J Prod Res 48(3):861–878

    Article  Google Scholar 

  • Almada-Lobo B, Klabjan D, Carravilla MA, Oliveira JF (2007) Single machine multi-product capacitated lot sizing with sequence-dependent setups. Int J Prod Res 45(20):4873–4894

    Article  Google Scholar 

  • Almada-Lobo B, Klabjan D, Carravilla MA, Oliveira JF (2010) Multiple machine continuous setup lotsizing with sequence-dependent setups. Comput Optim Appl 47(3):529–552

    Article  Google Scholar 

  • Almeder C, Almada-Lobo B (2011) Synchronisation of scarce resources for a parallel machine lotsizing problem. Int J Prod Res 49(24):7315–7335

    Article  Google Scholar 

  • Almeder C, Klabjan D, Traxler R, Almada-Lobo B (2015) Lead time considerations for the multi-level capacitated lot-sizing problem. Eur J Oper Res 241(3):727–738

    Article  Google Scholar 

  • Amorim P, Antunes CH, Almada-Lobo B (2011) Multi-objective lot-sizing and scheduling dealing with perishability issues. Ind Eng Chem Res 50(6):3371–3381

    Article  Google Scholar 

  • Amorim P, Günther H-O, Almada-Lobo B (2012) Multi-objective integrated production and distribution planning of perishable products. Int J Prod Econ 138(1):89–101

    Article  Google Scholar 

  • Amorim P, Pinto-Varela T, Almada-Lobo B, Barbósa-Póvoa APFD (2013) Comparing models for lot-sizing and scheduling of single-stage continuous processes: Operations research and process systems engineering approaches. Comput Chem Eng 52:177–192

    Article  Google Scholar 

  • Aras O, Swanson L (1982) A lot sizing and sequencing algorithm for dynamic demands upon a single facility. J Oper Manag 2(3):177–185

    Article  Google Scholar 

  • Babaei M, Mohammadi M, Ghomi SMTF (2014) A genetic algorithm for the simultaneous lot sizing and scheduling problem in capacitated flow shop with complex setups and backlogging. Int J Adv Manuf Technol 70(1–4):125–134

    Article  Google Scholar 

  • Baker T, Muckstadt J Jr (1989) The CHES problems. Chesapeake Decision Sciences Inc, Tech. rep

  • Baldo TA, Santos MO, Almada-Lobo B, Neto RM (2014) An optimization approach for the lot sizing and scheduling problem in the brewery industry. Comput Ind Eng 72:58–71

    Article  Google Scholar 

  • Brüggemann W, Fischer K, Jahnke H (2003a) Problems, models and complexity. Part I: theory. J Math Model Algorithms 2(2):121–151

    Article  Google Scholar 

  • Brüggemann W, Fischer K, Jahnke H (2003b) Problems, models and complexity. Part II: application to the DLSP. J Math Model Algorithms 2(2):153–169

    Article  Google Scholar 

  • Brüggemann W, Jahnke H (1994) DLSP for two-stage multi-item batch production. Int J Prod Res 32(4):755–768

    Article  Google Scholar 

  • Brüggemann W, Jahnke H (2000a) The discrete lot-sizing and scheduling problem: complexity and modification for batch availability. Eur J Oper Res 124(3):511–528

    Article  Google Scholar 

  • Brüggemann W, Jahnke H (2000b) Erratum to “The discrete lot-sizing and scheduling problem: complexity and modification for batch availability” [EJOR 124 (3) (2000) 511–528]. Eur J Oper Res 126(3):688

  • Buschkühl L, Sahling F, Helber S, Tempelmeier H (2010) Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectr 32(2):231–261

    Article  Google Scholar 

  • Camargo VCB, Toledo FMB, Almada-Lobo B (2012) Three time-based scale formulations for the two stage lot sizing and scheduling in process industries. J Oper Res Soc 63:1613–1630

    Article  Google Scholar 

  • Camargo VCB, Toledo FMB, Almada-Lobo B (2014) HOPS—hamming-oriented partition search for production planning in the spinning industry. Eur J Oper Res 234(1):266–277

    Article  Google Scholar 

  • Campbell GM (1992) Using short-term dedication for scheduling multiple products on parallel machines. Prod Oper Manag 1(3):295–307

    Article  Google Scholar 

  • Cattrysse D, Salomon M, Kuik R, Van Wassenhove LN (1993) A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times. Manag Sci 39(4):477–486

    Article  Google Scholar 

  • Chang P, Chang C, Chen C (2004) An extension of the multi-machine multi-level proportional lot sizing and scheduling model for product-life-cycle demand. Int J Oper Res 1(1):11–22

    Google Scholar 

  • Clark AR (2003) Optimization approximations for capacity constrained material requirements planning. Int J Prod Econ 84(2):115–131

    Article  Google Scholar 

  • Clark AR, Clark SJ (2000) Rolling-horizon lot-sizing when set-up times are sequence-dependent. Int J Prod Res 38(10):2287–2307

    Article  Google Scholar 

  • Clark AR, Mahdieh M, Rangel S (2014) Production lot sizing and scheduling with non-triangular sequence-dependent setup times. Int J Prod Res 52(8):2490–2503

    Article  Google Scholar 

  • Clark AR, Morabito R, Toso EAV (2010) Production setup-sequencing and lot-sizing at an animal nutrition plant through ATSP subtour elimination and patching. J Sched 13(2):111–121

    Article  Google Scholar 

  • Constantino M (2000) A polyhedral approach to a production planning problem. Ann Oper Res 96(1–4):75–95

    Article  Google Scholar 

  • Dastidar SG, Nagi R (2005) Scheduling injection molding operations with multiple resource constraints and sequence dependent setup times and costs. Comput Oper Res 32(11):2987–3005

    Article  Google Scholar 

  • Dauzère-Pérès S, Lasserre J-B (1994) Integration of lotsizing and scheduling decisions in a job-shop. Eur J Oper Res 28(3):413–426

    Article  Google Scholar 

  • Dauzère-Pérès S, Lasserre J-B (2002) On the importance of sequencing decisions in production planning and scheduling. Int Trans Oper Res 9(6):779–793

    Article  Google Scholar 

  • de Araujo SA, Arenales MN, Clark AR (2007) Joint rolling-horizon scheduling of materials processing and lot-sizing with sequence-dependent setups. J Heuristics 13(4):337–358

    Article  Google Scholar 

  • de Araujo SA, Arenales MN, Clark AR (2008) Lot sizing and furnace scheduling in small foundries. Comput Oper Res 35(3):916–932

    Article  Google Scholar 

  • de Araujo SA, Clark AR (2013) A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem. Comput Ind Eng 65(4):577–585

    Article  Google Scholar 

  • de Matta R (1994) A Lagrangean decomposition solution to a single line multiproduct scheduling problem. Eur J Oper Res 79(1):25–37

    Article  Google Scholar 

  • de Matta R, Guignard M (1994a) Dynamic production scheduling for a process industry. Oper Res 42(3):492–503

    Article  Google Scholar 

  • de Matta R, Guignard M (1994b) Studying the effects of production loss due to setup in dynamic production scheduling. Eur J Oper Res 72(1):62–73

    Article  Google Scholar 

  • de Matta R, Guignard M (1995) The performance of rolling production schedules in a process industry. IIE Trans 27(5):564–573

    Article  Google Scholar 

  • de Souza PS, Talukdar SN (1993) Asynchronous organizations for multialgorithm problems. In: Proceedings of the 1993 ACM/SIGAPP symposium on applied computing: states of the art and practice, SAC n++93, pp 286–293

  • Drexl A, Haase K (1995) Proportional lotsizing and scheduling. Int J Prod Econ 40(1):73–87

    Article  Google Scholar 

  • Drexl A, Haase K (1996) Sequential-analysis based randomized-regret-methods for lot-sizing and scheduling. J Oper Res Soc 47(2):251–265

    Article  Google Scholar 

  • Drexl A, Haase K, Kimms A (1995) Losgrößen- und Ablaufplanung in PPS-Systemen auf der Basis randomisierter Opportunitätskosten. Z Betriebswirtschaft 65(3):267–285

    Google Scholar 

  • Drexl A, Kimms A (1997) Lot sizing and scheduling—survey and extensions. Eur J Oper Res 99(2):221–235

    Article  Google Scholar 

  • Dumas Y, Desrosiers J, Gelinas E, Solomon MM (1995) An optimal algorithm for the traveling salesman problem with time windows. Oper Res 43(2):367–371

    Article  Google Scholar 

  • Eppen GD, Martin RK (1987) Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper Res 35(6):832–848

    Article  Google Scholar 

  • Erdirik-Dogan M, Grossmann IE (2008) Simultaneous planning and scheduling of single-stage multi-product continuous plants with parallel lines. Comput Chem Eng 32(11):2664–2684

    Article  Google Scholar 

  • Fandel G, Stammen-Hegener C (2006) Simultaneous lot sizing and scheduling for multi-product multi-level production. Int J Prod Econ 104(2):308–316

    Article  Google Scholar 

  • Ferreira D, Clark AR, Almada-Lobo B, Morabito Neto R (2012) Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production. Int J Prod Econ 136(2):255–265

    Article  Google Scholar 

  • Ferreira D, Morabito Neto R, Rangel S (2009) Solution approaches for the soft drink integrated production lot sizing and scheduling problem. Eur J Oper Res 196(2):697–706

    Article  Google Scholar 

  • Ferreira D, Morabito Neto R, Rangel S (2010) Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants. Comput Oper Res 37(4):684–691

    Article  Google Scholar 

  • Figueira G, Santos MO, Almada-Lobo B (2013) A hybrid VNS approach for the short-term production planning and scheduling: a case study in the pulp and paper industry. Comput Oper Res 40(7):1804–1818

    Article  Google Scholar 

  • Filho MAF, Santos MO, Meneses CN (2012) Asynchronous teams for joint lot-sizing and scheduling problem in flow shops. Int J Prod Res 50(20):5809–5822

    Article  Google Scholar 

  • Fleischmann B (1990) The discrete lot-sizing and scheduling problem. Eur J Oper Res 44(3):337–348

    Article  Google Scholar 

  • Fleischmann B (1994) The discrete lot-sizing and scheduling problem with sequence-dependent setup costs. Eur J Oper Res 75(2):395–404

    Article  Google Scholar 

  • Fleischmann B, Meyr H (1997) The general lotsizing and scheduling problem. OR Spectr 19(1):11–21

    Article  Google Scholar 

  • Furlan MM, Almada-Lobo B, Santos MO, Morabito Neto R (2013) A genetic algorithm-based heuristic with unequal individuals to tackle the lot-sizing and scheduling problem. In: Proceedings of XLV SBPO—Simpösio Brasileiro de Pesquisa Operacional, pp 3505–3516

  • Furlan MM, Almada-Lobo B, Santos MO, Morabito Neto R (2015) Unequal individual genetic algorithm with intelligent diversification for the lot-scheduling problem in integrated mills using multiple-paper machines. Comput Oper Res 59:33–50

    Article  Google Scholar 

  • Gaglioppa F, Miller LA, Benjaafar S (2008) Multitask and multistage production planning and scheduling for process industries. Oper Res 56(4):1010–1025

    Article  Google Scholar 

  • Gicquel C (2008) MIP models and exact methods for the discrete lot-sizing and scheduling problem with sequence-dependent changeover costs and times. Ph.D. thesis, École Centrale Paris

  • Gicquel C, Lisser A, Minoux M (2014) An evaluation of semidefinite programming based approaches for discrete lot-sizing problems. Eur J Oper Res 237(2):498–507

    Article  Google Scholar 

  • Gicquel C, Miègeville N, Minoux M, Dallery Y (2009a) Discrete lot sizing and scheduling using product decomposition into attributes. Comput Oper Res 36(9):2690–2698

    Article  Google Scholar 

  • Gicquel C, Minoux M (2015) Multi-product valid inequalities for the discrete lot-sizing and scheduling problem. Comput Oper Res 54:12–20

    Article  Google Scholar 

  • Gicquel C, Minoux M, Dallery Y (2009b) On the discrete lot-sizing and scheduling problem with sequence-dependent changeover times. Oper Res Lett 37(1):32–36

    Article  Google Scholar 

  • Gicquel C, Minoux M, Dallery Y (2011) Exact solution approaches for the discrete lot-sizing and scheduling problem with parallel resources. Int J Prod Res 49(9):2587–2603

    Article  Google Scholar 

  • Gicquel C, Wolsey LA, Minoux M (2012) On discrete lot-sizing and scheduling on identical parallel machines. Optim Lett 6(3):545–557

    Article  Google Scholar 

  • Göthe-Lundgren M, Lundgren JT, Persson JA (2002) An optimization model for refinery production scheduling. Int J Prod Econ 78(3):255–270

    Article  Google Scholar 

  • Grünert T (1998) Multi-level sequence-dependent dynamic lotsizing and scheduling. Shaker Verlag, Aachen

    Google Scholar 

  • Guimarães L, Klabjan D, Almada-Lobo B (2013) Pricing, relaxing and fixing under lot sizing and scheduling. Eur J Oper Res 230(2):399–411

    Article  Google Scholar 

  • Guimarães L, Klabjan D, Almada-Lobo B (2014) Modeling lotsizing and scheduling problems with sequence dependent setups. Eur J Oper Res 239(3):644–662

    Article  Google Scholar 

  • Günther H-O (2014) The block planning approach for continuous time-based dynamic lot sizing and scheduling. Bus Res 7(1):51–76

    Article  Google Scholar 

  • Günther H-O, Grunow M, Neuhaus U (2006) Realizing block planning concepts in make-and-pack production using MILP modelling and SAP APO. Int J Prod Res 44(18–19):3711–3726

    Article  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(4):727–747

    Article  Google Scholar 

  • Haase K (1994) Lotsizing and scheduling for production planning. Springer, Berlin

    Book  Google Scholar 

  • Haase K (1996) Capacitated lot-sizing with sequence dependent setup costs. OR Spectr 18(1):51–59

    Article  Google Scholar 

  • Haase K, Kimms A (2000) Lot sizing and scheduling with sequence-dependent setup costs and times and efficient rescheduling opportunities. Int J Prod Econ 66(2):159–169

    Article  Google Scholar 

  • Harris FW (1913) How many parts to make at once. Fact Mag Manag 10(2):135–136, 152

  • Heuts RMJ, Seidel HP, Selen WJ (1992) A comparison of two lot sizing-sequencing heuristics for the process industry. Eur J Oper Res 59(3):413–424

    Article  Google Scholar 

  • James RJW, Almada-Lobo B (2011) Single and parallel machine capacitated lotsizing and scheduling: new iterative MIP-based neighborhood search heuristics. Comput Oper Res 38(12):1816–1825

    Article  Google Scholar 

  • Jans R, Degraeve Z (2004) An industrial extension of the discrete lot-sizing and scheduling problem. IIE Trans 36(1):47–58

    Article  Google Scholar 

  • Jans R, Degraeve Z (2008) Modeling industrial lot sizing problems: a review. Int J Prod Res 46(6):1619–1643

    Article  Google Scholar 

  • Jordan C, Drexl A (1998) Discrete lotsizing and scheduling by batch sequencing. Manag Sci 44(5):698–713

    Article  Google Scholar 

  • Kaczmarczyk W (2011) Proportional lot-sizing and scheduling problem with identical parallel machines. Int J Prod Res 49(9):2605–2623

    Article  Google Scholar 

  • Kang S, Malik K, Thomas LJ (1999) Lotsizing and scheduling on parallel machines with sequence-dependent setup costs. Manag Sci 45(2):273–289

    Article  Google Scholar 

  • Karimi-Nasab M, Modarres M (2015) Lot sizing and job shop scheduling with compressible process times: a cut and branch approach. Comput Ind Eng 85:196–205

    Article  Google Scholar 

  • Karimi-Nasab M, Modarres M, Seyedhoseini S (2015) A self-adaptive PSO for joint lot sizing and job shop scheduling with compressible process times. Appl Soft Comput 27:137–147

    Article  Google Scholar 

  • Karimi-Nasab M, Seyedhoseini SM (2013) Multi-level lot sizing and job shop scheduling with compressible process times: a cutting plane approach. Eur J Oper Res 231(3):598–616

    Article  Google Scholar 

  • Karimi-Nasab M, Seyedhoseini SM, Modarres M, Heidari M (2013) Multi-period lot sizing and job shop scheduling with compressible process times for multilevel product structures. Int J Prod Res 51(20):6229–6246

    Article  Google Scholar 

  • Karmarkar US, Schrage L (1985) The deterministic dynamic product cycling problem. Oper Res 33(2):326–345

    Article  Google Scholar 

  • Kilger C, Meyr H (2015) Demand fulfillment and ATP. In: Stadtler H, Kilger C, Meyr H (eds) Supply chain management and advanced planning, 5th edn. Springer texts in business and economics, vol 9. Springer, Berlin, pp 177–194

  • Kimms A (1996a) Competitive methods for multi-level lot sizing and scheduling: tabu search and randomized regrets. Int J Prod Res 34(8):2279–2298

    Article  Google Scholar 

  • Kimms A (1996b) Multi-level, single-machine lot sizing and scheduling (with initial inventory). Eur J Oper Res 89(1):86–99

    Article  Google Scholar 

  • Kimms A (1997a) Demand shuffle—a method for multilevel proportional lot sizing and scheduling. Nav Res Logist 44(4):319–340

    Article  Google Scholar 

  • Kimms A (1997b) Multi-level lot sizing and scheduling. Physics, Heidelberg

    Book  Google Scholar 

  • Kimms A (1999) A genetic algorithm for multi-level, multi-machine lot sizing and scheduling. Comput Oper Res 26(8):829–848

    Article  Google Scholar 

  • Kimms A, Drexl A (1998) Proportional lot sizing and scheduling: some extensions. Networks 32(2):85–101

    Article  Google Scholar 

  • Koçlar A, Süral H (2005) A note on “The general lot sizing and scheduling problem”. OR Spectr 27(1):145–146

    Article  Google Scholar 

  • Kopanos GM, Puigjaner L, Maravelias CT (2011) Production planning and scheduling of parallel continuous processes with product families. Ind Eng Chem Res 50(3):1369–1378

    Article  Google Scholar 

  • Kovács A, Brown KN, Tarim SA (2009) An efficient MIP model for the capacitated lot-sizing and scheduling problem with sequence-dependent setups. Int J Prod Econ 118(1):282–291

    Article  Google Scholar 

  • Kwak I, Jeong I (2011) A hierarchical approach for the capacitated lot-sizing and scheduling problem with a special structure of sequence-dependent setups. Int J Prod Res 49(24):7425–7439

    Article  Google Scholar 

  • Laguna M (1999) A heuristic for production scheduling and inventory control in the presence of sequence-dependent setup time. IIE Trans 31(2):125–134

    Google Scholar 

  • Lang JC (2010) Production and inventory management with substitutions. In: Lecture notes in economics and mathematical systems. Springer, Heidelberg

  • Lang JC, Shen ZM (2011) Fix-and-optimize heuristics for capacitated lot-sizing with sequence-dependent setups and substitutions. Eur J Oper Res 214(3):595–605

    Article  Google Scholar 

  • Lasdon L, Terjung RC (1971) An efficient algorithm for multi-item scheduling. Oper Res 19(4):946–969

    Article  Google Scholar 

  • Liberatore M, Miller T (1985) A hierarchical production planning system. Interfaces 15(4):1–11

    Article  Google Scholar 

  • Mac Cawley AF (2014) The international wine supply chain: challenges from bottling to the glass. Ph.D. thesis, Georgia Institute of Technology

  • Magnanti TL, Vachani R (1990) A strong cutting plane algorithm for production scheduling with changeover costs. Oper Res 38(3):456–473

    Article  Google Scholar 

  • Maldonado M, Rangel S, Ferreira D (2014) A study of different subsequence elimination strategies for the soft drink production planning. J Appl Res Technol 12(4):631–641

    Article  Google Scholar 

  • Marinelli F, Nenni ME, Sforza A (2007) Capacitated lot sizing and scheduling with parallel machines and shared buffers: a case study in a packaging company. Ann Oper Res 150(1):177–192

    Article  Google Scholar 

  • Mateus GR, Ravetti MG, de Souza MC, Valeriano TM (2010) Capacitated lot sizing and sequence dependent setup scheduling: an iterative approach for integration. J Sched 13(3):245–259

    Article  Google Scholar 

  • Menezes AA, Clark AR, Almada-Lobo B (2011) Capacitated lot-sizing and scheduling with sequence-dependent, period-overlapping and non-triangular setups. J Sched 14(2):209–219

    Article  Google Scholar 

  • Meyr H (1999) Simultane Losgrößen- und Reihenfolgeplanung für kontinuierliche Produktionslinien. Deutscher Universitätsverlag, Wiesbaden

    Book  Google Scholar 

  • Meyr H (2000) Simultaneous lotsizing and scheduling by combining local search with dual reoptimization. Eur J Oper Res 120(2):311–326

    Article  Google Scholar 

  • Meyr H (2002) Simultaneous lotsizing and scheduling on parallel machines. Eur J Oper Res 139(2):277–292

    Article  Google Scholar 

  • Meyr H (2004) Simultane Losgrößen- und Reihenfolgeplanung bei mehrstufiger kontinuierlicher Fertigung. Z Betriebswirtschaft 74(6):585–610

    Google Scholar 

  • Meyr H, Mann M (2013) A decomposition approach for the general lotsizing and scheduling problem for parallel production lines. Eur J Oper Res 229(3):718–731

    Article  Google Scholar 

  • Miller AJ, Wolsey LA (2003) Tight MIP formulations for multi-item discrete lot-sizing problems. Oper Res 51(4):557–565

    Article  Google Scholar 

  • Mohammadi M (2010) Integrating lotsizing, loading, and scheduling decisions in flexible flow shops. Int J Adv Manuf Technol 50(9–12):1165–1174

    Article  Google Scholar 

  • Mohammadi M, Ghomi SMTF (2011) Genetic algorithm-based heuristic for capacitated lotsizing problem in flow shops with sequence-dependent setups. Expert Syst Appl 38(6):7201–7207

    Article  Google Scholar 

  • Mohammadi M, Ghomi SMTF, Jafari N (2011) A genetic algorithm for simultaneous lotsizing and sequencing of the permutation flow shops with sequence-dependent setups. Int J Comput Integr Manuf 24(1):87–93

    Article  Google Scholar 

  • Mohammadi M, Ghomi SMTF, Karimi B, Torabi SA (2010a) MIP-based heuristics for lotsizing in capacitated pure flow shop with sequence-dependent setups. Int J Prod Res 48(10):2957–2973

    Article  Google Scholar 

  • Mohammadi M, Ghomi SMTF, Karimi B, Torabi SA (2010b) Rolling-horizon and fix-and-relax heuristics for the multi-product multi-level capacitated lotsizing problem with sequence-dependent setups. J Intell Manuf 21(4):501–510

    Article  Google Scholar 

  • Mohammadi M, Karimi B, Ghomi SMTF, Torabi SA (2010c) A new algorithmic approach for capacitated lot-sizing problem in flow shops with sequence-dependent setups. Int J Adv Manuf Technol 49(1–4):201–211

    Article  Google Scholar 

  • Mohammadi M, Poursabzi O (2014) A rolling horizon-based heuristic to solve a multi-level general lot sizing and scheduling problem with multiple machines (MLGLSP\(\_\)MM) in job shop manufacturing system. Uncertain Supply Chain Manag 2(3):167–178

    Article  Google Scholar 

  • Muramatsu K, Warman A, Kobayashi M (2003) A near-optimal solution method of multi-item multi-process dynamic lot size scheduling problem. JSME Int J Ser C Mech Syst Mach Elem Manuf 46(1):46–53

    Article  Google Scholar 

  • Pahl J, Voß S (2010) Discrete lot-sizing and scheduling including deterioration and perishability constraints. In: Dangelmaier W, Blecken A, Delius R, Klöpfer S (eds) Advanced manufacturing and sustainable logistics, vol 46. Lecture notes in business information processing. Springer, Berlin, pp 345–357

  • Pahl J, Voß S, Woodruff DL (2011) Discrete lot-sizing and scheduling with sequence-dependent setup times and costs including deterioration and perishability constraints. In: Proceedings of the 44th Hawaii international conference on system sciences. IEEE Computer Society, Los Alamitos, pp 1–10

  • Persson JA, Göthe-Lundgren M, Lundgren JT, Gendron B (2004) A tabu search heuristic for scheduling the production processes at an oil refinery. Int J Prod Res 42(3):445–471

    Article  Google Scholar 

  • Pochet Y, Wolsey LA (1991) Solving multi-item lot-sizing problems using strong cutting planes. Manag Sci 37(1):53–67

    Article  Google Scholar 

  • Pochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer, New York

    Google Scholar 

  • Quadt D, Kuhn H (2005) Conceptual framework for lot-sizing and scheduling of flexible flow lines. Int J Prod Res 43(11):2291–2308

    Article  Google Scholar 

  • Quadt D, Kuhn H (2008) Capacitated lot-sizing with extensions: a review. 4OR 6(1):61–83

  • Quadt D, Kuhn H (2009) Capacitated lot-sizing and scheduling with parallel machines, back-orders and setup carry-over. Nav Res Logist 56(4):366–384

    Article  Google Scholar 

  • Ramezanian R, Saidi-Mehrabad M, Fattahi P (2013a) MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints. J Manuf Syst 32(2):392–401

    Article  Google Scholar 

  • Ramezanian R, Saidi-Mehrabad M, Teimoury E (2013b) A mathematical model for integrating lot-sizing and scheduling problem in capacitated flow shop environments. Int J Adv Manuf Technol 66(1–4):347–361

    Article  Google Scholar 

  • Rocha LR, Ravetti MG, Meteus GR, Pardalos PM (2008) Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput Oper Res 35(4):1250–1264

    Article  Google Scholar 

  • Rohaninejad M, Kheirkhah A, Fattahi P (2015) Simultaneous lot-sizing and scheduling in flexible job shop problems. Int J Adv Manuf Technol 78(1):1–18

    Article  Google Scholar 

  • Salomon M, Solomon MM, Van Wassenhove LN, Dumas Y, Dauzère-Pérès S (1997) Solving the discrete lotsizing and scheduling problem with sequence dependent set-up costs and set-up times using the traveling salesman problem with time windows. Eur J Oper Res 100(3):494–513

    Article  Google Scholar 

  • Santos MO, Almada-Lobo B (2012) Integrated pulp and paper mill planning and scheduling. Comput Ind Eng 63(1):1–12

    Article  Google Scholar 

  • Schrage L (1982) The multiproduct lot scheduling problem. In: Dempster M, Lenstra J, Rinnooy Kan A (eds) Deterministic and stochastic scheduling. Kluwer Academic Publishers, Dordrecht, pp 233–244

  • Seeanner F (2013) Multi-stage simultaneous lot-sizing and scheduling—planning of flow lines with shifting bottlenecks. In: Produktion und Logistik, Springer Gabler, Wiesbaden

  • Seeanner F, Almada-Lobo B, Meyr H (2013) Combining the principles of variable neighborhood decomposition search and the fix&optimize heuristic to solve multi-level lot-sizing and scheduling problems. Comput Oper Res 40(1):303–317

    Article  Google Scholar 

  • Seeanner F, Meyr H (2013) Multi-stage simultaneous lot-sizing and scheduling for flow line production. OR Spectr 35(1):33–73

    Article  Google Scholar 

  • Shim I, Kim H, Doh H, Lee D (2011) A two-stage heuristic for single machine capacitated lot-sizing and scheduling with sequence-dependent setup costs. Comput Ind Eng 61(4):920–929

    Article  Google Scholar 

  • Sikora R, Chhajed D, Shaw MJ (1996) Integrating the lot-sizing and sequencing decisions for scheduling a capacitated flow line. Comput Ind Eng 30(4):659–679

    Article  Google Scholar 

  • Sikora RT (1996) A genetic algorithm for integrating lot-sizing and sequencing in scheduling a capacitated flow line. Comput Ind Eng 30(4):969–981

    Article  Google Scholar 

  • Smith-Daniels VL, Ritzman LP (1988) A model for lot sizing and sequencing in process industries. J Prod Res 26(4):647–674

    Article  Google Scholar 

  • Smith-Daniels VL, Smith-Daniels DE (1986) A mixed integer programming model for lot sizing and sequencing packaging lines in the process industries. IIE Trans 18(3):278–285

    Article  Google Scholar 

  • Stadtler H (2011) Multi-level single machine lot-sizing and scheduling with zero lead times. Eur J Oper Res 209(3):241–252

    Article  Google Scholar 

  • Stadtler H, Sahling F (2013) A lot-sizing and scheduling model for multi-stage flow lines with zero lead times. Eur J Oper Res 225(3):404–419

    Article  Google Scholar 

  • Suerie C (2005) Campaign planning in time-indexed model formulations. Int J Prod Res 43(1):49–66

    Article  Google Scholar 

  • Suerie C (2006) Modeling of period overlapping setup times. Eur J Oper Res 174(2):874–886

    Article  Google Scholar 

  • Supithak W, Liman SD, Montes EJ (2010) Lot-sizing and scheduling problem with earliness tardiness and setup penalties. Comput Ind Eng 58(3):363–372

    Article  Google Scholar 

  • Tempelmeier H, Buschkühl L (2008) Dynamic multi-machine lotsizing and sequencing with simultaneous scheduling of a common setup resource. Int J Prod Econ 113(1):401–412

    Article  Google Scholar 

  • Tempelmeier H, Copil K (2015) Capacitated lot sizing with parallel machines, sequence-dependent setups and a common setup operator. OR Spectr doi:10.1007/s00291-015-0410-2

  • Tiacci L, Saetta S (2012) Demand forecasting, lot sizing and scheduling on a rolling horizon basis. Int J Prod Econ 140(2):803–814

    Article  Google Scholar 

  • Toledo CFM, Arantes MDS, de Oliveira RRR, Almada-Lobo B (2013) Glass container production scheduling through hybrid multi-population based evolutionary algorithm. Appl Soft Comput 13(3):1352–1364

  • Toledo CFM, de Jesus Filho JEF, França PM (2008) Meta-heuristic approaches for a soft drink industry problem. IEEE Int Conf Emerg Technol Fact Autom 2008:1384–1391

    Google Scholar 

  • Toledo CFM, de Oliveira L, de Freitas Pereira R, França PM, Morabito R (2014) A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem. Comput Oper Res 48(1):40–52

    Article  Google Scholar 

  • Toledo CFM, de Oliveira L, de Oliveira RRR, Pereira MR (2010) Parallel genetic algorithm approaches applied to solve a synchronized and integrated lot sizing and scheduling problem. In: Proceedings of the 2010 ACM symposium on applied computing (SAC’10). ACM, New York, pp 1148–1152

  • Toledo CFM, França PM, Morabito R, Kimms A (2009) Multi-population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem. Int J Prod Res 47(11):3097–3119

    Article  Google Scholar 

  • Toledo CFM, França PM, Rosa KA (2008) Evaluating genetic algorithms with different population structures on a lot sizing and scheduling problem. In: Proceedings of the 2008 ACM symposium on applied computing (Fortaleza. Ceara, Brazil), pp 1777–1781

  • Toledo CFM, Kimms A, França PM, Morabito R (2006) A mathematical model for the synchronized and integrated two-level lot sizing and scheduling problem. University of Campinas, Brazil

  • Toledo CFM, Kimms A, França PM, Morabito R (2015) The synchronized and integrated two-level lot sizing and scheduling problem: evaluating the generalized mathematical model. Math Probl Eng (Article ID 182781)

  • Toso EAV, Morabito R, Clark AR (2009) Lot sizing and sequencing optimisation at an animal-feed plant. Comput Ind Eng 57(3):813–821

    Article  Google Scholar 

  • Transchel S, Minner S, Kallrath J, Löhndorf N, Eberhard U (2011) A hybrid general lot-sizing and scheduling formulation for a production process with a two-stage product structure. Int J Prod Res 49(9):2463–2480

    Article  Google Scholar 

  • Urrutia EDG, Aggoune R, Dauzère-Pérères S (2014) Solving the integrated lot-sizing and job-shop scheduling problem. Int J Prod Res 17(52):5236–5254

    Article  Google Scholar 

  • van Eijl CA, van Hoesel CPM (1997) On the discrete lot-sizing and scheduling problem with Wagner–Whitin costs. Oper Res Lett 20(1):7–13

    Article  Google Scholar 

  • van Hoesel S, Kolen A (1994) A linear description of the discrete lot-sizing and scheduling problem. Eur J Oper Res 75(2):342–353

    Article  Google Scholar 

  • Vanderbeck F (1998) Lot-sizing with start-up times. Manag Sci 44(10):1409–1425

    Article  Google Scholar 

  • Wagner HM, Whitin TM (1958) Dynamic version of the economic lot size model. Manag Sci 5(1):89–96

    Article  Google Scholar 

  • Wolosewicz C, Dauzère-Pérès S, Aggoune R (2015) A Lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem. Eur J Oper Res 244(1):3–12

    Article  Google Scholar 

  • Wolsey LA (1997) MIP modelling of changeovers in production planning and scheduling problems. Eur J Oper Res 99(1):154–165

    Article  Google Scholar 

  • Wolsey LA (2002) Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation. Manag Sci 48(12):1587–1602

    Article  Google Scholar 

  • Xiao J, Yang H, Zhang C, Zheng L, Gupta JND (2015) A hybrid lagrangian-simulated annealing-based heuristic for the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times. Comput Oper Res 63:72–82

    Article  Google Scholar 

  • Xiao J, Zhang C, Zheng L, Gupta JND (2013) MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem. Int J Prod Res 51(16):5011–5028

    Article  Google Scholar 

  • Zhu X, Wilhelm WE (2006) Scheduling and lot sizing with sequence-dependent setup: a literature review. IIE Trans 38(11):987–1007

    Article  Google Scholar 

Download references

Acknowledgments

We thank the anonymous reviewers and area editor for their helpful comments.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Karina Copil or Martin Wörbelauer.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Copil, K., Wörbelauer, M., Meyr, H. et al. Simultaneous lotsizing and scheduling problems: a classification and review of models. OR Spectrum 39, 1–64 (2017). https://doi.org/10.1007/s00291-015-0429-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-015-0429-4

Keywords

Navigation