Skip to main content
SpringerLink
Log in

Lot streaming with variable sublots: an integer programming formulation

  • Theoretical Paper
  • Published:
Journal of the Operational Research Society

Abstract

This paper deals with the question of how to split a given lot into sublots so as to allow their overlapping production in a flow shop environment. The size of each sublot may vary over the stages. We consider an arbitrary number of stages and assume sublot availability, that is, only completed sublots are allowed to be transferred to the next stage. A mixed integer programming formulation is presented, which enables us to find optimal solutions for medium sized instances. The model is extended further to deal with different settings and objectives. Computational results confirm that the exploitation of variable sublots is advantageous and may lead to a significant increase in productivity.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2

Similar content being viewed by others

References

  • Enns ST (2002). MRP performance effects due to forecast bias and demand uncertainty. Eur J Opl Res 138: 87–102.

    Article  Google Scholar 

  • Yeung JHY, Wong WCK and Ma L (1998). Parameters affecting the effectiveness of MRP systems: a review. Int J Prod Res 36: 313–331.

    Article  Google Scholar 

  • Szendrovits AZ (1975). Manufacturing cycle time determination for a multistage economic production quantity model. Mngt Sci 22: 298–308.

    Article  Google Scholar 

  • Drezner Z, Szendrovits AZ and Wesolowsky GO (1984). Multi-stage production with variable lot sizes and transportation of partial lots. Eur J Opl Res 17: 227–237.

    Article  Google Scholar 

  • Goyal SK and Szendrovits AZ (1986). A constant lot size model with equal and unequal sized batch shipments between production stages. Eng Cost Prod Econ 10: 203–210.

    Article  Google Scholar 

  • Bogaschewsky RW, Buscher UD and Lindner G (2001). Optimizing multi-stage production with constant lot size and varying number of unequal sized batches. Omega—Int J Mngt S 29: 183–191.

    Article  Google Scholar 

  • Graves SC and Kostreva M (1987). Overlapping operations in material requirements planning. J Opl Mngt 6: 283–294.

    Google Scholar 

  • Ramasesh RV, Fu H, Fong DKH and Hayya JC (2000). Lot streaming in multistage production systems. Int J Prod Econ 66: 199–211.

    Article  Google Scholar 

  • French S (1982). Sequencing and Scheduling. Wiley & Sons: New York.

    Google Scholar 

  • Potts CN and Kovalyov MY (2000). Scheduling with batching: a review. Eur J Opl Res 120: 228–249.

    Article  Google Scholar 

  • Brucker P, Heitmann S and Hurink J (2003). How useful are preemptive schedules? Opns Res Lett 31: 129–136.

    Article  Google Scholar 

  • Hancock T (1991). Effects of lot-splitting under various routing strategies. Int J Opns Prod Mngt 11: 68–75.

    Article  Google Scholar 

  • Cheng TCE and Sin CCS (1990). A state-of-the-art review of parallel-machine scheduling research. Eur J Opl Res 47: 271–292.

    Article  Google Scholar 

  • Smunt TL, Buss AH and Kropp DH (1996). Lot splitting in stochastic flow shop and job shop environments. Decision Sci 27: 215–237.

    Article  Google Scholar 

  • Bukchin J, Tzur M and Jaffe M (2002). Lot-splitting to minimize average flow time in a two-machine flowshop. IIE Trans 34: 953–970.

    Google Scholar 

  • Reiter S (1966). A system for managing job-shop production. J Bus 39: 371–393.

    Article  Google Scholar 

  • Lee CY, Lei L and Pinedo M (1997). Current trends in deterministic scheduling. Ann Opns Res 70: 1–41.

    Article  Google Scholar 

  • Allahverdi A, Gupta JND and Aldowaisan T (1999). A review of scheduling research involving setup considerations. Omega—Int J Mngt S 27: 219–239.

    Article  Google Scholar 

  • Jacobs FR (1983). The OPT scheduling system: a review of a new production scheduling system. Prod Inv Mngt J 24: 47–51.

    Google Scholar 

  • Jacobs FR and Bragg DJ (1988). Repetitive lots: flow-time reductions through sequencing and dynamic batch sizing. Decision Sci 19: 281–294.

    Article  Google Scholar 

  • Potts CN and Baker KR (1989). Flow shop scheduling with lot streaming. Opns Res Lett 8: 297–303.

    Article  Google Scholar 

  • Baker KR and Jia D (1993). A comparative study of lot streaming procedures. Omega—Int J Mngt S 21: 561–566.

    Article  Google Scholar 

  • Trietsch D and Baker KR (1993). Basic techniques for lot streaming. Opns Res 41: 1065–1076.

    Article  Google Scholar 

  • Potts CN and Van Wassenhove LN (1992). Integrating scheduling with batching and lot- sizing: a review of algorithms and complexity. J Opns Res Soc 43: 395–406.

    Article  Google Scholar 

  • Vickson RG and Alfredsson BE (1992). Two- and three-machine flow shop scheduling problems with equal sized transfer batches. Int J Prod Res 30: 1551–1574.

    Article  Google Scholar 

  • Kalir AA (1999). Optimal and heuristic solutions for the single and multiple batch flow shop lot streaming problems with equal sublots. PhD thesis, State University, Virginia, US.

  • Kalir AA and Sarin SC (2001). A near-optimal heuristic for the sequencing problem in multiple-batch flow shops with small equal sublots. Omega—Int J Mngt S 29: 577–584.

    Article  Google Scholar 

  • Glass CA, Gupta JND and Potts CN (1994). Lot streaming in three-stage production processes. Eur J Opl Res 75: 378–394.

    Article  Google Scholar 

  • Glass CA and Potts CN (1998). Structural properties of lot streaming in a flow shop. Math Opns Res 23: 624–639.

    Article  Google Scholar 

  • Baker KR and Pyke DF (1990). Solution procedures for the lot-streaming problem. Decision Sci 21: 475–491.

    Article  Google Scholar 

  • Williams EF, Tüfekçi S and Akansel M (1997). O(m2) algorithms for the two and three sublot lot streaming problem. Prod Opns Mngt 6: 74–96.

    Google Scholar 

  • Baker KR (1998). Elements of Sequencing and Scheduling. Amos Tuck School of Business Administration, Dartmouth College: Hanover, NH 03755.

    Google Scholar 

  • Hall NG, Laporte G, Selvarajah E and Sriskandarajah C (2003). Scheduling and lot streaming in flowshops with no-wait in process. J Sched 6: 339–354.

    Article  Google Scholar 

  • Çetinkaya FC and Kayaligil MS (1992). Unit sized transfer batch scheduling with setup times. Comput Ind Eng 22: 177–183.

    Article  Google Scholar 

  • Çetinkaya FC (1994). Lot streaming in a two-stage flow shop with set-up, processing and removal times separated. J Opns Res Soc 45: 1445–1455.

    Article  Google Scholar 

  • Baker KR (1995). Lot streaming in the two-machine flow shop with setup times. Ann Oper Res 57: 1–11.

    Article  Google Scholar 

  • Chen J and Steiner G (1997). Lot streaming with detached setups in three-machine flow shops. Eur J Opns Res 96: 591–611.

    Article  Google Scholar 

  • Chen J and Steiner G (1998). Lot streaming with attached setups in three-machine flow shops. IIE Trans 30: 1075–1084.

    Google Scholar 

  • Chen J and Steiner G (1997b). Approximation methods for discrete lot streaming in flow shops. Opns Res Lett 21: 139–145.

    Article  Google Scholar 

  • Chen J and Steiner G (1999). Discrete lot streaming in two-machine flow shops. Information 37: 160–173.

    Google Scholar 

  • Vickson RG (1995). Optimal lot streaming for multiple products in a two-machine flow shop. Eur J Opns Res 85: 556–575.

    Article  Google Scholar 

  • Sriskandarajah C and Wagneur E (1999). Lot streaming and scheduling multiple products in two-machine no-wait flowshops. IIE Trans 31: 695–707.

    Google Scholar 

  • Dauzère-Pérès S and Lasserre JB (1997). Lot streaming in job-shop scheduling. Opns Res 45: 584–595.

    Article  Google Scholar 

  • Şen A and Benli ÖS (1999). Lot streaming in open shops. Oper Res Lett 23: 135–142.

    Google Scholar 

  • Şen A, Topaloǧlu E and Benli ÖS (1998). Optimal streaming of a single job in a two-stage flow shop. Eur J Opl Res 110: 42–62.

    Article  Google Scholar 

  • Petroff JN and Hill AV (1991). A framework for the design of lot-tracing systems for the 1990's. Prod Inv Mngt J 32: 55–61.

    Google Scholar 

  • Steele DC (1995). A structure for lot-tracing design. Prod Inv Mngt J 36: 53–59.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bielefeld University, Bielefeld, Germany

    D Biskup & M Feldmann

Authors
  1. D Biskup
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M Feldmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M Feldmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Biskup, D., Feldmann, M. Lot streaming with variable sublots: an integer programming formulation. J Oper Res Soc 57, 296–303 (2006). https://doi.org/10.1057/palgrave.jors.2602016

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/palgrave.jors.2602016

Keywords

Search

Navigation