A queueing model for a two-stage stochastic manufacturing system with overlapping operations



This paper presents analytical expressions for estimating average process batch flow times through a stochastic manufacturing system with overlapping operations. It is shown that the traditional queueing methodology cannot be directly applied to this setting, as the use of the overlapping operations principle causes the arrival process of sublots at the second stage to be a non-renewal process. An embedded queueing model is then proposed, which provides a tool to estimate the flow time reductions caused by the use of overlapping operations. Moreover, we provide expressions to estimate the production disruptions occurring at the second stage. The results of our research confirm the general intuition that the overlapping operations principle leads to less congestion, and hence a smoother flow of work through the system. On the other hand however, lot splitting inevitably requires more material handling on the shop floor. The expressions provided in this paper allow the quantification of the trade-off between these two effects, e.g., by gauging them within the scope of a cost model.


Lot splitting Overlapping operations Queueing theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baker KR, Jia D (1993) A comparative study of lot streaming techniques. Omega 21:561–566CrossRefGoogle Scholar
  2. Benjaafar S (1996) On production batches, transfer batches, and lead times. IIE Trans 28:357–362Google Scholar
  3. Blumenfeld D (2001) Operations research calculations handbook, CRC Press, Boca Raton, FLMATHGoogle Scholar
  4. Bozer YA, Kim J (1996) Determining transfer batch sizes in trip-based material handling systems. Int J Flex Manuf Syst 8(4):313–356CrossRefGoogle Scholar
  5. Bukchin J, Tzur M, Jaffe M (2002) Lot splitting to minimize average flow time in a two-machine flow shop. IIE Trans 34:953–970CrossRefGoogle Scholar
  6. Buzacott JA, Shantikumar JG (1985) On approximate queueing models of dynamic job shops. Manag Sci 31:870–887Google Scholar
  7. Chen J, Steiner G (1998) Lot streaming with attached setups in three-machine flowshops. IIE Trans 30:1075–1084CrossRefGoogle Scholar
  8. Goldratt EM, Cox J (1984) The goal: A process of ongoing improvement, North River Press, New York, NYGoogle Scholar
  9. Graves SC, Kostreva MM (1986) Overlapping operations in materials requirements planning. J Oper Manag 6:283–294CrossRefGoogle Scholar
  10. Hopp WJ, Spearman ML, Woodruff DL (1990) Practical strategies for lead time reduction. Manufact Rev 3:78–84Google Scholar
  11. Hopp WJ, Spearman ML (2000) Factory physics: Foundations of manufacturing management, Irwin/McGraw-Hill, New York, NYGoogle Scholar
  12. Jacobs FR, Bragg DJ (1988) Repetitive lots: Flow- time reductions through sequencing and dynamic batch sizing. Dec Sci 19:281–294Google Scholar
  13. Karmarkar U, Kekre S, Freeman S (1985a) Lot sizing and lead time performance in a manufacturing cell. Interfaces 15:1–9Google Scholar
  14. Karmarkar U, Kekre S, Kekre S (1985b) Lot sizing in multi-item multi-machine job shops. IIE Trans 17:290–298Google Scholar
  15. Karmarkar U (1987) Lot sizes, lead times and in-process inventories. Manag Sci 33:409–417Google Scholar
  16. Kleinrock L (1975) Queueing systems, John Wiley & Sons, New York, NYMATHGoogle Scholar
  17. Kramer W, Lagenbach-Belz M (1976) Approximate formulae for the delay in the queueing system GI/GI/1. In: The Congressbook of the Eight International Teletraffic Congress, Melbourne, pp. 2351–2358Google Scholar
  18. Kropp DH, Smunt TL (1990) Optimal and heuristic models for lot splitting in a flow shop. Dec Sci 21:691–709Google Scholar
  19. Lambrecht MR, Ivens PL, Vandaele NJ (1998) ACLIPS: A capacity and lead time integrated procedure for scheduling. Manag Sci 44:1548–1561Google Scholar
  20. Langevin A, Riopel D, Stecke KE (1999) Transfer batch sizing in flexible manufacturing systems. J Manuf Syst 18:140–151Google Scholar
  21. Litchfield JL, Narasimhan R (2000) Improving job shop performance through process queue management under transfer batching. Prod Oper Manag 9:336–348Google Scholar
  22. Marshall KT (1968) Some inequalities in queueing. Oper Res 16:651–665MATHMathSciNetCrossRefGoogle Scholar
  23. Potts CN, Kovalyov MY (2000) Scheduling with batching: A review. Europ J Oper Res 120:228–249MathSciNetCrossRefMATHGoogle Scholar
  24. Ramasesh RV, Fu H, Fong DKH, Hayya JC (2000) Lot streaming in multistage production systems. Int J Prod Econ 66:199–211CrossRefGoogle Scholar
  25. Ruben RA, Mahmoodi F (1998) Lot splitting in unbalanced production systems. Dec Sci 29:921–949Google Scholar
  26. Santos C, Magazine M (1985) Batching in single-operations manufacturing systems. Oper Res Lett 4:99–103CrossRefMATHGoogle Scholar
  27. Smunt TL, Buss AH, Kropp DH (1996) Lot splitting in stochastic flow shop and job shop environments. Dec Sci 27:215–238Google Scholar
  28. Suri R (1998) Quick Response Manufacturing: A companywide approach to reducing lead times, Productivity Press, Portland ORGoogle Scholar
  29. Suri R, Sanders JL, Kamath M (1993) Performance evaluation of production networks. In: S. C. Graves et al. (Eds), Logistics of Production and Inventory, Handbooks in Operations Research and Management Science, North-Holland, pp. 199–286Google Scholar
  30. Umble M, Srikanth ML (1995) Synchronous manufacturing: Principles for world-class excellence. The Spectrum Publishing Company, Wallingford, CTGoogle Scholar
  31. Vandaele NJ, Van Nieuwenhuyse I, Cupers S (2003) Optimal grouping for a nuclear magnetic resonance scanner. Europ J Oper Res 151:181–192CrossRefMATHGoogle Scholar
  32. Van Nieuwenhuyse I. (2004) Lot splitting in single-product flowshops: issues of delivery reliability, production disruptions and flow times. PhD thesis, Department of Applied Economics, University of Antwerp, Antwerp, BelgiumGoogle Scholar
  33. Van Nieuwenhuyse I, Vandaele N (2004a) Determining the optimal number of sublots in a single-product, Deterministic flow shop with overlapping operations. Int J Prod Econ 92:221–239CrossRefGoogle Scholar
  34. Van Nieuwenhuyse I, Vandaele N (2004b) The impact of delivery frequency on delivery reliability in a two-stage supply chain. In: Proceedings of the 13th International Workshop on Production Economics 3:367–392Google Scholar
  35. Van Nieuwenhuyse I, Vandaele N (2006) The impact of delivery lot splitting on delivery reliability in a two-stage supply chain. Int J Prod Econ, forthcomingGoogle Scholar
  36. Van Nieuwenhuyse I, Vandaele N (2005) Analysis of gap times in a two-stage stochastic flowshop with overlapping operations. Department of Applied Economics, University of Antwerp, Research paper 2005–004Google Scholar
  37. Wagner BJ, Ragatz GL (1994) The impact of lot splitting on due date performance. J Oper Manag 12:13–25CrossRefGoogle Scholar
  38. Whitt W (1983) The queueing network analyzer. The Bell Sys Techn J 62:2779–2815Google Scholar
  39. Whitt W (1993) Approximations for the GI/G/m queue. Prod Oper Manag 2:114–161Google Scholar
  40. Whitt W. (1994) Towards better multi-class parametric-decomposition approximations for open queueing networks. Ann Oper Res 48:221–248MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Centre for Modelling and SimulationEuropean University College BrusselsBrusselsBelgium
  2. 2.Department of Applied EconomicsUniversity of AntwerpAntwerpBelgium

Personalised recommendations