Skip to main content
SpringerLink
Log in

Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds

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

Abstract

The allocation of buffer space in flow lines with stochastic processing times is an important decision, as buffer capacities influence the performance of these lines. The objective of this problem is to minimize the overall number of buffer spaces achieving at least one given goal production rate. We optimally solve this problem with a mixed-integer programming approach by sampling the effective processing times. To obtain robust results, large sample sizes are required. These incur large models and long computation times using standard solvers. This paper presents a Benders Decomposition approach in combination with initial bounds and different feasibility cuts for the Buffer Allocation Problem, which provides exact solutions while reducing the computation times substantially. Numerical experiments are carried out to demonstrate the performance and the flexibility of the proposed approaches. The numerical study reveals that the algorithm is capable to solve long lines with reliable and unreliable machines, including arbitrary distributions as well as correlations of processing times.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Alfieri A, Matta A (2012) Mathematical programming formulations for approximate simulation of multistage production systems. Eur J Oper Res 219(3):773–783

    Article  Google Scholar 

  • Alfieri A, Matta A (2013) Mathematical programming time-based decomposition algorithm for discrete event simulation. Eur J Oper Res 231(3):557–566

    Article  Google Scholar 

  • Bai L, Rubin PA (2009) Combinatorial benders cuts for the minimum tollbooth problem. Oper Res 57(6):1510–1522

    Article  Google Scholar 

  • Benders J (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252

    Article  Google Scholar 

  • Burman M, Gershwin SB, Suyematsu C (1998) Hewlett-packard uses operations research to improve the design of a printer production line. Interfaces 28(1):24–36

    Article  Google Scholar 

  • Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems, vol 4. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Caramanis M (1987) Production system design: A discrete event dynamic system and generalized benders’ decomposition approach. Int J Prod Res 25(8):1223–1234

    Google Scholar 

  • Chan WKV, Schruben L (2008) Optimization models of discrete-event system dynamics. Oper Res 56(5):1218–1237

    Article  Google Scholar 

  • Codato G, Fischetti M (2006) Combinatorial benders cuts for mixed-integer linear programming. Oper Res 54(4):756–766

    Article  Google Scholar 

  • Colledani M, Ekvall M, Lundholm T, Moriggi P, Polato A, Tolio T (2010) Analytical methods to support continuous improvements at scania. Int J Prod Res 48(7):1913–1945

    Article  Google Scholar 

  • Cooke RM, Bosma A, Härte F (2005) A practical model of heineken’s bottle filling line with dependent failures. Eur J Oper Res 164(2):491–504

    Article  Google Scholar 

  • Dallery Y, Gershwin SB (1992) Manufacturing flow line systems: a review of models and analytical results. Queueing Syst 12(1):3–94

    Article  Google Scholar 

  • Demir L, Tunali S, Eliiyi DT (2014) The state of the art on buffer allocation problem: a comprehensive survey. J Intell Manuf 25(3):371–392

    Article  Google Scholar 

  • Diamantidis A, Papadopoulos C (2004) A dynamic programming algorithm for the buffer allocation problem in homogeneous asymptotically reliable serial production lines. Math Probl Eng 2004(3):209–223

    Article  Google Scholar 

  • Gershwin SB, Schor JE (2000) Efficient algorithms for buffer space allocation. Ann Oper Res 93(1):117–144

    Article  Google Scholar 

  • Gürkan G (2000) Simulation optimization of buffer allocations in production lines with unreliable machines. Ann Oper Res 93(1–4):177–216

    Article  Google Scholar 

  • Helber S, Schimmelpfeng K, Stolletz R, Lagershausen S (2011) Using linear programming to analyze and optimize stochastic flow lines. Ann Oper Res 182(1):193–211

    Article  Google Scholar 

  • Hillier FS, So KC, Boling RW (1993) Toward characterizing the optimal allocation of storage space in production line systems with variable processing times. Manag Sci 39(1):126–133

    Article  Google Scholar 

  • Hillier MS (2000) Characterizing the optimal allocation of storage space in production line systems with variable processing times. IIE Transactions 32(1):1–8

    Google Scholar 

  • Inman RR (1999) Empirical evaluation of exponential and independence assumptions in queueing models of manufacturing systems. Prod Oper Manag 8(4):409–432

    Article  Google Scholar 

  • Levantesi R, Matta A, Tolio T (2001) A new algorithm for buffer allocation in production lines. In: Proceedings of the 3rd Aegean international conference on design and analysis of manufacturing systems, pp 19–22

  • Li J (2013) Continuous improvement at toyota manufacturing plant: applications of production systems engineering methods. Int J Prod Res 51(23–24):7235–7249

    Article  Google Scholar 

  • Li J, Meerkov SM (2009) Production Systems Engineering. Springer Science+ Business Media LLC, Boston

    Book  Google Scholar 

  • Liberopoulos G, Tsarouhas P (2005) Reliability analysis of an automated pizza production line. J Food Eng 69(1):79–96

    Article  Google Scholar 

  • Lutz CM, Davis KR, Sun M (1998) Determining buffer location and size in production lines using tabu search. Eur J Oper Res 106(2):301–316

    Article  Google Scholar 

  • MacGregor Smith J, Cruz F (2005) The buffer allocation problem for general finite buffer queueing networks. IIE Trans 37(4):343–365

    Article  Google Scholar 

  • Matta A (2008) Simulation optimization with mathematical programming representation of discrete event systems. In: Proceedings of the 2008 winter simulation conference, Miami, pp 1393–1400

  • Matta A, Chefson R (2005) Formal properties of closed flow lines with limited buffer capacities and random processing times. In: Proceedings of the European simulation and modelling conference, Portugal, pp 190–194

  • Powell SG, Pyke DF (1996) Allocation of buffers to serial production lines with bottlenecks. IIE Trans 28(1):18–29

    Article  Google Scholar 

  • Saliby E (1990a) Descriptive sampling: a better approach to monte carlo simulation. J Oper Res Soc 41(12):1133–1142

    Article  Google Scholar 

  • Saliby E (1990b) Understanding the variability of simulation results: an empirical study. J Oper Res Soc 41(4):319–327

    Article  Google Scholar 

  • Schruben LW (2000) Mathematical programming models of discrete event system dynamics. In: Proceedings of the 32nd conference on winter simulation, Orlando, pp 381–385

  • Spinellis DD, Papadopoulos CT (2000) A simulated annealing approach for buffer allocation in reliable production lines. Ann Oper Res 93(1–4):373–384

    Article  Google Scholar 

  • Stolletz R, Weiss S (2013) Buffer allocation using exact linear programming formulations and sampling approaches. In: 7th IFAC conference on manufacturing modelling, management, and control, St. Petersburg, pp 1435–1440

  • Yamashita H, Altiok T (1998) Buffer capacity allocation for a desired throughput in production lines. IIE Trans 30(10):883–892

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Business School, Chair of Production Management, University of Mannheim, Schloss, 68131, Mannheim, Germany

    Sophie Weiss & Raik Stolletz

Authors
  1. Sophie Weiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raik Stolletz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sophie Weiss.

Appendix: Detailed results for Erlang-k and Cox-2 distributed instances

Appendix: Detailed results for Erlang-k and Cox-2 distributed instances

See Tables 10, 11, and 12.

Table 10 Detailed results (Cox-2 distribution, \(S\) = 5)
Full size table
Table 11 Detailed results (Erlang-k distribution, \(S\) = 7)
Full size table
Table 12 Detailed results (Cox-2 distribution, \(S\) = 7)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weiss, S., Stolletz, R. Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds. OR Spectrum 37, 869–902 (2015). https://doi.org/10.1007/s00291-015-0393-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-015-0393-z

Keywords

Search

Navigation