OR Spectrum

, Volume 37, Issue 4, pp 869–902 | Cite as

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

  • Sophie WeissEmail author
  • Raik Stolletz
Regular Article


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.


Buffer allocation Stochastic flow lines Benders Decomposition Sampling Bounds 


  1. Alfieri A, Matta A (2012) Mathematical programming formulations for approximate simulation of multistage production systems. Eur J Oper Res 219(3):773–783CrossRefGoogle Scholar
  2. Alfieri A, Matta A (2013) Mathematical programming time-based decomposition algorithm for discrete event simulation. Eur J Oper Res 231(3):557–566CrossRefGoogle Scholar
  3. Bai L, Rubin PA (2009) Combinatorial benders cuts for the minimum tollbooth problem. Oper Res 57(6):1510–1522CrossRefGoogle Scholar
  4. Benders J (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252CrossRefGoogle Scholar
  5. Burman M, Gershwin SB, Suyematsu C (1998) Hewlett-packard uses operations research to improve the design of a printer production line. Interfaces 28(1):24–36CrossRefGoogle Scholar
  6. Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems, vol 4. Prentice Hall, Englewood CliffsGoogle Scholar
  7. Caramanis M (1987) Production system design: A discrete event dynamic system and generalized benders’ decomposition approach. Int J Prod Res 25(8):1223–1234Google Scholar
  8. Chan WKV, Schruben L (2008) Optimization models of discrete-event system dynamics. Oper Res 56(5):1218–1237CrossRefGoogle Scholar
  9. Codato G, Fischetti M (2006) Combinatorial benders cuts for mixed-integer linear programming. Oper Res 54(4):756–766CrossRefGoogle Scholar
  10. 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):1913–1945CrossRefGoogle Scholar
  11. 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):491–504CrossRefGoogle Scholar
  12. Dallery Y, Gershwin SB (1992) Manufacturing flow line systems: a review of models and analytical results. Queueing Syst 12(1):3–94CrossRefGoogle Scholar
  13. Demir L, Tunali S, Eliiyi DT (2014) The state of the art on buffer allocation problem: a comprehensive survey. J Intell Manuf 25(3):371–392CrossRefGoogle Scholar
  14. 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):209–223CrossRefGoogle Scholar
  15. Gershwin SB, Schor JE (2000) Efficient algorithms for buffer space allocation. Ann Oper Res 93(1):117–144CrossRefGoogle Scholar
  16. Gürkan G (2000) Simulation optimization of buffer allocations in production lines with unreliable machines. Ann Oper Res 93(1–4):177–216CrossRefGoogle Scholar
  17. Helber S, Schimmelpfeng K, Stolletz R, Lagershausen S (2011) Using linear programming to analyze and optimize stochastic flow lines. Ann Oper Res 182(1):193–211CrossRefGoogle Scholar
  18. 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):126–133CrossRefGoogle Scholar
  19. Hillier MS (2000) Characterizing the optimal allocation of storage space in production line systems with variable processing times. IIE Transactions 32(1):1–8Google Scholar
  20. Inman RR (1999) Empirical evaluation of exponential and independence assumptions in queueing models of manufacturing systems. Prod Oper Manag 8(4):409–432CrossRefGoogle Scholar
  21. 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 19–22Google Scholar
  22. Li J (2013) Continuous improvement at toyota manufacturing plant: applications of production systems engineering methods. Int J Prod Res 51(23–24):7235–7249CrossRefGoogle Scholar
  23. Li J, Meerkov SM (2009) Production Systems Engineering. Springer Science+ Business Media LLC, BostonCrossRefGoogle Scholar
  24. Liberopoulos G, Tsarouhas P (2005) Reliability analysis of an automated pizza production line. J Food Eng 69(1):79–96CrossRefGoogle Scholar
  25. Lutz CM, Davis KR, Sun M (1998) Determining buffer location and size in production lines using tabu search. Eur J Oper Res 106(2):301–316CrossRefGoogle Scholar
  26. MacGregor Smith J, Cruz F (2005) The buffer allocation problem for general finite buffer queueing networks. IIE Trans 37(4):343–365CrossRefGoogle Scholar
  27. Matta A (2008) Simulation optimization with mathematical programming representation of discrete event systems. In: Proceedings of the 2008 winter simulation conference, Miami, pp 1393–1400Google Scholar
  28. 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 190–194Google Scholar
  29. Powell SG, Pyke DF (1996) Allocation of buffers to serial production lines with bottlenecks. IIE Trans 28(1):18–29CrossRefGoogle Scholar
  30. Saliby E (1990a) Descriptive sampling: a better approach to monte carlo simulation. J Oper Res Soc 41(12):1133–1142CrossRefGoogle Scholar
  31. Saliby E (1990b) Understanding the variability of simulation results: an empirical study. J Oper Res Soc 41(4):319–327CrossRefGoogle Scholar
  32. Schruben LW (2000) Mathematical programming models of discrete event system dynamics. In: Proceedings of the 32nd conference on winter simulation, Orlando, pp 381–385Google Scholar
  33. Spinellis DD, Papadopoulos CT (2000) A simulated annealing approach for buffer allocation in reliable production lines. Ann Oper Res 93(1–4):373–384CrossRefGoogle Scholar
  34. 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 1435–1440Google Scholar
  35. Yamashita H, Altiok T (1998) Buffer capacity allocation for a desired throughput in production lines. IIE Trans 30(10):883–892Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Business School, Chair of Production ManagementUniversity of MannheimMannheimGermany

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