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, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Alfieri A, Matta A (2012) Mathematical programming formulations for approximate simulation of multistage production systems. Eur J Oper Res 219(3):773–783
Alfieri A, Matta A (2013) Mathematical programming time-based decomposition algorithm for discrete event simulation. Eur J Oper Res 231(3):557–566
Bai L, Rubin PA (2009) Combinatorial benders cuts for the minimum tollbooth problem. Oper Res 57(6):1510–1522
Benders J (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252
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
Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems, vol 4. Prentice Hall, Englewood Cliffs
Caramanis M (1987) Production system design: A discrete event dynamic system and generalized benders’ decomposition approach. Int J Prod Res 25(8):1223–1234
Chan WKV, Schruben L (2008) Optimization models of discrete-event system dynamics. Oper Res 56(5):1218–1237
Codato G, Fischetti M (2006) Combinatorial benders cuts for mixed-integer linear programming. Oper Res 54(4):756–766
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
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
Dallery Y, Gershwin SB (1992) Manufacturing flow line systems: a review of models and analytical results. Queueing Syst 12(1):3–94
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
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
Gershwin SB, Schor JE (2000) Efficient algorithms for buffer space allocation. Ann Oper Res 93(1):117–144
Gürkan G (2000) Simulation optimization of buffer allocations in production lines with unreliable machines. Ann Oper Res 93(1–4):177–216
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
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
Hillier MS (2000) Characterizing the optimal allocation of storage space in production line systems with variable processing times. IIE Transactions 32(1):1–8
Inman RR (1999) Empirical evaluation of exponential and independence assumptions in queueing models of manufacturing systems. Prod Oper Manag 8(4):409–432
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
Li J, Meerkov SM (2009) Production Systems Engineering. Springer Science+ Business Media LLC, Boston
Liberopoulos G, Tsarouhas P (2005) Reliability analysis of an automated pizza production line. J Food Eng 69(1):79–96
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
MacGregor Smith J, Cruz F (2005) The buffer allocation problem for general finite buffer queueing networks. IIE Trans 37(4):343–365
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
Saliby E (1990a) Descriptive sampling: a better approach to monte carlo simulation. J Oper Res Soc 41(12):1133–1142
Saliby E (1990b) Understanding the variability of simulation results: an empirical study. J Oper Res Soc 41(4):319–327
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
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
About this article
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
- Buffer allocation
- Stochastic flow lines
- Benders Decomposition