Annals of Operations Research

, Volume 182, Issue 1, pp 193–211 | Cite as

Using linear programming to analyze and optimize stochastic flow lines

  • Stefan HelberEmail author
  • Katja Schimmelpfeng
  • Raik Stolletz
  • Svenja Lagershausen


This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time, to determine a production rate estimate. As our methodology is purely numerical, it offers the full modeling flexibility of stochastic simulation with respect to the probability distribution of processing times. However, unlike discrete-event simulation models, it also offers the optimization power of linear programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines.


Buffer Size Inventory Level Buffer Space Buffer Allocation Longe Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdul-Kader, W. (2006). Capacity improvement of an unreliable production line–an analytical approach. Computers & Operations Research, 33, 1695–1712. CrossRefGoogle Scholar
  2. Altiok, T. (1996). Performance analysis of manufacturing systems. New York: Springer. Google Scholar
  3. Buzacott, J. A., & Shanthikumar, J. G. (1993). Stochastic models of manufacturing systems. Englewood Cliffs: Prentice Hall. Google Scholar
  4. Dallery, Y., & Gershwin, S. B. (1992). Manufacturing flow line systems: A review of models and analytical results. Queuing Systems Theory and Applications, 12(1–2), 3–94. Special issue on queuing models of manufacturing systems. CrossRefGoogle Scholar
  5. Gaver, D. (1962). A waiting line with interrupted service, including priorities. Journal of the Royal Statistical Society, 24, 73–90. Google Scholar
  6. Gershwin, S. B. (1994). Manufacturing systems engineering. Englewood Cliffs: PTR/Prentice Hall. Google Scholar
  7. Gershwin, S.B., & Schick, I. (1983). Modeling and analysis of three-stage transfer lines with unreliable machines and finite buffers. Operations Research, 31(2), 354–380. CrossRefGoogle Scholar
  8. Gershwin, S. B., & Schor, J. E. (2000). Efficient algorithms for buffer space allocation. Annals of Operations Research, 93, 117–144. CrossRefGoogle Scholar
  9. Helber, S. (1999). Lecture notes in economics and mathematical systems : Vol. 473. Performance analysis of flow lines with non-linear flow of material. Berlin: Springer. Google Scholar
  10. Helber, S. (2001). Cash-flow-oriented buffer allocation in stochastic flow lines. International Journal of Production Research, 39, 3061–3083. CrossRefGoogle Scholar
  11. Helber, S., & Henken, K. (2010). Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials. Operations Research Spectrum, 32, 109–134. Google Scholar
  12. Ho, Y., Eyler, M., & Chien, T. (1979). A gradient technique for general buffer storage design in production line. International Journal of Production Research, 17, 6 557–580. CrossRefGoogle Scholar
  13. Isermann, R. (1987). Digitale Regelsysteme. Band I: Deterministische Regelungen. Berlin/Heidelberg/New York: Springer. Google Scholar
  14. Johri, P. K. (1987). A linear programming approach to capacity estimation of automated production lines with finite buffers. International Journal of Production Research, 25, 851–866. CrossRefGoogle Scholar
  15. Kelton, W. D., Sadowski, R. P., & Sturrock, D. T. (2006). Simulation with Arena with CDROM (4th ed.). New York: McGraw Hill. Google Scholar
  16. Law, A. M., & Kelton, W. D. (1991). Simulation modeling and analysis (2nd ed.). New York: McGraw-Hill. Google Scholar
  17. Liberopoulos, G., Papadopoulos, C. T., Tan, B., Smith, J. M., & Gershwin, J. M. (Eds.) (2006). Stochastic modeling of manufacturing systems. Advances in design, performance evaluation, and control issues. Berlin/Heidelberg/New York: Springer. Google Scholar
  18. Matta, A., & Chefson, R. (2005). Formal properties of closed flow lines with limited buffer capacities and random processing times. In J. M. Felix-Teixera & A. E. C. Brito (Eds.), The 2005 European simulation and modelling conference (pp. 190–198), Porto. Google Scholar
  19. Schruben, L. W. (2000). Mathematical programming models of discrete event system dynamics. In J. A. Joines, R. R. Barton, K. Kang, & P. A. Fishwick (Eds.), Proceedings of the 2000 winter simulation conference (pp. 381–385). Google Scholar
  20. Swain, J. J. (2007). Simulation software survey. OR/MS Today, 34(5). Google Scholar
  21. Tan, B. (2003). State-space modeling and analysis of pull-controlled production systems. In S. B. Gershwin, Y. Dallery, C. T. Papadopoulos, & Smith MacGregor, J. (Eds.), Analysis and modeling of manufacturing systems (pp. 363–398). Amsterdam: Kluwer. Chapter 15. Google Scholar
  22. Tijms, H. C. (1994). Stochastic models. Chichester: Wiley. Google Scholar
  23. Tran-Gia, P. (1996). Analytische Leistungsbewertung verteilter Systeme. Eine Einführung. Berlin: Springer. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Stefan Helber
    • 1
    Email author
  • Katja Schimmelpfeng
    • 2
  • Raik Stolletz
    • 3
  • Svenja Lagershausen
    • 4
  1. 1.Institut für ProduktionswirtschaftLeibniz Universität HannoverHannoverGermany
  2. 2.Lehrstuhl ABWL und Besondere des Rechnungswesens und ControllingBrandenburgische Technische Universität CottbusCottbusGermany
  3. 3.Department of Management Engineering/Operations ManagementTechnical University of DenmarkKgs. LyngbyDenmark
  4. 4.Seminar für Supply Chain Management und ProduktionUniversität zu KölnKölnGermany

Personalised recommendations