A general model for batch building processes under the timeout and capacity rules

Abstract

In manufacturing systems, batch building processes are very common, as goods are often transported or processed in batches and must therefore be collected before these transport or processing steps can occur. In this paper, we present a method for the performance analysis of general batch building processes in material flow systems under the timeout and capacity rules. The proposed model allows for stochastic collecting times and incorporates no restrictions with respect to the number of arriving units and their interarrival times. The accuracy of the discrete-time approach is demonstrated by comparing this approach with a discrete-event simulation model in continuous-time. Subsequently, the model is applied to two cases: a transportation case from the health care industry and the process of building a batch for a batch processor.

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References

  1. Ackroyd, H. M. (1980). Computing the waiting time distribution for the G/G/1 queue by signal processing methods. IEEE Transactions on Communications, 38(1), 52–58.

    Article  Google Scholar 

  2. Bitran, G. R., & Tirupati, D. (1989). Approximation for product departures from a single-server station with batch processing in multi-product queues. Management Science, 35(7), 851–878.

    Article  Google Scholar 

  3. Buzacott, J. A., & Shanthikumar, G. (1993). Stochastic models of manufacturing systems. Englewood Cliffs: Prentice Hall.

    Google Scholar 

  4. Di Mascolo, M., Gouin, A., & Ngo Cong, K. (2006). Organization of the production of sterile medical devices. In Proceedings of the 12th IFAC symposium on information control problems in manufacturing—INCOM 2006: Saint Etienne, France (pp. 35–40).

    Google Scholar 

  5. Fowler, J., Phojanamongkolkij, N., Cochran, J., & Montgomery, D. (2002). Optimal batching in a wafer fabrication facility using a multiproduct G/G/c model with batch processing. International Journal of Production Research, 40(2), 275–292.

    Article  Google Scholar 

  6. Furmans, K. (2004). A framework of stochastic finite elements for models of material handling systems, progress. In Material handling research: 2004 (Vol. 8). International Material Handling Research Colloquium, Graz.

    Google Scholar 

  7. Grassmann, W. K., & Jain, J. L. (1989). Numerical solutions of the waiting time distribution and idle time distribution of the arithmetic GI/G/1 queue. Operations Research, 37(1), 141–150.

    Article  Google Scholar 

  8. Hasslinger, G., & Klein, T. (1999). Breitband-ISDN und ATM-Netze. Leipzig: Teubner.

    Google Scholar 

  9. Hopp, W. L., & Spearman, M. L. (1996). Factory physics: foundation of manufacturing management. New York: McGraw-Hill.

    Google Scholar 

  10. Hübner, F., & Tran-Gia, P. (1995). Discrete-time analysis of cell spacing in ATM systems. Telecommunications Systems, 3, 379–395.

    Article  Google Scholar 

  11. Kim, J.-H., Lee, T.-E., Lee, H.-Y., & Park, D.-B. (2003). Scheduling analysis of time-constrained dual armed cluster tools. IEEE Transactions on Semiconductor Manufacturing, 16(3), 521–534.

    Article  Google Scholar 

  12. Kim, J.-H., & Lee, T.-E. (2008). Schedulability analysis of time-constraint cluster tools with bounded time variation by an extended petri net. IEEE Transactions on Automation Science and Engineering, 5(3), 490–503.

    Article  Google Scholar 

  13. Kitamura, S., Mori, K., & Ono, A. (2006). Capacity planning method for semiconductor fab with time constraints between operations. In Proceedings of the 2006 SICE-ICASE international joint conference, Busan, Korea (pp. 1100–1103).

    Google Scholar 

  14. Lee, T.-E., & Park, S.-H. (2005). An extended event graph with negative places and tokens for time window constraints. IEEE Transactions on Automation Science and Engineering, 2(4), 319–332.

    Article  Google Scholar 

  15. Matzka, J., Di Mascolo, M., & Furmans, K. (2011). Queueing analysis of the production of sterile medical devices by means of a hybrid model. In 8th conference on Stochastic Models of Manufacturing and Service Operations (SMMSO 2011), Kusadasi, Turkey.

    Google Scholar 

  16. Matzka, J. (2011). Discrete time analysis of Multi-Server Queueing Systems in Material Handling and Service. Ph.D. thesis, Karlsruhe Institute of Technology, Institut für Fördertechnik und Logistiksysteme.

  17. Meng, G., & Heragu, S. (2004). Batch size modeling in a multi-item, discrete manufacturing system via an open queueing network. IIE Transactions, 36(8), 743–753.

    Article  Google Scholar 

  18. Omosigho, S., & Worthington, D. (1988). An approximation of known accuracy for single server queues with inhomogeneous arrival rate and continuous service time distribution. European Journal of Operational Research, 33(3), 304–313.

    Article  Google Scholar 

  19. Özden, E., & Furmans, K. (2011). Discrete time analysis of takted milk-run systems. In 8th conference on Stochastic Models of Manufacturing and Service Operations (SMMSO 2011), Kusadasi, Turkey.

    Google Scholar 

  20. Özden, E. (2011). Discrete time analysis of consolidated transport processes. Ph.D. thesis, Karlsruhe Institute of Technology, Institut für Fördertechnik und Logistiksysteme.

  21. Robinson, J. K., & Giglio, R. (1999). Capacity planning for semiconductor wafer fabrication with time constraints between operations. In Proceedings of the 1999 winter simulation conference, Phoenix, Arizona, USA (pp. 880–887).

    Google Scholar 

  22. Rostami, S., Hamidzadeh, D., & Camporese, D. (2001). An optimal periodic scheduler for dual-arm robots in cluster tools with residency constraints. IEEE Transactions on Robotics and Automation, 17(5), 609–618.

    Article  Google Scholar 

  23. Schleyer, M. (2007). Discrete time analysis of batch processes in material flow systems. Ph.D. thesis, Universität Karlsruhe, Institut für Fördertechnik und Logistiksysteme.

  24. Schleyer, M. (2012). An analytical method for the calculation of the number of units at the arrival instant in a discrete time G/G/1-queueing system with batch arrivals. OR Spektrum, 34(1), 293–310.

    Article  Google Scholar 

  25. Schleyer, M., & Furmans, K. (2005). Analysis of batch building processes. In Proceedings of the 20th IAR annual meeting, Mulhouse, France.

    Google Scholar 

  26. Schleyer, M., & Furmans, K. (2007). An analytical method for the calculation of the waiting time distribution of a discrete time G/G/1-queueing system with batch arrivals. OR Spektrum, 29(4), 745–763.

    Article  Google Scholar 

  27. Schleyer, M., & Gue, K. (2012). Throughput time distribution analysis for a one-block warehouse. Transportation Research. Part E, Logistics and Transportation Review, 48(3), 652–666.

    Article  Google Scholar 

  28. Shi, C., & Gershwin, S. B. (2011). Part waiting time distribution in a two-machine line. In 8th conference on Stochastic Models of Manufacturing and Service Operations (SMMSO 2011), Kusadasi, Turkey.

    Google Scholar 

  29. Tajan, J., Sivakumar, A., & Gershwin, S. (2011) Controlling job arrivals with processing time windows into batch processor buffer. Annals of Operations Research, 191(1), 193–218.

    Article  Google Scholar 

  30. Tran-Gia, P. (1996). Analytische Leistungsbewertung verteilter Systeme. Berlin: Springer.

    Google Scholar 

  31. Worthington, D., & Wall, A. (1999). Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems. Journal of the Operational Research Society, 50(8), 777–788.

    Article  Google Scholar 

  32. Yang, D.-L., & Chern, M.-S. (1995). A two-machine flowshop sequencing problem with limited waiting time constraints. Computers & Industrial Engineering, 28(1), 63–70.

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the quality of the paper. This research is supported by the research project “Quantitative Analyse stochastischer Einflüsse auf die Leistungsfähigkeit von Produktionssystemen mittels analytischer und simulativer Modellierung”, which is funded by the Deutsche Forschungsgemeinschaft (DFG) (reference number FU-273/8-1)

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Correspondence to Judith Stoll née Matzka.

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Schwarz, J.A., Stoll née Matzka, J. & Özden, E. A general model for batch building processes under the timeout and capacity rules. Ann Oper Res 231, 5–31 (2015). https://doi.org/10.1007/s10479-013-1398-0

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Keywords

  • Batch building
  • Discrete-time modeling
  • Queueing theory
  • Stochastic finite elements