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.
Similar content being viewed by others
References
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.
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.
Buzacott, J. A., & Shanthikumar, G. (1993). Stochastic models of manufacturing systems. Englewood Cliffs: Prentice Hall.
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).
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.
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.
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.
Hasslinger, G., & Klein, T. (1999). Breitband-ISDN und ATM-Netze. Leipzig: Teubner.
Hopp, W. L., & Spearman, M. L. (1996). Factory physics: foundation of manufacturing management. New York: McGraw-Hill.
Hübner, F., & Tran-Gia, P. (1995). Discrete-time analysis of cell spacing in ATM systems. Telecommunications Systems, 3, 379–395.
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.
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.
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).
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.
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.
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.
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.
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.
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.
Özden, E. (2011). Discrete time analysis of consolidated transport processes. Ph.D. thesis, Karlsruhe Institute of Technology, Institut für Fördertechnik und Logistiksysteme.
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).
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.
Schleyer, M. (2007). Discrete time analysis of batch processes in material flow systems. Ph.D. thesis, Universität Karlsruhe, Institut für Fördertechnik und Logistiksysteme.
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.
Schleyer, M., & Furmans, K. (2005). Analysis of batch building processes. In Proceedings of the 20th IAR annual meeting, Mulhouse, France.
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.
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.
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.
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.
Tran-Gia, P. (1996). Analytische Leistungsbewertung verteilter Systeme. Berlin: Springer.
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.
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.
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-013-1398-0