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ANALYTIC PROPERTIES OF TWO-CAROUSEL SYSTEMS

Published online by Cambridge University Press:  10 December 2012

Ruben Bossier ,
Maria Vlasiou  and
Ivo Adan
Ruben Bossier
Affiliation:
Department of Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
Maria Vlasiou
Affiliation:
Department of Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands and Eurandom, Eindhoven University of Technology, Eindhoven, The Netherlands
Ivo Adan
Affiliation:
Eurandom, Eindhoven University of Technology, Eindhoven, The Netherlandsand Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
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Abstract

We present analytic results for warehouse systems involving pairs of carousels. Specifically, for various picking strategies, we show that the sojourn time of the picker satisfies an integral equation that is a contraction mapping. As a result, numerical approximations for performance measures such as the throughput of the system are extremely accurate and converge fast (e.g., within five iterations) to their real values. We present simulation results validating our results and examining more complicated strategies for pairs of carousels.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 57 - 84
Copyright
Copyright © Cambridge University Press 2013

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References

REFERENCES

1.Bartholdi, J.J. III, & Platzman, L.K. (1986). Retrieval strategies for a carousel conveyor. IIE Transactions 18: 166–173.CrossRefGoogle Scholar
2.Emerson, C.R. & Schmatz, D.S. (1981). Results of modeling an automated warehouse system. Industrial Engineering 13: 28–32, cont. on p. 90.Google Scholar
3.Friedman, D.C.W., Dosher, J., Kowalewski, T., Rosen, J. & Hannaford, B. (2007). Automated tool handling for the trauma pod surgical robot. In 2007 IEEE International Conference on Robotics and Automation, pp. 1936–1941.CrossRefGoogle Scholar
4.Hassini, E. & Vickson, R.G. (2003). A two-carousel storage location problem. Computers & Operations Research 30: 527–539.CrossRefGoogle Scholar
5.Hwang, H. & Ha, J.-W. (1991). Cycle time models for single/double carousel system. International Journal of Production Economics 25: 129–140.CrossRefGoogle Scholar
6.Hwang, H., Kim, C.-S. & Ko, K.-H. (1999). Performance analysis of carousel systems with double shuttle. Computers & Industrial Engineering 36: 473–485.CrossRefGoogle Scholar
7.Istrăţescu, V.I. (1981). Fixed point theory vol. 7 of Mathematics and its Applications. D. Reidel Publishing Co., Dordrecht.Google Scholar
8.Kohler, C. & Schultz-Wild, R. (1985). Flexible manufacturing systems — manpower problems and policies. Journal of Manufacturing Systems 4: 135–146.CrossRefGoogle Scholar
9.Le-Duc, T. (2005). Design and control of efficient order picking processes. Ph.D. thesis, Erasmus University Rotterdam.Google Scholar
10.LeBaron, T. & Hoffman, M.L. (1998). Using simulation to optimize a horizontal carousel storage system. In Proceedings of the 30th Conference on Winter Simulation. WSC ’98. Los Alamitos, CA, USA: IEEE Computer Society Press, pp. 1247–1254.CrossRefGoogle Scholar
11.Litvak, N. & Vlasiou, M. (2010). A survey on performance analysis of warehouse carousel systems. Statistica Neerlandica 64: 401–447.CrossRefGoogle Scholar
12.McGinnis, L.F., Han, M.H. & White, J.A. (1986). Analysis of rotary rack operations. In Proceedings of the 7th International Conference on Automation in Warehousing. ed. White, J.. Springer, San Francisco, California. pp. 165–171.Google Scholar
13.Park, B.C., Park, J.Y. & Foley, R.D. (2003). Carousel system performance. Journal of Applied Probability 40: 602–612.CrossRefGoogle Scholar
14.Piasecki, D.J. (2003). Invetory Accuracy: People, Processes, and Technology. Kenosha, WI: Ops Publishing.Google Scholar
15.Roodbergen, K. Warehousing literature. Available from http://www.roodbergen.com/literature/, Last visited in August 2011.Google Scholar
16.Seshadri, S., Rotem, D. & Arie, S. (1994). Optimal arrangement of cartridges in carousel type mass storage systems. The Computer Journal 37: 873–887.CrossRefGoogle Scholar
17.Vlasiou, M. (2006). Lindley-type recursions. Ph.D. thesis, Eindhoven University of Technology Eindhoven, The Netherlands.Google Scholar
18.Vlasiou, M. (2007). A non-increasing Lindley-type equation. Queueing Systems. Theory and Applications 56: 41–52.CrossRefGoogle Scholar
19.Vlasiou, M., Adan, I.J.-B.F. & Wessels, J. (2004). A Lindley-type equation arising from a carousel problem. Journal of Applied Probability 41: 1171–1181.CrossRefGoogle Scholar
20.Wen, U.-P., Lin, J.T. & Chang, D.-T. (1989). Order picking for a two-carousel-single-server system in an automated warehouse. In Proceedings of the 10th International Conference on Automation in Warehousing. White, J. (ed.) Dallas, TX: IFS(Publications), pp. 87–93.Google Scholar
21.Williams, E.J. & Fosso, K.A. (1995). A simulation modeler's view of a carousel. In Simulation Conference Proceedings, 1995. Winter, pp. 925–929.Google Scholar