Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T14:49:17.578Z Has data issue: false hasContentIssue false
  • English
  • Français

The travel time in carousel systems under the nearest item heuristic

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Nelly Litvak  and
Ivo Adan
Nelly Litvak*
Affiliation:
EURANDOM
Ivo Adan*
Affiliation:
Eindhoven University of Technology
*
∗ Postal address: EURANDOM, PO Box 513, 5600 MB, Eindhoven, The Netherlands. Email address: litvak@eurandom.tue.nl
∗∗ Postal address: Department of Mathematics and Computing Science, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

A carousel is an automated warehousing system consisting of a large number of drawers rotating in a closed loop. In this paper, we study the travel time needed to pick a list of items when the carousel operates under the nearest item heuristic. We find a closed form expression for the distribution and all moments of the travel time. We also analyse the asymptotic behaviour of the travel time when the number of items tends to infinity. All results follow from probabilistic arguments based on properties of uniform order statistics.

Keywords

order pickinguniform order statisticsspacingsmemory-less property

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 90B99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 45 - 54
Copyright
Copyright © by the Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ali, M. M. (1973). Content of the frustum of a simplex. Pacific J. Math. 48, 313–322.CrossRefGoogle Scholar
Ali, M. M., and Obaidullah, M. (1982). Distribution of linear combination of exponential variates. Commun. Statist. Theory Meth. 11, 1453–1463.CrossRefGoogle Scholar
Bartholdi, J. J. III, and Platzman, L. K. (1986). Retrieval strategies for a carousel conveyor. IIE Trans. 18, 166–173.Google Scholar
Chung, K. L. (1974). A Course in Probability Theory, 2nd edn. Academic Press, London.Google Scholar
Karlin, S., and Taylor, H. M. (1981). A Second Course in Stochastic Processes. Academic Press, London.Google Scholar
Litvak, N., Adan, I., Wessels, J., and Zijm, W. H. M. (2001). Order picking in carousel systems under the nearest item heuristic. To appear in Prob. Eng. Inform. Sci.CrossRefGoogle Scholar
Pyke, R. (1965). Spacings. J. R. Statist. Soc. 27, 395–436.Google Scholar
Pyke, R. (1972). Spacings revisited. In Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 1. University of California Press, Berkeley, pp. 417–427.Google Scholar
Van den Berg, J. P. (1996). Planning and control of warehousing systems. Doctoral Thesis, Faculty of Mechanical Engineering, University of Twente.Google Scholar
Whittaker, E. T., and Watson, G. N. (1980). A Course of Modern Analysis, 4th edn. Cambridge University Press.Google Scholar