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EFFICIENT ALGORITHMS FOR TRAVELLING SALESMAN PROBLEMS ARISING IN WAREHOUSE ORDER PICKING

Part of: Operations research and management science Computational number theory

Published online by Cambridge University Press:  22 September 2015

H. CHARKHGARD Open the ORCID record for H. CHARKHGARD [Opens in a new window]  and
M. SAVELSBERGH
H. CHARKHGARD*
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia email Hadi.Charkhgard@uon.edu.au
M. SAVELSBERGH
Affiliation:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA email Martin.Savelsbergh@isye.gatech.edu
*
✉Hadi.Charkhgard@uon.edu.au
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Abstract

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We investigate two routing problems that arise when order pickers traverse an aisle in a warehouse. The routing problems can be viewed as Euclidean travelling salesman problems with points on two parallel lines. We show that if the order picker traverses only a section of the aisle and then returns, then an optimal solution can be found in linear time, and if the order picker traverses the entire aisle, then an optimal solution can be found in quadratic time. Moreover, we show how to approximate the routing cost in linear time by computing a minimum spanning tree for the points on the parallel lines.

Keywords

order batchingorder pickingpicker routingtravelling salesman problemminimum spanning tree problem

MSC classification

Primary: 90B06: Transportation, logistics
Secondary: 11Y16: Algorithms; complexity
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 2 , October 2015 , pp. 166 - 174
Copyright
© 2015 Australian Mathematical Society 

References

Bartholdi, J. and Hackman, S. T., Warehouse & distribution science (2011);http://www.warehouse-science.com.Google Scholar
Chew, E. P. and Tang, L. C., “Travel time analysis for general item location assignment in a rectangular warehouse”, European J. Oper. Res. 112 (1999) 582–597 ;doi:10.1016/S0377-2217(97)00416-5.CrossRefGoogle Scholar
de Koster, R., Le-Duc, T. and Roodbergen, K. J., “Design and control of warehouse order picking: a literature review”, European J. Oper. Res. 182 (2007) 481–501; doi:10.1016/j.ejor.2006.07.009.CrossRefGoogle Scholar
de Koster, R., Roodbergen, K. and van Voorden, R., “Reduction of walking time in the distribution center of De Bijenkorf”, in: New trends in distribution logistics, Volume 480 ofLect. Notes Econom. Math. Syst. (eds Speranza, M. G. and Stähly, P.), (Springer, Berlin, 1999) 215–234.CrossRefGoogle Scholar
Frazelle, E., World-class warehousing and material handling (McGraw-Hill, New York, 2002).Google Scholar
Hall, R. W., “Distance approximations for routing manual pickers in a warehouse”, IIE Trans. 25 (1993) 76–87; doi:10.1080/07408179308964306.CrossRefGoogle Scholar
Henn, S., “Algorithms for on-line order batching in an order picking warehouse”, Comput. Oper. Res. 39 (2012) 2549–2563; doi:10.1016/j.cor.2011.12.019.CrossRefGoogle Scholar
Petersen II, C. G., “An evaluation of order picking routing policies”, Int. J. Oper. Prod. Manage. 17 (1997) 1098–1111; doi:10.1108/01443579710177860.CrossRefGoogle Scholar
Ratliff, H. D. and Rosenthal, A. S., “Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem”, Oper. Res. 31 (1983) 507–521; doi:10.1287/opre.31.3.507.CrossRefGoogle Scholar
Roodbergen, K. J., Layout and routing methods for warehouses (RSM Erasmus University, The Netherlands, 2001) hdl.handle.net/1765/861.Google Scholar
Tompkins, J. A., White, J. A., Bozer, Y. A. and Tanchoco, J. M. A., Facilities planning (John Wiley, Hoboken, NJ, 2003).Google Scholar