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Picker routing in rectangular mixed shelves warehouses. (English) Zbl 1458.90045
Summary: Scattered storage (also denoted as mixed shelves storage) is a warehousing strategy often found in business-to-consumer online retailing. Unit loads are broken down into single items that are spread throughout the warehouse, leading to multiple storage positions per stock keeping unit. This paper investigates the picker routing problem in a rectangular scattered storage warehouse, which differs from classical picker routing problems by being a combined selection and routing problem. A proof of NP-hardness in the strong sense is provided and suited solution procedures are presented. Additionally, the impact of the degree of scatter on the length of picking tours is investigated for differing levels of heterogeneity of the order lines, providing managerial insights on when scattered storage should or should not be applied.

90B05 Inventory, storage, reservoirs
Full Text: DOI
[1] Bartholdi, J. J., Hackman, S. T., 2014. Warehouse & distribution science: release 0.96. Atlanta, GA, The Supply Chain and Logistics Institute, School of Industrial and Systems Engineering, Georgia Institute of Technology.
[2] CNET, 2015. Amazon prime now: a peek inside the manhattan warehouse. https://www.cnet.com/pictures/amazon-prime-now-a-peek-inside-the-manhattan-warehouse/4/ [accessed 2017-12].
[3] Daniels, R. L.; Rummel, J. L.; Schantz, R., A model for warehouse order picking, Eur. J. Oper. Res., 105, 1-17, (1998) · Zbl 0957.90002
[4] De Koster, R.; Le-Duc, T.; Roodbergen, K. J., Design and control of warehouse order picking: a literature review, Eur. J. Oper. Res., 182, 481-501, (2007) · Zbl 1121.90385
[5] De Koster, R.; Le-Duc, T.; Zaerpour, N., Determining the number of zones in a Pick-and-sort order picking system, Int. J. Prod. Res., 50, 757-771, (2012)
[6] De Koster, R.; Van Der Poort, E., Routing orderpickers in a warehouse: a comparison between optimal and heuristic solutions, IIE Trans., 30, 469-480, (1998)
[7] Dickie, H. F., ABC inventory analysis shoots for dollars not pennies, Factory Manag. Maintenance, 109, 92-94, (1951)
[8] Garey, M. R.; Johnson, D. S., Computers and intractability: A guide to NP-completeness, (1979), Freeman, San Francisco · Zbl 0411.68039
[9] Gu, J.; Goetschalckx, M.; McGinnis, L. F., Research on warehouse operation: a comprehensive review, Eur. J. Oper. Res., 177, 1-21, (2007) · Zbl 1111.90321
[10] Gu, J.; Goetschalckx, M.; McGinnis, L. F., Research on warehouse design and performance evaluation: a comprehensive review, Eur. J. Oper. Res., 203, 539-549, (2010) · Zbl 1177.90268
[11] Hall, R. W., Distance approximations for routing manual pickers in a warehouse, IIE Trans., 25, 76-87, (1993)
[12] Heskett, J. L., Cube-per-order index-a key to warehouse stock location, Transp. Distrib. Manag., 3, 27-31, (1963)
[13] LOGISTIK HEUTE, 2016. E-commerce: Zu besuch im neuen amazon prime now-lager. https://www.logistik-heute.de/Fotogalerie/15389/E-Commerce-Zu-Besuch-im-neuen-Amazon-Prime-Now-Lager/amazon-prime-muc-nbr-1-1-3416 [accessed 2017-12].
[14] Hwang, H.; Oh, Y. H.; Lee, Y. K., An evaluation of routing policies for order-picking operations in low-level picker-to-part system, Int. J. Prod. Res., 42, 3873-3889, (2004) · Zbl 1060.90569
[15] Jarvis, J. M.; McDowell, E. D., Optimal product layout in an order picking warehouse, IIE Trans., 23, 93-102, (1991)
[16] Karp, R. M., Reducibility among combinatorial problems, (Miller, R. E.; Thatcher, J. W., Complexity of Computer Computations, Vol. 1972, (1972), Plenum Press, New York), 85-103
[17] Kulak, O.; Sahin, Y.; Taner, M. E., Joint order batching and picker routing in single and multiple-cross-aisle warehouses using cluster-based tabu search algorithms, Flexible Serv. Manuf. J., 24, 52-80, (2012)
[18] Lewis, S., 2014. Amazon warehouse. https://www.flickr.com/photos/99781513@N04/15733221648, licensed under CC BY 2.0 [accessed 2016-08].
[19] Lin, S.; Kernighan, B. W., An effective heuristic algorithm for the traveling-salesman problem, Oper. Res., 21, 498-516, (1973) · Zbl 0256.90038
[20] Miller, C. E.; Tucker, A. W.; Zemlin, R. A., Integer programming formulation of traveling salesman problems, J. ACM (JACM), 7, 326-329, (1960) · Zbl 0100.15101
[21] Petersen, C. G., An evaluation of order picking routeing policies, Int. J. Oper. Prod. Manag., 17, 1098-1111, (1997)
[22] Petersen, C. G., The impact of routing and storage policies on warehouse efficiency, Int. J. Oper. Prod. Manag., 19, 1053-1064, (1999)
[23] Petersen, C. G.; Aase, G. R.; Heiser, D. R., Improving order-picking performance through the implementation of class-based storage, Int. J. Phys. Distrib. Logist. Manag., 34, 534-544, (2004)
[24] Ratliff, H. D.; Rosenthal, A. S., Order-picking in a rectangular warehouse: a solvable case of the traveling salesman problem, Oper. Res., 31, 507-521, (1983) · Zbl 0523.90060
[25] Roodbergen, K. J.; De Koster, R., Routing methods for warehouses with multiple cross aisles, Int. J. Prod. Res., 39, 1865-1883, (2001) · Zbl 1060.90519
[26] Roodbergen, K. J.; De Koster, R., Routing order pickers in a warehouse with a middle aisle, Eur. J. Oper. Res., 133, 32-43, (2001) · Zbl 0989.90025
[27] Simpson, E. H., Measurement of diversity, Nature, 163, 688, (1949) · Zbl 0032.03902
[28] Theys, C.; Bräysy, O.; Dullaert, W.; Raa, B., Using a TSP heuristic for routing order pickers in warehouses, Eur. J. Oper. Res., 200, 755-763, (2010) · Zbl 1177.90044
[29] Valle, C. A.; Beasley, J. E.; Cunha, A. S., Optimally solving the joint order batching and picker routing problem, Eur. J. Oper. Res., 262, 817-834, (2017) · Zbl 1375.90025
[30] Van Gils, T.; Ramaekers, K.; Caris, A.; Cools, M., The use of time series forecasting in zone order picking systems to predict order pickers’ workload, Int. J. Prod. Res., 55, 6380-6393, (2017)
[31] Weidinger, F.; Boysen, N., Scattered storage: how to distribute stock keeping units all around a mixed-shelves warehouse, Transp. Sci., (2017)
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