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Robust storage assignment in stack- and queue-based storage systems. (English) Zbl 1458.90061

Summary: In stack- and queue-based storage systems, items stored behind the foremost position are only accessible once all blocking items have been removed. A prominent example are deep-lane storage systems, which are often applied in the refrigerated warehouses of the food industry. The price for the high space utilization of these compact storage systems is, thus, a larger retrieval effort whenever items are not properly stored according to increasing due dates. Due dates, however, are often bound to uncertainties, e.g., due to untimely arrivals of the outbound vehicles picking up the stored items. This paper introduces a new way to derive robust storage assignments, such that excessive retrieval effort is avoided in spite of due date uncertainty. Specifically, we aim to maximize the minimum time difference between due dates of items dedicated to different vehicles and stored in the same stack or queue. The resulting optimization problem is defined, computational complexity is proven, and suited solution procedures are derived. Furthermore, a simulation study investigates whether our novel storage assignments are indeed more robust against unforeseen delays than previous approaches.

MSC:

90B06 Transportation, logistics and supply chain management
90B35 Deterministic scheduling theory in operations research
90B80 Discrete location and assignment
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[1] Aytug, H.; Lawley, M. A.; McKay, K.; Mohan, S.; Uzsoy, R., Executing production schedules in the face of uncertainties: a review and some future directions, Eur. J. Oper. Res., 161, 86-110, (2005) · Zbl 1115.90025
[2] Barber, D.; Grobar, L. M., Implementing a statewide goods movement strategy and performance measurement of goods movement in California, (2001), METRANS Transportation Center
[3] Ben-Tal, A.; Nemirovski, A., Robust optimization methodology and applications, Math. Program. Ser. B, 92, 453-480, (2002) · Zbl 1007.90047
[4] Ben-Tal, A.; Nemirovski, A., Selected topics in robust convex optimization, Math. Program. Ser. B, 112, 125-158, (2008) · Zbl 1135.90046
[5] Blasum, U.; Bussieck, M. R.; Hochstättler, W.; Moll, C.; Scheel, H. H.; Winter, T., Scheduling trams in the morning, Math. Methods Oper. Res., 49, 137-148, (1999) · Zbl 0947.90044
[6] Borgman, B.; van Asperen, E.; Dekker, R., Online rules for container stacking, OR Spectr., 32, 687-716, (2010) · Zbl 1200.90018
[7] Bortfeldt, A.; Wäscher, G., Constraints in container loading - a state-of-the-art review, Eur. J. Oper. Res., 229, 1-20, (2013) · Zbl 1317.90172
[8] Boysen, N.; Boywitz, D.; Weidinger, F., Deep-Lane storage of time-critical items: one-sided vs. two-sided access, OR Spectr, (2018)
[9] Boysen, N.; Fliedner, M.; Jaehn, F.; Pesch, E., Shunting yard operations: theoretical aspects and applications, Eur. J. Oper. Res., 220, 1-14, (2012)
[10] Briskorn, D.; Leung, J.; Pinedo, M., Robust scheduling on a single machine using time buffers, IIE Trans., 43, 383-398, (2011)
[11] Carlo, H. J.; Vis, I. F.; Roodbergen, K. J., Storage yard operations in container terminals: literature overview, trends, and research directions, Eur. J. Oper. Res., 235, 412-430, (2014) · Zbl 1305.90007
[12] Caserta, M.; Schwarze, S.; Voss, S., Container rehandling at maritime container terminals, Handbook of Terminal Planning, 247-269, (2011), Springer
[13] Chen, Z.; Li, X.; Gupta, J. N., A bi-directional flow-rack automated storage and retrieval system for unit-load warehouses, Int. J. Prod. Res., 53, 4176-4188, (2015)
[14] Dekker, R.; Voogd, P.; Asperen, E., Advanced methods for container stacking, OR Spectr., 28, 563-586, (2006) · Zbl 1098.90505
[15] Freling, R.; Lentink, R. M.; Kroon, L. G.; Huisman, D., Shunting of passenger train units in a railway station, Transp. Sci., 39, 261-272, (2005)
[16] Garey, M. R.; Johnson, D. S., Computers and intractability: A guide to the theory of NP-completeness, (1979), Freeman New York · Zbl 0411.68039
[17] Gharehgozli, A. H.; Yu, Y.; de Koster, R.; Udding, J. T., A decision-tree stacking heuristic minimising the expected number of reshuffles at a container terminal, Int. J. Prod. Res., 52, 2592-2611, (2014)
[18] Goerigk, M.; Knust, S.; Le, X. T., Robust storage loading problems with stacking and payload constraints, Eur. J. Oper. Res., 253, 51-67, (2016) · Zbl 1346.90493
[19] Herroelen, W.; Leus, R., Robust and reactive project scheduling: a review and classification of procedures, Int. J. Prod. Res., 42, 1599-1620, (2004)
[20] Jacobsen, P. M.; Pisinger, D., Train shunting at a workshop area, Flex. Serv. Manuf. J., 23, 156-180, (2011)
[21] Jensen, T. R.; Toft, B., Graph coloring problems (vol. 39), (2011), John Wiley & Sons
[22] Kang, J.; Ryu, K. R.; Kim, K. H., Deriving stacking strategies for export containers with uncertain weight information, J. Intell. Manuf., 17, 399-410, (2006)
[23] Kim, K. H.; Park, Y. M.; Ryu, K. R., Deriving decision rules to locate export containers in container yards, Eur. J. Oper. Res., 124, 89-101, (2000) · Zbl 0960.90002
[24] Kolen, A. W.; Lenstra, J. K.; Papadimitriou, C. H.; Spieksma, F. C., Interval scheduling: a survey, Nav. Res. Logist., 54, 530-543, (2007) · Zbl 1143.90337
[25] Kouvelis, P.; Yu, G., Robust discrete optimization and its applications, (1997), Kluwer Academic Publishers · Zbl 0873.90071
[26] Le, X. T.; Knust, S., MIP-based approaches for robust storage loading problems with stacking constraints, Comput. Oper. Res., 78, 138-153, (2017) · Zbl 1391.90433
[27] Lehnfeld, J.; Knust, S., Loading, unloading and premarshalling of stacks in storage areas: survey and classification, Eur. J. Oper. Res., 239, 297-312, (2014) · Zbl 1339.90006
[28] Leus, R.; Herroelen, W., Scheduling for stability in single-machine production systems, J. Sched., 10, 223-235, (2007) · Zbl 1168.90409
[29] Nishi, T.; Konishi, M., An optimisation model and its effective beam search heuristics for floor-storage warehousing systems, Int. J. Prod. Res., 48, 1947-1966, (2010) · Zbl 1197.90030
[30] Schäfer, S., 2014. That’s cool: Cold storage warehouse with shuttles at -24°c. https://www.youtube.com/watch?v=Y_bBbYA6tts&index=4&ist=PLVaqLKsJmZmmbXK46utF7ezKXKSqrSiTx; Schäfer, S., 2014. That’s cool: Cold storage warehouse with shuttles at -24°c. https://www.youtube.com/watch?v=Y_bBbYA6tts&index=4&ist=PLVaqLKsJmZmmbXK46utF7ezKXKSqrSiTx
[31] Stadtler, H., An operational planning concept for deep Lane storage systems, Prod. Oper. Manag., 5, 266-282, (1996)
[32] Steenken, D.; Voss, S.; Stahlbock, R., Container terminal operation and operations research - a classification and literature review, OR Spectr., 26, 3-49, (2004) · Zbl 1160.90322
[33] Tang, L.; Zhao, R.; Liu, J., Models and algorithms for shuffling problems in steel plants, Nav. Res. Logist., 59, 502-524, (2012)
[34] Tierney, K.; Voss, S., Solving the robust container pre-marshalling problem, Proceedings of the International Conference on Computational Logistics, 131-145, (2016), Springer · Zbl 1374.90276
[35] Van de Vonder, S.; Demeulemeester, E.; Herroelen, W.; Leus, R., The use of buffers in project management: the trade-off between stability and makespan, Int. J. Prod. Econ., 97, 227-240, (2005)
[36] Winter, T.; Zimmermann, U. T., Real-time dispatch of trams in storage yards, Ann. Oper. Res., 96, 287-315, (2000) · Zbl 0966.90006
[37] Zaerpour, N.; Yu, Y.; de Koster, R. B., Storing fresh produce for fast retrieval in an automated compact cross-dock system, Prod. Oper. Manag., 24, 1266-1284, (2015)
[38] Zäpfel, G.; Wasner, M., Warehouse sequencing in the steel supply chain as a generalized job shop model, Int. J. Prod. Econ., 104, 482-501, (2006)
[39] Zhang, C.; Chen, W.; Shi, L.; Zheng, L., A note on deriving decision rules to locate export containers in container yards, Eur. J. Oper. Res., 205, 483-485, (2010) · Zbl 1188.90045
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