Linear Time Ordering of Bins using a Conveyor System
A local food wholesaler company is using an automated commissioning system, which brings the bins containing the appropriate product to the commissioning counter, where the worker picks the needed amounts to 12 bins corresponding to the same number of orders. To minimize the number of bins to pick from, they pick for several different spreading tours, so the order of bins containing the picked products coming from the commissioning counter can be considered random in this sense. Recently, the number of bins containing the picked orders increased over the available storage space, and it was necessary to find a new way of storing and ordering the bins to spreading tours. We developed a conveyor system which (after a preprocessing step) can order the bins in linear space and time.
Boysen, Nils and Emde, Simon. The parallel stack loading problem to minimize blockages. European Journal of Operational Research, 249(2):618–627, 2016. DOI: 10.1016/j.ejor.2015.09.033.
Brandstädt, Andreas and Kratsch, Dieter. On partitions of permutations into increasing and decreasing subsequences. Elektronische Informationsverarbeitung und Kybernetik, 22(5/6):263–273, 1986.
Erdős, Pál and Szekeres, György. A combinatorial problem in geometry. Compositio Mathematica, 2:463–470, 1935.
Haneyah, S.W.A., Schutten, J.M.J., Schuur, P.C., and Zijm, W.H.M. Generic planning and control of automated material handling systems. Computers in Industry, 64(3):177–190, 2013. DOI: 10.1016/j.compind.2012.11.003.
Yang, Bing, Chen, Jing, Lu, En-Yue, and Zheng, Si-Qing. Design and performance evaluation of sequence partition algorithms. Journal of Computer Science and Technology, 23(5):711–718, 2008. DOI: 10.1007/s11390-008-9183-2.
Yehuda, Reuven~Bar and Fogel, Sergio. Partitioning a sequence into few monotone subsequences. Acta Informatica, 35(5):421–440, 1998. DOI: 10.1007/s002360050126.