Multi aisle automated storage and retrieval systems correspond to multiple picking aisles served by a single storage and retrieval machine. These systems are used in practice when the need for pallet places is high and the throughput capacity is relatively low. Therefore, considerable savings of initial investment costs due to single aisle systems can be achieved using such systems. The objective of the presented study is to develop analytical travel time models for multi aisle automated storage and retrieval systems considering the operating characteristics of the storage and retrieval machine. With the proposed analytical travel time models, average travel time of the storage and retrieval machine, from which the performance of multi aisle automated storage and retrieval systems can be evaluated is determined. A simulation model of multi aisle automated storage and retrieval systems was developed to compare the performances of the proposed analytical travel time models. An example of multi aisle automated storage and retrieval systems with five picking aisles was presented for the evaluation purpose. The results show that proposed analytical travel time models perform satisfactory according to the results of simulation analysis and could be very useful tools for designing of multi aisle automated storage and retrieval systems in real-world applications.

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V prispevku podamo trenutno stanje znanstvenih ugotovitev o obrnjenem učenju v krizni situaciji in primerjamo dva modela, kitajskega in slovenskega. Marca 2020 je izšel priročnik, ki opisuje kitajsko izkušnjo o tem kako zagotavljati učenje tudi med izbruhom COVID-19. V Sloveniji je konec marca zaživelo gibanje Razlagamo.si, ki ponuja asinhrone (vnaprej posnete) video razlage, ki učečemu omogočajo samostojno razpolaganje s časom in dodatno sinhrono komunikacijo o evidentiranih problemih v skupinskih ali individualnih pogovorih. V prispevku opišemo portal Razlagamo.si in ga primerjamo s kitajskimi smernicami. Na osnovi zaznanih prednosti in slabosti ponudimo model, ki je vzdržen tudi v situaciji, ko je le del populacije učencev in dijakov vključen v izobraževanje na daljavo. Ponudimo tudi kvantitativni pregled video razlag po predmetih in področjih. Prispevek bo v pomoč učiteljem, ki poučujejo po načelih obrnjenega učenja in odločevalcem, ki razmišljajo o modelu izobraževanja v prihodnosti.

Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.