Mother child ASRS for 1 pallet deep!

Often during solution designing for pallet ASRS system, there are questions like "What is ideal pallets/ SKU or batch size for selecting the mother child ASRS over stacker crane ASRS? What is too low batch size or what is too high? how does too low batch size affects productivity of a shuttle due to reshuffling? And then the question that got my curiosity is,

Can we use mother child ASRS where the batch size is 1 pallet?

The answer depends on the factors such as, what is the productivity requirement? How much deep the system would be? and the most important question that we will try to answer is how much productivity loss would occur due to reshuffling?

Defining the probabilities in calculating reshuffling time

For Child shuttle travel

X: Probability of selecting a pallet to be picked is (1/Total number of pallet positions in that level)
Y: Probability of selecting a pallet to be picked from a given depth = (X) x (number of bays) x (2)

For Mother shuttle travel

Z: Probability of choosing a bay for reshuffling by mother shuttle = (1/ Number of bays on one side of track)

Now these probabilities can be adjusted with slotting to keep all the fast movers in forward locations, but the methodology suggested here ignores the slotting.

Total time required for reshuffling comprise of three components

Avg. time taken by by child shuttle to relocate pallet: Here we need to estimate the Avg. distance travelled by child shuttle and Avg number of pallets to be reshuffled
Avg. time taken by by mother shuttle to relocate pallet: Here we need to estimate the Avg distance a mother shuttle travels to reach the relocation bay and number of pallets required to be reshuffled
Number of times a child shuttle will perform pick and drop activity: This is the simple multiplication of avg. number of pallets reshuffled in a reshuffling cycle multiplied by lift+drop time in secs

Let us solve for calculating relocation time with an generic example.

In the image, pallets in deep are D1, D2, D3 to D5 in either side of mother track, and assuming effective depth of a location to be 1.1M. B1 through B9 be number of bays along the mother track with effective length of an bay be 1.4M.

Child shuttle travel

Each depth location has different distance to reach it, weighted average of these distances and probabilities of picking pallets from that depth will give avg. distance travelled by child shuttle to reach any depth, (Check A in above calculation)

To reach a required deep location, number of pallets required to be digged out are (deep-1)(Check B in above calculation). Hence, (Deep-1) x Weighted avg. distance required to reach the pallet = Distance travelled by child to remove all the pallets (Check (AxB) in above calculation) and multiplied by 2 will give distance travelled by child to relocate these pallets in an empty location (Check (AxB)x2 in above calculation). This is the total distance that a child travels while relocating all pallets to reach the required pallet for picking.

Mother Shuttle Travel

For reshuffling mother shuttle has to take the child to the nearest empty bay where child can relocate the pallet. The avg. distance travelled by the mother shuttle can be estimated using the weighted avg. distance required to be travelled based on length of bays and number of bays in a level. Refer Mother shuttle travel calculation table.

Now that we have avg. distance travelled by child and mother shuttle which will provide the time required to reshuffle the pallets to reach the required pick pallet, we can add reshuffling time on standard picking cycle time and estimate the effective cycle time for picking a pallet where reshuffling is required.

Reshuffling will certainly reduce the productivity of the system, but to take decision on selecting or eliminating the mother child ASRS for the solution we must know how much does it reduces the productivity. An effective slotting, Bin digging based on dynamic ABC profiling and increased batch size will also help in reducing the impact of reshuffling by constantly brining out fast moving SKUs near to pick faces in ;lean period, but to start with, methodology explained in this article should be sufficient to point us to towards probable solution.

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