Determination of Single- and Dual-command Cycle Times for Unit Load AS/RS

Single-command Cycle

This performs either storage or a retrieval operation. There are sure steps that are followed in storage or retrieval cycle to find out the cycle time. In case of storage cycle, machine picks up a load, deposits the load, travels to the storage location, and returns empty to the P/D station. Likewise, in a retrieval cycle, the S/R machine starts at the P/D station & travels empty to the retrieval location. Afterwards, it picks up the load, travels to the P/D station, and deposits the load.

Dual-command Cycle

Cycle time is resolute in case of dual-command cycle when it begins its operation with the S/R machine at the P/D station. The machine picks up the load & travel to the storage position to put down the load. After that, the machine travels to the retrieval location to recover the load. At last, it travels back to the P/D station to deposit the load.

Bozer & White (1984) derived an expression for cycle time depend on following assumptions:

• Randomised storage of loads in the AS/RS
• Horizontal & vertical velocities of the S/R machines are constant
• Rack openings are of single-size
• P/D station is situated at the base & at the end of the aisle
• Simultaneous horizontal & vertical travel of S/R machine

The storage space dimensions help to find out the length (L₁) and height (H₁) of an AS/RS aisle and this is given as follows:

L₁ = n (l + x)

H₁ = m (h + z)

Here n and m are the number of bays & storage spaces per system height.

Time needed travelling full horizontal length & vertical height of an aisle is specified by

T = L₁ /V_h and T = H₁/V_v

where V_h and V_v are the average horizontal & vertical speeds of S/R machines. For single-command cycle, cycle time is specified as :

Tsc  = T (  (M ² /3 ) +1) + 2T_pd

For dual-command cycle, cycle time is:

T _dc =  T/30  (40 + 15 M ²-M³) + 4T_td

where

T_sc = single-command cycle time,

T_dc = dual-command cycle time,

T   = max (T_h, T_v),

M = min (T_h / T, T_v / T),

T_pd = time to perform either a pick up or deposit,      

T_h   = time taken to traverse full horizontal aisle distance, and

T_v   = time taken to traverse full vertical aisle distance.