A unit load AS$/$RS is to be designed to store $E$ pallet loads in a distribution center as shown in

the figure below. Standard pallet dimensions are: width $=1000mm,$ length $=1200mm$; and the

maximum height of a unit load $=1300mm.$ Recommended allowances are $150mm$ in the

direction of width, $300mm$ in the direction of length, and $300mm$ in the direction of height. It is

desired to design a sufficient AS$/$RS with the following specifications:

Random storage strategy

Crane horizontal and vertical speeds are the same and equal to $2\mathrm{.}5\frac{m}{sec}.$

The number of single command cycles equal to the number of duel command cycles.

Rack height is needed to be one third $(1/3)$ of the length; but shouldn't exceed $11m$ in all

cases.

Rack length can't exceed $38m$ due to the limited space in this distribution center.

Throughput rate is required to be $119$ transaction$/$hour; assuming $86\%$ utilization.

Pick$-$up and deposit time is $8$ sec$.$

That is you need to determine:

a$-$ The length $L$ of the aisles

b$-$ Number of compartments in the direction of the length

c$-$ Number of compartments in the direction of the height

d$-$ Number of aisles needed

e$-$ The total required floor area if it is estimated to be one and a half of the exact floor area

occupied by all aisles together