An AS$/$RS is designed for a facility with aisles of storage with an S$/$R machine dedicated to

each aisle. Each aisle is $360ft.$ long and $64ft.$ high. The shuttle on the S$/$R requires $20$

seconds to perform a P$/$D operation. The average horizontal speed of the S$/$R is $400$ feet per

minute $($fpm$)$ and average vertical speed is $80fpm.$ The horizontal and vertical movement

is simultaneous. It is assumed that $40\%$ of the operations $($storage and retrieval$)$ are

performed on a dual$-$command basis. Also, a peak rate of $100$ storages per hour and $100$

retrievals per hour is assumed.

$($a$)[9$ points$]$ Calculate the expected single command and dual command cycle times.

$($b$)[6$ points$]$ Calculate number of single commands and dual commands, respectively,

based on the peak rate.

$($c$)[8$ points$]$ determine the minimum number of $\frac{S}{R}$ machines required without having

greater than $85\%$ utilization of the $\frac{S}{R}$ machines.

$($d$)[2$ points$]$ Assuming a rack with fixed area but variable dimensions, are your E$($SC$)$

and $E(DC)$ minimal? Give a reason for your answer.