In a factory, there is a batch production system consisting of four

workstations: Workstation A$,$ B$,$ C$,$ and D$.$ Below is the

information regarding the capacity and production process for

each workstation:

Three different product types pass through the following

workstations:

Product X$$ABCD

Product Y$//$CBD

Product Z$|$ABBD

Our goal is to produce $1,000$ units of each product type per day,

with an $8-$hour shift.

Tasks: $(20$ pts each$)$

a$.$ Using the Hollier Algorithm, determine the optimal layout

for the workstations.

b$.$ Calculate the efficiency of each workstation, and the cycle

time for each product.

c$.$ Determine the number of workstations needed at each

station to meet the target production.

d$.$ Identify whether there is a bottleneck in the system. Explain

your reasoning.

e$.$ If one workstation is to be updated to a fully automated

system $($i$.$e$.,$ with T$\_($n$")=0),$ which workstation would be the most

suitable for this update? Justify your answer.

$($Bonus question$)$ f$.$ How many defected products of each type do

we have at the end of each day? $(5$ pts$)$ also need to use this formula T$\_$std$=$T$\_$nw $(1+$A$\_$pfd$)+$T$\_$m $(1+$A$\_$m$)$