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Problem $6-5($Algo$)$

As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of $260$ units per $7-$hour day. Task times and precedence relationships are as follows:

Task Duration

$($minutes$)$ Immediate

Predecessor

a $0\mathrm{.}1-$

b $0\mathrm{.}6$ a

c $0\mathrm{.}3$ b

d $0\mathrm{.}3-$

e $1\mathrm{.}5$ d

f $1\mathrm{.}4$ c

g $1\mathrm{.}3$ e$,$ f

Do each of the following:

a$.$ Determine the number of followers for each task.

b$.$ Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. $($Round all answers up to one decimal point. For example, round $1\mathrm{.}83$ up to $1\mathrm{.}9.)$

c$.$ Determine the minimum number of stations needed. $($Use your rounded cycle time from Part b$.$ Round up your answer to a whole number. Note that rounding up to one decimal point may reduce output to slightly less than $260$ and this is fine.$)$

d$.$ Using the calculated cycle time, assign tasks to workstations on the basis of most following tasks. Use shortest processing time as a tiebreaker. Specify tasks in the exact order they were assigned.

e$.$ Compute the percent efficiency and percent idle time for the assignment in part d$.$ Note: if the calculated cycle time and the actual bottleneck station time are different, use the actual bottleneck time in your calculations. $($Round your answers to $2$ decimal places$)$