Question $1$ You decided to open a production facility. The following figure shows the process flow diagram. You hired $5$ employees, and each employee performs one task.

A :$10$ min B: $8$ min C: $2$ min D:$12$ min E:$2$ min

A $$ How many units can you produce in $10$ hours? $(2)$

B $$ Where do you have work$-$in$-$process inventory? $($show it on the above flow chart$)(2)$

C $$ What is the labor productivity? $(2)$

D $$ How many people do you hire at least to make Task B the new bottleneck? $(2)$

Now you decided to eliminate two tasks $($so now you have three employees$).$ And the following is the new process design.

C:$2$ min D:$12$ min E: $2$ min

E $$ What is the percent output increase? $(2)$

F $$ What is the percent labor productivity increase? $(2)$

G $$ What is the capacity utilization of Task E $($revised process$)?(2)$

H $$ State four practices to improve this process $(2)$

Question $2$ A drive$-$through process a Subway has three activities. The first activity is ordering; on average this process takes $1$ minute. Then, a car proceeds to the payment window; on average this process takes $2$ minute. The last activity is picking$-$up the order, which on average this process takes $3$ minute. There is a waiting before each of these activities. On average, there are usually $1$ cars waiting to place their orders; $2$ cars waiting to pay the total; and $3$ cars waiting to pick$-$up order. On average $10$ cars an hour enters the line, and assume no cars leave this process until they pick$-$up their order.

a $$ Clearly draw the process flow diagram for cars. Make sure you label each activity and buffer with appropriate Little$$s Law variables. $(6)$

b $$ On average, how long does the entire process flow take? $(3)$

Question $3$ Now, you supervise the construction of your new production facility. The following table shows the activities be done compete project.

Activity

Time $($days$)$

Precedence

A

$4$

$$

B

$6$

$($A$)$

C

$5$

$($A$)$

D

$7$

$($A$)$

E

$3$

$($B$)$

F

$6$

$($B$)$

G

$10$

$($B$)$

H

$12$

$($C$)$

I

$12$

$($D$)$

J

$2$

$($E$),($F$)$

K

$5$

$($G$),($H$),($I$)$

L

$2$

$($J$),($K$)$

A $$ Draw the network diagram $(3)$

B $$ What are the early start, late start, early finish and late finish time of each task? $($show them on the diagram$)(6)$

C $$ Identify the critical path $(2)$