Question: Francis Johnson’s plant needs to design an efficient assembly line to make a new product. The assembly line needs to produce 15 units per hour, and there is room for only four workstations. The tasks and the order in which they must be performed are shown in the following table. Tasks cannot be split, and it would be too expensive to duplicate any task.

Task	Task Time (Minutes)	Immediate Predecessor
A	1	-
B	2	-
C	3	-
D	1	A,B,C
E	3	C
F	2	E
G	3	E

a. Draw the precedence diagram.

b. What is the workstation cycle time required to produce 15 units per hour?

c. Balance the line so that only four workstations are required. Use whatever method you feel is appropriate.

d. What is the efficiency of your line balance, assuming the cycle time from part (b)?

We can form the precedence diagram using the below steps:

1. Make a zero node with zero terms at the furthest left end.
2. Show the exercises with none as their predecessor on the right-hand side of the beginning node.

Address exercises utilizing a circle, compose the action name inside the circle and length outside the circle

$$\begin{gathered} \mathrm{Cycle}\mathrm{time}=\frac{\mathrm{Production}\mathrm{time}}{\mathrm{Desired}\mathrm{output}} \\ =\frac{60}{15} \\ =4\mathrm{minutes}. \end{gathered}$$

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{workstations}=\frac{\mathrm{Total}\mathrm{task}\mathrm{time}}{\mathrm{Cycle}\mathrm{time}} \\ =\frac{1+2+3+1+3+2+3}{4} \\ =3.75=4\mathrm{workstations}. \end{gathered}$$

To assign tasks according to the workstations:

1. A successor activity cannot be assigned until all predecessor activities have been completed.
2. Proceed to assigntasks to channels until each channel's lengthis fully utilized, i.e. 1.7 minutes.
3. Subtract the assigned time first from cycle time to get all the idle time.

$$\begin{gathered} \mathrm{Efficiency}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{task}\mathrm{times}}{\mathrm{Number}\mathrm{of}\mathrm{workstations}\times \mathrm{Workstation}\mathrm{cycle}\mathrm{time}} \\ =\frac{15}{(5\times 4)} \\ =0.75\mathrm{or} \\ =75\% \end{gathered}$$