Question

The desired daily output for an assembly line is 360 units. This assembly line will operate for 450 minutes per day. The following table contains information on this product’s task times and precedence relationships:

TASK	Task Time (Seconds)	Immediate Predecessor
A	30	-
B	35	A
C	30	A
D	35	B
E	15	C
F	65	C
G	40	E, F
h	25	D, G

a. Draw the precedence diagram.

b. What is the workstation cycle time required to produce 360 units per day?

c. Balance this line using the largest number of following tasks. Use the longest task time as a secondary criterion.

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

Short answer

The precedence diagram method (PDM) is an instrument for booking exercises in a task plan.

Step-by-step solution

The details of a product X are-

Everyday demand = 360 units

Production time = 450 min.

= 450 x 60

= 27000 sec

Total Task time = Sum of every single task times

= 30+35+30 +35+15+65 +40+25

=275 seconds

(a)The precedence diagram

The precedence diagram method (PDM) is a device for booking exercises in a task plan. It is a method of developing a venture plan network diagram that utilizations boxes, alluded to as hubs, to address exercises and interfaces them with bolts that show the conditions. For the above details, the precedence diagram is:

(b) Ascertain the workstation cycle time expected to deliver 360 units each day as follows

$$\begin{gathered} \mathrm{cycle}\mathrm{time}=\frac{\mathrm{production}\mathrm{time}\mathrm{per}\mathrm{day}}{\mathrm{required}\mathrm{output}\mathrm{per}\mathrm{day}(\mathrm{in}\mathrm{units})} \\ =\frac{2700}{360} \\ =75\mathrm{seconds} \end{gathered}$$

Subsequently, the workstation cycle time expected to deliver 360 units each day is 75 seconds.

Calculate, the number of workstations utilizing the longest cycle time as follow:

$$\begin{gathered} \mathrm{number}\mathrm{of}\mathrm{workstations}\mathrm{required}=\frac{\mathrm{total}\mathrm{task}\mathrm{time}}{\mathrm{cycle}\mathrm{time}} \\ =\frac{275}{75} \\ =3.67~4 \end{gathered}$$

Subsequently, four workstations are expected for the product.

(c) Balance the line, utilizing the greatest number of tasks primarily and the longest task time optionally, as follows

The standard is to relegate the action having generally some adherent exercises first. Assuming there is a tie, select the action having the longest task time first. Additionally, continue to allot exercises with the end goal that it doesn't surpass the cycle time. The exercises must be doled out assuming all of its ancestor exercises have proactively been relegated.

First, relegate action A to workstation 1 since it has the most elevated 7 adherent exercises. Presently, appoint movement C to workstation 1 since it has the second most noteworthy that is 5 supporter exercises. Presently, E, F, and B have the same number of supporter exercises; however, we can't take F and B since our cycle time will surpass its cutoff. In this manner, action E is picked.

Presently, relegate actions B and D to workstation 2 since it is more possible to follow through with task tasks in grouping and applying needed rules to residual exercises. Presently dole out F to workstation 3. No other action can be picked since it will surpass the cycle time limit. Presently, allot remaining exercises G and H to workstation 4.

D2=30+30+15

D3=35+35

D2=65

D2=40+25

(d) Calculate, the efficiency of line balance, utilizing the part (b) as follows

$$\begin{gathered} \mathrm{Efficiency}=\frac{\mathrm{total}\mathrm{task}\mathrm{time}}{\mathrm{number}\mathrm{of}\mathrm{workstation}\times \mathrm{cycle}\mathrm{time}} \\ =\frac{275}{4\times 75}\times 100 \\ =91.67\% \end{gathered}$$