A firm is planning to set up an assembly line to assemble 40 units per hour. Assume that 57 minutes per hour are productive. The time to perform each task and the tasks preceding each task are as follows:
Task Preceding Task Time to Perform (Min)
A - 0.69
B A 0.55
C B 0.92
D B 0.59
E B 0.70
F B 1.10
G C, D, E 0.75
H G, F 0.43
I H 0.29
Draw a network diagram of precedence relationships. Compute the cycle time per unit in minutes. Compute the minimum number of workstations required to produce 40 units per hour. Balance the assembly line using the longest processing time. Calculate the efficiency of the balanced assembly line.
Microsoft Excel sheet.
A ball-bearing assembly firm wants to set up an assembly line which must have an output of 60 units per hour.
To create the network diagram of the precedence relationships, we need to identify the dependencies between tasks. Here is the network diagram:
A(0.69)
|
|
V
B(0.55)
_______/\________
| |
V V
C(0.92) D(0.59)
| |
| |
V V
G(0.75) E(0.70)
| |
| |
____/\_____ F(1.10)
| |
V V
H(0.43) I(0.29)
To compute the cycle time per unit in minutes, we need to find the critical path, which is the longest path through the network diagram. The critical path is A -> B -> G -> H -> I.
The cycle time per unit is the total time taken by the tasks on the critical path. Adding up the times:
0.69 + 0.55 + 0.75 + 0.43 + 0.29 = 2.71 minutes
To compute the minimum number of workstations required to produce 40 units per hour, we divide the available productive time (57 minutes) by the cycle time per unit:
Number of workstations = 57 minutes / 2.71 minutes = 21.03 (round up to 22 workstations)
To balance the assembly line using the longest processing time, we assign the longest task time (1.10 minutes) to each workstation. The remaining time for each workstation is the cycle time per unit minus the longest processing time:
Remaining time = 2.71 minutes - 1.10 minutes = 1.61 minutes
The efficiency of the balanced assembly line is the sum of the longest processing time and the remaining time:
Efficiency = 1.10 minutes / (1.10 minutes + 1.61 minutes) = 0.4058 or 40.58%
To draw a network diagram of precedence relationships, we need to determine the sequence of tasks and their dependencies.
Based on the given information, the precedence relationships are as follows:
A does not have any preceding tasks.
B depends on A.
C, D, E, and F depend on B.
G depends on C, D, and E.
H depends on G and F.
I depends on H.
Using this information, we can create a network diagram by representing each task as a node and drawing arrows to show their dependencies. Here is the network diagram:
A
\
B
/ | \
C D E
\ | /
G
/ \
F H
\
I
To compute the cycle time per unit in minutes, we need to sum up the time to perform each task in the longest path. In this case, the longest path is A -> B -> G -> H -> I. Adding up the times for these tasks, we get:
Cycle time per unit = 0.69 + 0.55 + 0.75 + 0.43 + 0.29 = 2.71 minutes
To compute the minimum number of workstations required to produce 40 units per hour, we need to calculate the total time available per hour and divide it by the cycle time per unit.
Total time available per hour = 57 minutes (productive time per hour)
Minimum number of workstations = Total time available per hour / Cycle time per unit
= 57 minutes / 2.71 minutes ≈ 21 workstations
To balance the assembly line using the longest processing time, we need to assign tasks to workstations in a way that minimizes the idle time. Since the longest processing time is 2.71 minutes, we should assign tasks with a total processing time equal to or less than this value to each workstation.
Starting with the first workstation, we assign tasks in the order of precedence until the total processing time for that workstation exceeds the cycle time per unit or no more tasks are available. Then, we move on to the next workstation and repeat this process until all tasks are assigned.
Here is a possible assignment of tasks to workstations (denoted by numbers):
Workstation 1: A (0.69 min), B (0.55 min), C (0.92 min) - Total processing time: 2.16 min
Workstation 2: D (0.59 min), E (0.70 min), F (1.10 min) - Total processing time: 2.39 min
Workstation 3: G (0.75 min), H (0.43 min) - Total processing time: 1.18 min
Workstation 4: I (0.29 min) - Total processing time: 0.29 min
Now, we calculate the efficiency of the balanced assembly line. The efficiency is defined as the total sum of task times divided by (total workstation time × number of workstations).
Total sum of task times = 0.69 + 0.55 + 0.92 + 0.59 + 0.70 + 1.10 + 0.75 + 0.43 + 0.29 = 5.92 min
Total workstation time = 2.16 + 2.39 + 1.18 + 0.29 = 6.02 min
Efficiency = Total sum of task times / (Total workstation time × Number of workstations)
= 5.92 min / (6.02 min × 4 workstations)
≈ 0.25 or 25%
To create a Microsoft Excel sheet for these calculations, you can use the software's features for drawing network diagrams, calculating sums, and setting up formulas for efficiency calculations.