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USB Corp. is designing a product layout for a new product. They plan to use this production line ten hours a day in order to meet forecasted demand of 900 units per day. The following table describes the tasks necessary to produce this product:
Task Time (secs) Immediate Predecessor
| Task | time(sec) | immediate Predecessor |
|---|---|---|
| I | 36 | none |
| J | 14 | I |
| K | 8 | J |
| L | 18 | J |
| M | 14 | K |
| N | 24 | L,M |
| O | 38 | N |
a. Draw the precedence diagram for this line with the processing times for each task displayed.
b. Assign tasks to work stations using the greatest number of following tasks as the heuristic rule. Use the tiebreaker rule of assigning the task with the longest processing time.
c. Compute the efficiency and the percentage of idle time for the system.
Expert Answer
Production Line balancing
Workstation Cycle time = Production time per day/output per day
Production time per day = 10 * 3600 seconds = 36,000 seconds
Workstation Cycle time = 36000 / 900 = 40 seconds per product
a. Precedence diagram
The Precedence diagram for the given line with the processing times for each task has been shown below,
b. Line balancing
Shown below is tabulation of no of following tasks for each of the tasks
| Task | time(sec) | No of following tasks |
|---|---|---|
| I | 36 | 6 |
| J | 14 | 3 |
| K | 8 | 3 |
| L | 18 | 2 |
| M | 14 | 2 |
| N | 24 | 1 |
| O | 38 | 0 |
Now, Staring from the first workstation, lets assign each task, one by one, until the sum of the task times is equal to the workstation cycle time or until no other tasks can be assigned due to sequence or time restrictions. Doing the same for stations 1 – 4, we get
| Station # | Task(s) assigned | Total time (Seconds) |
| Station1 | I | 36 |
| Station2 | J, K, L | 40 |
| Station3 | M, N | 38 |
| Station4 | O | 38 |
c. Efficiency of the line
Efficiency = (sum of all task times) / (actual no of workstations * cycle time)
We know, sum of all task times = 152 seconds
Actual no of workstations = 4
Cycle time = 40 seconds
Upon substituting, Efficiency = 152 / (4 * 40) = 0.95 = 95%
And, Idle percent = 1- Efficiency = 1 – 0.95 = 5%
Idle time = 5% * 10 = 0.5 hours or 30 minutes
