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A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.
| Type | 1 | 2 | 3 | 4 | 5 |
| Machine A | 16 | 20 | 12 | 14 | 22 |
| Machine B | 10 | 12 | 4 | 6 | 8 |
| Machine C | 8 | 18 | 16 | 12 | 10 |
Solve the problem for minimizing the total elapsed time.
A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.
| Type | 1 | 2 | 3 | 4 | 5 |
| Machine A | 16 | 20 | 12 | 14 | 22 |
| Machine B | 10 | 12 | 4 | 6 | 8 |
| Machine C | 8 | 18 | 16 | 12 | 10 |
Find the total elapsed time and also find idle time for machine B.
Solution
| Type | 1 | 2 | 3 | 4 | 5 |
| Machine A | 16 | 20 | 12 | 14 | 22 |
| Machine B | 10 | 12 | 4 | 6 | 8 |
| Machine C | 8 | 18 | 16 | 12 | 10 |
Here min A = 12, max B = 12, min C = 8.
Since min A ≥ max B is satisfied, the problem can be converted into a two-machine problem.
Let G and H be two fictitious machines such that G = A + B and H = B + C
Then the problem can be written as
| Type | 1 | 2 | 3 | 4 | 5 |
| Machine G | 26 | 32 | 16 | 20 | 30 |
| Machine H | 18 | 30 | 20 | 18 | 18 |
Using the optimal sequence algorithm, any one is an optimal sequence that can be obtained.
| 3 | 2 | 5 | 4 | 1 | |
| or | 3 | 2 | 5 | 1 | 4 |
| or | 3 | 2 | 4 | 5 | 1 |
| or | 3 | 2 | 4 | 1 | 5 |
| or | 3 | 2 | 1 | 4 | 5 |
| or | 3 | 2 | 1 | 5 | 4 |
| Type | Machine A | Machine B | Machine C | |||
| 3 | 0 | 12 | 12 | 16 | 16 | 32 |
| 2 | 12 | 32 | 32 | 44 | 44 | 62 |
| 5 | 32 | 54 | 54 | 62 | 62 | 72 |
| 4 | 54 | 68 | 68 | 74 | 74 | 86 |
| 1 | 68 | 84 | 84 | 94 | 94 | 102 |
∴ Total elapsed time = 102 hrs.
Idle time for machine A = 102 – 84 = 18 hrs
Idle time for machine B = (102 – 94) + 54 = 62 hrs
Idle time for machine C = 16 + 12 + 2 + 8 = 38 hrs.
Notes
Students can refer to the provided solution According to their question.
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