Advertisement Remove all ads

Solve the following problem : 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 - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Chart
Sum

Solve the following problem :

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.

Advertisement Remove all ads

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

Observe that Min (G, H) = 16, corresponds to Type 3 on machine G.

∴ Type 3 is placed first in sequence.

3        

Then the problem reduces to

Type 1 2 4 5
Machine G 26 32 20 30
Machine H 18 30 18 18

Now, Min (G, H) = 18, corresponds to Type 1, Type 4 and Type 5 on machine H.

∴ Type 1, 4 and 5 are placed either last, second last or third last and Type 2 on remaining in the sequence.

3 2 5 4 1
OR
3 2 5 1 4
OR
3 2 1 4 5
OR
3 2 1 5 4
OR
3 2 4 1 5
OR
3 2 4 5 1

We take the optimal sequence as,

3 – 2 – 5 – 4 – 1

Total elapsed time

Job Machine A Machine B Machine C
In Out In Out In Out
3 (12, 4, 16) 0 12 12 16 16 32
2 (20, 12, 18) 12 32 32 44 44 62
5 (22, 8, 10) 32 54 54 62 62 72
4 (14, 6, 12) 54 68 68 74 74 86
1 (16, 10, 8) 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) + 12 + 16 + 10 + 6 + 10 = 62

Idle time for machine C = 16 + 12 + 2 + 8 = 38 hrs.

Concept: Types of Sequencing Problem
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×