Question

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.

Answer 1

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
	In	Out	In	Out	In	Out
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.