There are four jobs to be completed. Each job must go through machines $M_{1}, M_{2}, M_{3}$ in the order $M_{1} - M_{2} - M_{3}$ . Processing time in hours is given below. Determine idle time for Machine $M_{1}$
Jobs A B C D
$M_{1}$ 5 8 7 3
$M_{2}$ 6 7 2 5
$M_{3}$ 7 8 10 9

14 hrs

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15 hrs

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17 hrs

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19 hrs

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Solution

The correct option is D 19 hrs
$J o b$ $M_{1}$ $M_{1}$ $M_{2}$ $M_{2}$
$M_{3}$ $M_{3}$
Time In
Time Out
Time In Time Out Time In Time Out
$D$ $0$ $3$ $3$ $8$ $8$ $17$
$C$ $3$ $10$ $10$ $12$ $17$ $27$
$A$ $10$ $15$ $15$ $21$ $27$ $34$
$B$ $15$ $23$
$23$ $30$ $34$ $42$
$D$
$C$ $A$ $B$
$J o b s$ $A$ $B$ $C$ $D$
$G = M_{1} + M_{2}$ 11 15 9 8
$H = M_{1} + M_{2}$ 13 15 12 14
Table $3$ , Table $2$ , Table $1$
The given task is of $n$ jobs and three machines.
We change the task in of $n$ jobs and two machines.
For this either Min $M_{1} ⩽ M_{3} \times M_{2}$ or min $M_{3} ⩽$ max $M_{2}$
Here min $M - 3 = 7 = M_{1} \times M_{2}$
Hence, we write $M_{1} + M_{2} = G$ and $M_{2} + M_{3} = H$ the task will be as follows in the table $1$
And the sequence as follows in table $2$
The minimum elapsed time $= 42 h r s .$
Ideal time for $M_{1} = 42 - 23 = 19 h r s .$

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$J o b$	$M_{1}$	$M_{1}$	$M_{2}$	$M_{2}$	$M_{3}$	$M_{3}$
	Time In	Time Out	Time In	Time Out	Time In	Time Out
$D$	$0$	$3$	$3$	$8$	$8$	$17$
$C$	$3$	$10$	$10$	$12$	$17$	$27$
$A$	$10$	$15$	$15$	$21$	$27$	$34$
$B$	$15$	$23$	$23$	$30$	$34$	$42$

$J o b s$	$A$	$B$	$C$	$D$
$G = M_{1} + M_{2}$	11	15	9	8
$H = M_{1} + M_{2}$	13	15	12	14

	M1	M2	M3	M4	M5
J1	40	30	50	50	58
J2	26	38	60	26	38
J3	40	34	28	24	30
J4	28	40	40	32	48
J5	28	32	38	22	44

	M1	M2	M3	M4	M5
J1	40	30	50	50	58
J2	26	38	60	26	38
J3	40	34	28	24	30
J4	28	40	40	32	48
J5	28	32	38	22	44

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Jobs A B C D
$M_{1}$ 5 8 7 3
$M_{2}$ 6 7 2 5
$M_{3}$ 7 8 10 9

	M1	M2	M3	M4	M5
J1	40	30	50	50	58
J2	26	38	60	26	38
J3	40	34	28	24	30
J4	28	40	40	32	48
J5	28	32	38	22	44