Advertisement Remove all ads

A machine operator has to perform two operations, turning and threading on 6 different jobs. The time required to perform these operations (in minutes) for each job is known. Determine the order in - Mathematics and Statistics

Sum

A machine operator has to perform two operations, turning and threading on 6 different jobs. The time required to perform these operations (in minutes) for each job is known. Determine the order in which the jobs should be processed in order to minimize the total time required to complete all the jobs. Also find the total processing time and idle times for turning and threading operations.

Job 1 2 3 4 5 6
Time of turning 3 12 5 2 9 11
Time for threading 8 10 9 6 3 1
Advertisement Remove all ads

Solution

Job 1 2 3 4 5 6
Time of turning 3 12 5 2 9 11
Time for threading 8 10 9 6 3 1

Observe that Min (turning, threading) = 1, which corresponds to job 6 on threading machine.
Therefore, job 6 is placed last in sequence.

          6

Then the problem reduces to

Job 1 2 3 4 5
Time of turning 3 12 5 2 9
Time for threading 8 10 9 6 3

Now, Min (turning, threading) = 2, which corresponds to job 4 on turning machine
∴ Job 4 is placed first in sequence.

4         6

Then the problem reduces to

Job 1 2 3 5
Time of turning 3 12 5 9
Time for threading 8 10 9 3

Now, Min (turning, threading) = 3, which corresponds to job 1 on turning and job 5 on threading.
∴ Job 1 is placed second and job 5 is placed second last.

4 1     5 6

Then the problem reduces to

Job 2 3
Time of turning 12 5
Time for threading 10 9

Now, Min (turning, threading) = 5, which corresponds to job 3 on turning.
∴ Job 3 is placed third on sequence and job 2 on remaining.
∴ Optimal solution is

4 1 3 2 5 6

Total elapsed time

Job Turning Threading
In Out In Out
4(2, 6) 0 2 2 8
1(3, 8) 2 5 8 16
3(5, 9) 5 10 16 25
2(12, 10) 10 22 25 35
5(9, 3) 22 31 35 38
6(11, 1) 31 42 42 43

∴ Total elapsed time = 43 mins
Idle time for turning = 43 – 42 = 1 min
Idle time for threading = 2 + 4 = 6 mins.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 7 Assignment Problem and Sequencing
Exercise 7.2 | Q 1 | Page 125
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×