Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

Find the sequence that minimizes the total elapsed time to complete the following jobs in the order AB. Find the total elapsed time and idle times for both the machines. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Find the sequence that minimizes the total elapsed time to complete the following jobs in the order AB. Find the total elapsed time and idle times for both the machines.

Job I II IIII IV V VI VII
Machine A 7 16 19 10 14 15 5
Machine B 12 14 14 10 16 5 7
Advertisement Remove all ads

Solution

Observe that Min(A, B) = 5, corresponds to job VI on machine B and job VII on machine A.
∴ Job VI is placed last and job VII is placed first in sequence.

VII         VI

Then the problem reduces to

Job I II IIII IV V
Machine A 7 16 19 10 14
Machine B 12 14 14 10 6

Now, Min(A, B) = 7, corresponds to job I on machine A.
∴ Job I is placed second in sequence.

VII I         VI

Then the problem reduces to

Job II III IV V
Machine A 16 19 10 14
Machine B 14 14 10 16

Now, Min(A, B) = 10, corresponds to job IV on machine A as well as on machine B.
∴ Job IV is placed second or second last in sequence.

VII I IV       VI

                                             OR

VII I       IV VI

Then the problem reduces to

Job II III V
Machine A 16 19 14
Machine B 14 14 16

Now, Min (A, B) = 14, corresponds to job II and job III on machine B and job V on machine A.
∴ These three jobs can be placed in the sequence in order: V – III – II or V – II – III
∴ The optimal sequence can be

VII I IV V III II VI

                                          OR

VII I V III II IV VI

                                          OR

VII I IV V II III VI

                                          OR

VII I V II III IV VI

∴ We consider the optimal sequence as VII – I – IV – V – III – II – VI
Total Elapsed Time

Job Machine A Machine B
In Out In Out
VII (5, 7) 0 5 5 12
I (7, 12) 5 12 12 24
 IV (10, 10) 12 22 24 34
V (14, 16) 22 36 36 52
III (19, 14) 36 55 55 69
II (16, 14) 55 71 71 85
V (15, 5) 71 86 86 91

∴ Total elapsed time = 91 units
Idle time for Machine A = 91 – 86 = 5 units
Idle time for Machine B = 5 + 2 + 3 + 2 + 1 = 13 units.

Concept: Types of Sequencing Problem
  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 5 | Page 125
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×