# 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

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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

#### 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
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Chapter 7: Assignment Problem and Sequencing - Exercise 7.2 [Page 125]

#### 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
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