Processing n Jobs Through Three Machines This case is similar to previous case except that instead of two machines, there are three machines, Problems falling under this category can be solved by method developed by Jonson. Following are the two conditions of this approach: The smallest processing time on machine A is greater than or equal to the greatest processing time on machine B, i.e., Min. (Ai) >= Max. (Bi) Minimum of Machine A greater than or equal to Maximum of Machine B The smallest processing time on machine C is greater than or equal to the greatest processing time on machine B, i.e, Min. (Bi) <= Max. (Ci) Minimum of Machine B less than or equal Maximum of Machine C Maximum of Machine C greater than or equal to Maximum of Machine B If either or both of the above conditions are satisfied, then we replace the three machines by two fictitious machines G & H with corresponding processing times given by Gi = Ai + Bi Hi = Bi+ Ci Where Gi and Hi are the processing times for ith job on machine G and H respectively. After calculating the new processing times, we determine the optimal sequence of jobs for the machines G & H in the usual manner. Problem The MDH Masala Company has to process six items on three machines:- A,B &C. Processing times are given in the following table Find out the sequence that minimize the total elapse time. Calculate (1) Total elapse time (2) Idle time for machine A, B, and C. The processing order is CAB

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Processing n Jobs Through Three Machines

This case is similar to previous case except that instead of two machines, there are three machines, Problems falling under this category can be solved by method developed by Jonson.

Following are the two conditions of this approach:

The smallest processing time on machine A is greater than or equal to the greatest processing time on machine B, i.e.,

Min. (A_i) >= Max. (B_i)

Minimum of Machine A greater than or equal to Maximum of Machine B

The smallest processing time on machine C is greater than or equal to the greatest processing time on machine B, i.e,

Min. (B_i) <= Max. (C_i)

Minimum of Machine B less than or equal Maximum of Machine C
Maximum of Machine C greater than or equal to Maximum of Machine B

If either or both of the above conditions are satisfied, then we replace the three machines by two fictitious machines G & H with corresponding processing times given by

G_i= A_{i +}B_i

H_i= B_i+ C_i

Where G_iand H_iare the processing times for ith job on machine G and H respectively. After calculating the new processing times, we determine the optimal sequence of jobs for the machines G & H in the usual manner.

Problem
The MDH Masala Company has to process six items on three machines:- A,B &C. Processing times are given in the following table

Find out the sequence that minimize the total elapse time. Calculate (1) Total elapse time (2) Idle time for machine A, B, and C. The processing order is CAB