Question

A set of jobs A, B, C, D, E, F, G, H arrive at time \( t = 0 \) for processing on turning and grinding machines. Each job needs to be processed in sequence - first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below. 

If the makespan is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is 
 

• A. A-E-D-F-H-C-G-B
• B. A-D-E-F-H-C-G-B
• C. G-E-D-F-H-C-A-B
• D. B-G-C-H-F-D-E-A

Hint:

In two-machine job scheduling problems, applying Johnson's rule or similar strategies helps balance the job loads and minimizes the makespan.

Answer 1

The Correct Option is A

The problem asks us to find the optimal sequence of jobs to minimize the makespan, which is the total time required to process all jobs. In scheduling problems with two machines (turning and grinding), we need to use a minimizing method like the Johnson's rule or employ a scheduling strategy that balances the load on both machines.
To minimize the makespan, we must arrange the jobs such that the jobs with shorter processing times on the turning machine are done first, while ensuring that the jobs on the grinding machine follow immediately after turning, respecting the job dependency.
By applying the rule of balancing the job lengths for both machines, we find that the optimal sequence is: \[ \text{A-E-D-F-H-C-G-B} \] This sequence minimizes the total processing time (or makespan) when the jobs are processed on both the turning and grinding machines. Final Answer: (A)