(a) Jobs A, B, C, D, E, F and G must go through Machines M1 and M2 in that seque
ID: 356130 • Letter: #
Question
(a) Jobs A, B, C, D, E, F and G must go through Machines M1 and M2 in that sequence. Use Johnson’s Rule to determine the optimal sequence in which to schedule the jobs to minimise the total required time. How much total time is required to process all the seven jobs? Illustrate this using a Gantt Chart.
(b) Suppose there are six waiting jobs and the set-up costs incurred between any two jobs are shown below. Determine the sequence in which these jobs should be processed at lowest total set-up cost.
Job Processing time on M1 Processing time on M2 A 4 5 B 16 14 C 8 7 D 12 13 E 3 9 F 9 6 G 8 5Explanation / Answer
Job Processing time on M1 Processing time on M2 Part A A 4 5 B 16 14 C 8 7 D 12 13 E 3 9 F 9 6 G 8 5 Each of five jobs needs to go through work center A and B. Find the optimum sequence of jobs using Johnson's rule. 1. The smallest time is located in Job E (3). Since the time is in M1, schedule this job first. Eliminate Job E from further consideration. E ? ? ? ? ? ? 2. The next smallest time is located in Job A (4) . Since for Job F the time is M1, schedule this job first Eliminate Job A from further consideration. E A ? ? ? ? ? 3. The next smallest time after that is located in Job G (5). Since the time is in M2, schedule this job last. Eliminate Job G from further consideration. E A ? ? ? ? G 4. The next smallest time after is located in Job F (6 ) . Since for Job A the time is in M2, schedule this job last Eliminate Job F from further consideration. E A ? ? ? F G 5. The next smallest time after is located in Job C (7 ) . Since for Job C the time is in M2, schedule this job last Eliminate Job C from further consideration. E A ? ? C F G 6. The next smallest time after is located in Job D (12 ) . Since for Job D the time is in M1, schedule this job first Eliminate Job D from further consideration. Remaining job B shall be filled in the slot E A D B C F G So, the jobs must be processed in the order E ? A ? D ? B ? C?F?G, and must be processed in the same order on both Sanding and Polishing Part B work Seq M1 cumulative time to finish M2 cumulative time to finish E 3 3 9 9 A 4 7 5 14 D 12 19 13 27 B 16 35 14 41 C 8 43 7 48 F 9 52 6 54 G 8 60 5 59 Ie it will take 67 weeks for completion of the optimal solution Part C Gantt chart
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