Please help me out here ASAP. Also kindly mention each question number next to t
ID: 385301 • Letter: P
Question
Please help me out here ASAP. Also kindly mention each question number next to the solution. Highly Appreciate it thanks. tion 1: The following problem involves the sequencing of one machine. Pracessing time Due date 12 2 614 813 41 | 4 | 44 | 16 | 35|30 The manager mainly wants to minimize the maximum lateness but also wants to reduce the number of late operations a. What sequence do you suggest? Justify your choice b. Calculate Imax and U, for your solution. c. Is this result optimal for one of these measures? For both? Explain Question 2: Considering a single machine environment, prove the following a. If it is impossible for any job to be on time in any sequence, then 2T, is b. If SPT yields no jobs on time, then it minimizes How would you break c. To minimize T, any two jobs with agreeable processing times and due dates minimized by SPT sequencing. ties in this case? must be in SPT/EDD sequence even if some other jobs are inserted between them. Question 3: The following 11 operations are to be scheduled on four parallel machines 12 67 2 3 1517 20 14 19 Management's goals are: Minimize F, the overall time in the shop. . Reduce M, the maximum time in the shop. a. What sequence do you suggest? Justify your choice. b. Present your result in a Gantt chart, and calculate the F and M values. c. Is this result optimal for one of these measures? For both? Explain Question 4 Consider PmrprmpLmax: Show through a counterexample that the preemptive EDD rule does not necessarily yield an optimal scheduleExplanation / Answer
1.
Trying multiple approaches:
Critical ratio, SPT, EDD and FCFS
The best option is EDD for least tardiness.
We can see the L max is 188 (sum of the end times)
The Utilization is (Makespan/ Completion)
C.
And we see there are other ways to reduce to increase the completion before time, so only on 1 parameter, which is least average tardiness it is better than other methods)
Even the utilization is also low.
Eng Block Processing time Flow in Flow out Due Tardiness FCFS B A 12 0 12 41 0 C B 2 12 14 4 10 Avg flow time 35.4 E C 6 14 20 44 0 WIP 3.218181818 A D 14 20 34 16 18 Avg job lateness 10 F E 8 34 42 35 7 Late jobs 4 D F 13 42 55 30 25 Utilization 0.310734463 Makespan 55 Completion 177 Avg Tardiness 10 Eng Block Processing time Flow in Flow out Due Tardiness EDD B 2 0 2 4 0 D 14 2 16 16 0 Avg flow time 37.6 F 13 16 29 30 0 WIP 3.418181818 E 8 29 37 35 2 Avg job lateness 3.5 A 12 37 49 41 8 Late jobs 3 C 6 49 55 44 11 Utilization 0.292553191 Makespan 55 Completion 188 Avg Tardiness 3.5 Eng Block Processing time Flow in Flow out Due Tardiness SPT B 2 0 2 4 0 C 6 2 8 44 0 Avg flow time 30 E 8 8 16 35 0 WIP 2.727272727 A 12 16 28 41 0 Avg job lateness 8.333333333 F 13 28 41 30 11 Late jobs 4 D 14 41 55 16 39 Utilization 0.366666667 Makespan 55 Completion 150 Avg Tardiness 8.333333333 Current day 0 Job Date Order Received Processing Days Needed Date Order Due, End of Day __ Days left Critical ratio Priority Flow in Flow Out Tardiness Critical ratio A 12 41 41 3.416666667 4 29 41 0 B 2 4 4 2 2 14 16 12 Avg flow time 40.8 C 6 44 44 7.333333333 6 49 55 11 WIP 3.709091 D 14 16 16 1.142857143 1 0 14 0 Avg job lateness 6.17 E 8 35 35 4.375 5 41 49 14 Late jobs 3 F 13 30 30 2.307692308 3 16 29 0 Utilization 0.269608 Makespan 55 Completion 170 Completion 204 6.17