Question

3. [Challenging Question - Scheduling for Rescuing Scuba Divers (20 pts)] Tom Cruise has worked as an operations manager of Underwater Treasure Discovery Company in Miami, FL and recently he was assigned to make a schedule to dispatch deep-water robots to save five scuba divers needing urgent rescue out of danger under the deep sea. He must do a very brief assessment of how urgent each diver appears and need to determine the best sequence to save all five scuba divers. All the information he knows are dive-in time, remaining processing time to complete the assigned job, and dive time remaining scuba oxygen tank. Please do your best to save all five scuba divers with BEST OPTIMAL SEQUNECE using your knowledge of scheduling rules! (We assume that the current time is 11:00 AM and the time to rescue divers will not be considered for scheduling since a rescue robot called “Diving Bell" can rescue a diver immediately regardless of location.)

Answer 1

Alternative solution is also given below other the one here:

Dive in Seq. Diver Lateness time Ji Li = Fi-Di Ι -4 Α Ε B UNA 10:15 AM 10:35 AM 10:45 AM 10:00 AM 10:25 AM Start time (Ri) = 11:00 AM Remaining End Time Due Time Start Time processing time (Flow Time) Di Si =Fi-1 Fi = Si + Pi 11:06 AM 11:00 AM 11:02 AM 11:13 AM 11:02 AM 11:05 AM 11:28 AM 11:05 AM 11:14 AM 11:08 AM 11:14 AM 11:20 AM 11:20 AM 11:20 AM 11:28 AM Maximum Lateness = D 12 FCFS Priority Rule Dive in Seq. Diver time Ji 1 C 10:00 AM 2 A 10:15 AM 3 D 10:25 AM 4 E 10:35 AM 5 B 10:45 AM - Jobs are scheduled in ascending order of Dive in time Remaining End Time Due Time Start Time Lateness processing time (Flow Time) Di Si =Fi-1 Fi = Si + Pi Li = Fi-Di 11:08 AM 11:00 AM 11:06 AM -2 11:06 AM 11:06 AM 11:08 AM 2 11:20 AM 11:08 AM 11:16 AM 11:13 AM 11:16 AM 11:19 AM 11:28 AM 11:19 AM 11:28 AM Maximum Lateness = FCFS rule Number of Jobs in System = EFi/Pi Percentage Utilisation = {Pi/EFi 2.75 36.4% SPT Priority Rule Dive in Seq. Diver time SPT rule Number of Jobs in System = EFI/EPI 2.32143 Percentage Utilisation = {Pi/EFi 43.1% A E - Jobs are scheduled in order of remaining processing time Remaining End Time Due Time Start Time Lateness processing time (Flow Time) Di Si =Fi Fi = Si + Pi Li = Fi-Di 11:06 AM 11:00 AM 11:02 AM 11:13 AM 11:02 AM 11:05 AM 11:08 AM 11:05 AM 11:11 AM 11:20 AM 11:11 AM 11:19 AM 11:28 AM 11:19 AM 11:28 AM Maximum Lateness = 10:15 AM 10:35 AM 10:00 AM 10:25 AM 10:45 AM B

Alternative:

EDD Priority Rule Dive in Seq. Diver time Ji A 10:15 AM 2 C 10:00 AM 10:35 AM 10:25 AM | 10:45 AM - Jobs are scheduled in ascending order of Due Time Remaining End Time Due Time Start Time Lateness processing time (Flow Time) Di Si =Fi-1 Fi = Si + Pi Li = Fi-Di 11:06 AM 11:00 AM 11:02 AM 11:08 AM 11:02 AM 11:08 AM 11:13 AM 11:08 AM 11:11 AM 11:20 AM 11:11 AM 11:19 AM 11:28 AM 11:19 AM 11:28 AM Maximum Lateness = EDD rule Number of Jobs in System = Fi/Pi 2.42857 Percentage Utilisation = {Pi/EFi 41.2% LPT Priority Rule Dive in Seq. Diver time Ji 1 B 10:45 AM 2 D 10:25 AM | C 10:00 AM 4 E 10:35 AM 5 A 10:15 AM - Jobs are scheduled in descending order of remaining processing time Remaining End Time Critical Due Time Start Time Lateness processing time (Flow Time) Ratio Di Si =Fi-1 Fi = Si + Pi Li = Fi-Di Di / Pi 11:28 AM 11:00 AM 11:09 AM -19 3.11 11:20 AM 11:09 AM 11:17 AM -3 2.50 11:08 AM 11:17 AM 11:23 AM 1.33 11:13 AM 11:23 AM 11:26 AM 13 4.33 11:06 AM 11:26 AM 11:28 AM 22 3.00 Maximum Lateness = LPT rule Number of Jobs in System = EFi/Pi 3.67857 Percentage Utilisation = Pi/ZF 27.2% 15 22 CR Priority Rule Dive in Seq. Diver time CR rule Number of Jobs in System = EFi/EPi 3.17857 Percentage Utilisation = {Pi/Fi 31.5% C - Jobs are scheduled in ascending order of CR Remaining End Time Due Time Start Time Lateness processing time (Flow Time) Pi Di Si =Fi-1 Fi = Si + Pi Li = Fi-Di 11:08 AM 11:00 AM 11:06 AM - -2 8 11:20 AM 11:06 AM 11:14 AM -6 2 11:06 AM 11:14 AM 11:16 AM 9 11:28 AM 11:16 AM 11:25 AM 3 11:13 AM 11:25 AM 11:28 AM 15 Maximum Lateness = Critical Ratio Di / Pi 1.33 2.50 3.00 3.11 4.33 2 D 10:00 AM 10:25 AM 10:15 AM 10:45 AM 10:35 AM 3 4 5 10 A B E

Which scheduling rule is the most appropriate for saving all five scuba divers successfully? WHY? ([Part 1] Please select an appropriate scheduling rule for this case among FCFS (First Come First Served), SPT (Shortest Processing Time), EDD (Earliest Due Date), LPT (Longest Processing Time), CR (Critical Ratio). [Part 2] Explain the reason you’ve chosen that dispatching rule for this case.)

The best scheduling rule to use in this case is the shortest processing time. why? In this case we are talking about rescuing divers who have different periods of operation remaining in the sea, in that case we can’t us a rule like first come first served as the first case to be reported could be having more time to deal with compared to the second case to be reported. Therefore, the best here is save the person with the shortest processing time first.

In what sequence should the jobs be processed according to the scheduling rule you have determined in part (a) above?

As far as shortest processing time is concerned, the sequence at which the jobs should be processed is; start from D (2 min), A (3 min), B (6 min), E (8 min) and finish with C (9 min). the time in the brackets is the remaining processing time.

With the job sequence you have determined in part (b) above, what is the average number of jobs in the system for completing all jobs?

The total remaining time is 28 minutes. If the system could manage saving the divers at an interval of 3 minutes, then the average number of jobs (28÷3) which is approximately 8 jobs.

With the job sequence you have determined in part (b) above, what is the utilization for this case?

If the job sequence in part (b) above is followed by the operations manager, then, the probability of saving all the divers could be very high as compared to other sequences based on the other scheduling rules stated such as earliest due date.

References:

Panwalkar, S. S., & Iskandar, W. (1977). A survey of scheduling rules. Operations research, 25(1), 45-61.

Montazeri, M., & Van Wassenhove, L. N. (1990). Analysis of scheduling rules for an FMS. The International Journal of Production Research, 28(4), 785-802.