Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Certainly! Let’s consider and solve the given scheduling problem step by step.
### Develop Schedules Using FCFS (First Come, First Served) Rule
The FCFS rule processes orders in the order in which they arrived.
Given the orders and their times:
\begin{tabular}{cccc}
\hline Order & \begin{tabular}{c}
Time Since Order \\
Arrived (hours ago)
\end{tabular} & \begin{tabular}{c}
Estimated Machine \\
Time (hours)
\end{tabular} & \begin{tabular}{c}
Due Date \\
(hours from now)
\end{tabular} \\
\hline 1 & 1 & 9 & 20 \\
2 & 0 & 7 & 21 \\
3 & 6 & 8 & 12 \\
4 & 5 & 3 & 8 \\
5 & 3 & 12 & 18 \\
\hline
\end{tabular}
The FCFS sequence is:
\begin{tabular}{l|ccccc}
\hline Sequence & 1 & 2 & 3 & 4 & 5 \\
\hline Order & 2 & 1 & 5 & 4 & 3 \\
\hline
\end{tabular}
Now, we need to calculate the following for this sequence:
- Total Flow Time
- Average Flow Time
- Total Past Due Hours
- Average Past Due Hours
We define:
- Flow Time for an order as the elapsed time from when the machine begins processing the order until it completes.
- Due Difference as the difference between Flow Time and the adjusted due date (i.e., due date minus time since order arrived).
#### FCFS Calculations:
1. Order 2:
- Machine Time: 7 hours
- Flow Time: 7
- Due Date: 21 - 0 = 21
- Past Due: max(0, 7 - 21) = 0 hours
2. Order 1:
- Machine Time: 9 hours
- Flow Time: 7 + 9 = 16
- Due Date: 20 - 1 = 19
- Past Due: max(0, 16 - 19) = 0 hours
3. Order 5:
- Machine Time: 12 hours
- Flow Time: 16 + 12 = 28
- Due Date: 18 - 3 = 15
- Past Due: max(0, 28 - 15) = 13 hours
4. Order 4:
- Machine Time: 3 hours
- Flow Time: 28 + 3 = 31
- Due Date: 8 - 5 = 3
- Past Due: max(0, 31 - 3) = 28 hours
5. Order 3:
- Machine Time: 8 hours
- Flow Time: 31 + 8 = 39
- Due Date: 12 - 6 = 6
- Past Due: max(0, 39 - 6) = 33 hours
Summarizing FCFS results:
- Total Flow Time = 7 + 16 + 28 + 31 + 39 = 121
- Average Flow Time = 121 / 5 = 24.2
- Total Past Due Hours = 0 + 0 + 13 + 28 + 33 = 74
- Average Past Due Hours = 74 / 5 = 14.8
### Develop the Schedule Using EDD (Earliest Due Date) Rule
The EDD rule processes orders based on their due dates, starting with the earliest.
Ordered by due dates:
\begin{tabular}{cccc}
\hline Order & \begin{tabular}{c}
Time Since Order \\
Arrived (hours ago)
\end{tabular} & \begin{tabular}{c}
Estimated Machine \\
Time (hours)
\end{tabular} & \begin{tabular}{c}
Due Date \\
(hours from now)
\end{tabular} \\
\hline 4 & 5 & 3 & 8 \\
3 & 6 & 8 & 12 \\
5 & 3 & 12 & 18 \\
1 & 1 & 9 & 20 \\
2 & 0 & 7 & 21 \\
\hline
\end{tabular}
The EDD sequence is:
\begin{tabular}{l|ccccc}
\hline Sequence & 1 & 2 & 3 & 4 & 5 \\
\hline Order & 4 & 3 & 5 & 1 & 2 \\
\hline
\end{tabular}
#### EDD Calculations:
1. Order 4:
- Machine Time: 3 hours
- Flow Time: 3
- Due Date: 8 - 5 = 3
- Past Due: max(0, 3 - 3) = 0 hours
2. Order 3:
- Machine Time: 8 hours
- Flow Time: 3 + 8 = 11
- Due Date: 12 - 6 = 6
- Past Due: max(0, 11 - 6) = 5 hours
3. Order 5:
- Machine Time: 12 hours
- Flow Time: 11 + 12 = 23
- Due Date: 18 - 3 = 15
- Past Due: max(0, 23 - 15) = 8 hours
4. Order 1:
- Machine Time: 9 hours
- Flow Time: 23 + 9 = 32
- Due Date: 20 - 1 = 19
- Past Due: max(0, 32 - 19) = 13 hours
5. Order 2:
- Machine Time: 7 hours
- Flow Time: 32 + 7 = 39
- Due Date: 21 - 0 = 21
- Past Due: max(0, 39 - 21) = 18 hours
Summarizing EDD results:
- Total Flow Time = 3 + 11 + 23 + 32 + 39 = 108
- Average Flow Time = 108 / 5 = 21.6
- Total Past Due Hours = 0 + 5 + 8 + 13 + 18 = 44
- Average Past Due Hours = 44 / 5 = 8.8
### Comparison of FCFS and EDD Schedules
- FCFS:
- Total Flow Time = 121
- Average Flow Time = 24.2
- Total Past Due Hours = 74
- Average Past Due Hours = 14.8
- EDD:
- Total Flow Time = 108
- Average Flow Time = 21.6
- Total Past Due Hours = 44
- Average Past Due Hours = 8.8
The EDD schedule shows better performance metrics compared to the FCFS schedule, providing lower average flow times and significantly fewer past due hours. This indicates that EDD is a more efficient scheduling rule for reducing late orders and managing workflow.
### Develop Schedules Using FCFS (First Come, First Served) Rule
The FCFS rule processes orders in the order in which they arrived.
Given the orders and their times:
\begin{tabular}{cccc}
\hline Order & \begin{tabular}{c}
Time Since Order \\
Arrived (hours ago)
\end{tabular} & \begin{tabular}{c}
Estimated Machine \\
Time (hours)
\end{tabular} & \begin{tabular}{c}
Due Date \\
(hours from now)
\end{tabular} \\
\hline 1 & 1 & 9 & 20 \\
2 & 0 & 7 & 21 \\
3 & 6 & 8 & 12 \\
4 & 5 & 3 & 8 \\
5 & 3 & 12 & 18 \\
\hline
\end{tabular}
The FCFS sequence is:
\begin{tabular}{l|ccccc}
\hline Sequence & 1 & 2 & 3 & 4 & 5 \\
\hline Order & 2 & 1 & 5 & 4 & 3 \\
\hline
\end{tabular}
Now, we need to calculate the following for this sequence:
- Total Flow Time
- Average Flow Time
- Total Past Due Hours
- Average Past Due Hours
We define:
- Flow Time for an order as the elapsed time from when the machine begins processing the order until it completes.
- Due Difference as the difference between Flow Time and the adjusted due date (i.e., due date minus time since order arrived).
#### FCFS Calculations:
1. Order 2:
- Machine Time: 7 hours
- Flow Time: 7
- Due Date: 21 - 0 = 21
- Past Due: max(0, 7 - 21) = 0 hours
2. Order 1:
- Machine Time: 9 hours
- Flow Time: 7 + 9 = 16
- Due Date: 20 - 1 = 19
- Past Due: max(0, 16 - 19) = 0 hours
3. Order 5:
- Machine Time: 12 hours
- Flow Time: 16 + 12 = 28
- Due Date: 18 - 3 = 15
- Past Due: max(0, 28 - 15) = 13 hours
4. Order 4:
- Machine Time: 3 hours
- Flow Time: 28 + 3 = 31
- Due Date: 8 - 5 = 3
- Past Due: max(0, 31 - 3) = 28 hours
5. Order 3:
- Machine Time: 8 hours
- Flow Time: 31 + 8 = 39
- Due Date: 12 - 6 = 6
- Past Due: max(0, 39 - 6) = 33 hours
Summarizing FCFS results:
- Total Flow Time = 7 + 16 + 28 + 31 + 39 = 121
- Average Flow Time = 121 / 5 = 24.2
- Total Past Due Hours = 0 + 0 + 13 + 28 + 33 = 74
- Average Past Due Hours = 74 / 5 = 14.8
### Develop the Schedule Using EDD (Earliest Due Date) Rule
The EDD rule processes orders based on their due dates, starting with the earliest.
Ordered by due dates:
\begin{tabular}{cccc}
\hline Order & \begin{tabular}{c}
Time Since Order \\
Arrived (hours ago)
\end{tabular} & \begin{tabular}{c}
Estimated Machine \\
Time (hours)
\end{tabular} & \begin{tabular}{c}
Due Date \\
(hours from now)
\end{tabular} \\
\hline 4 & 5 & 3 & 8 \\
3 & 6 & 8 & 12 \\
5 & 3 & 12 & 18 \\
1 & 1 & 9 & 20 \\
2 & 0 & 7 & 21 \\
\hline
\end{tabular}
The EDD sequence is:
\begin{tabular}{l|ccccc}
\hline Sequence & 1 & 2 & 3 & 4 & 5 \\
\hline Order & 4 & 3 & 5 & 1 & 2 \\
\hline
\end{tabular}
#### EDD Calculations:
1. Order 4:
- Machine Time: 3 hours
- Flow Time: 3
- Due Date: 8 - 5 = 3
- Past Due: max(0, 3 - 3) = 0 hours
2. Order 3:
- Machine Time: 8 hours
- Flow Time: 3 + 8 = 11
- Due Date: 12 - 6 = 6
- Past Due: max(0, 11 - 6) = 5 hours
3. Order 5:
- Machine Time: 12 hours
- Flow Time: 11 + 12 = 23
- Due Date: 18 - 3 = 15
- Past Due: max(0, 23 - 15) = 8 hours
4. Order 1:
- Machine Time: 9 hours
- Flow Time: 23 + 9 = 32
- Due Date: 20 - 1 = 19
- Past Due: max(0, 32 - 19) = 13 hours
5. Order 2:
- Machine Time: 7 hours
- Flow Time: 32 + 7 = 39
- Due Date: 21 - 0 = 21
- Past Due: max(0, 39 - 21) = 18 hours
Summarizing EDD results:
- Total Flow Time = 3 + 11 + 23 + 32 + 39 = 108
- Average Flow Time = 108 / 5 = 21.6
- Total Past Due Hours = 0 + 5 + 8 + 13 + 18 = 44
- Average Past Due Hours = 44 / 5 = 8.8
### Comparison of FCFS and EDD Schedules
- FCFS:
- Total Flow Time = 121
- Average Flow Time = 24.2
- Total Past Due Hours = 74
- Average Past Due Hours = 14.8
- EDD:
- Total Flow Time = 108
- Average Flow Time = 21.6
- Total Past Due Hours = 44
- Average Past Due Hours = 8.8
The EDD schedule shows better performance metrics compared to the FCFS schedule, providing lower average flow times and significantly fewer past due hours. This indicates that EDD is a more efficient scheduling rule for reducing late orders and managing workflow.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
