Answer :
Answer:
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Step-by-step explanation:
To solve the single machine scheduling problem using the Weighted Shortest Processing Time (WSPT) rule, we need to follow these steps:
1. **Calculate WSPT for each job:**
WSPT is calculated as \( \frac{t_j}{w_j} \), where \( t_j \) is the processing time of job \( j \) and \( w_j \) is its weight.
Let's calculate WSPT for each job based on the given data:
Job \( j \): 1 2 3 4 5 6 7 8
Processing time: 16 18 5 20 12 18 22 14
Weights: 2 2 1 2 1 3 2 2
WSPT = \( \frac{t_j}{w_j} \):
- Job 1: \( \frac{16}{2} = 8 \)
- Job 2: \( \frac{18}{2} = 9 \)
- Job 3: \( \frac{5}{1} = 5 \)
- Job 4: \( \frac{20}{2} = 10 \)
- Job 5: \( \frac{12}{1} = 12 \)
- Job 6: \( \frac{18}{3} = 6 \)
- Job 7: \( \frac{22}{2} = 11 \)
- Job 8: \( \frac{14}{2} = 7 \)
2. **Sort the jobs based on WSPT in decreasing order:**
Jobs sorted by WSPT (descending):
- Job 1 (WSPT = 12)
- Job 4 (WSPT = 10)
- Job 7 (WSPT = 11)
- Job 2 (WSPT = 9)
- Job 8 (WSPT = 7)
- Job 6 (WSPT = 6)
- Job 3 (WSPT = 5)
- Job 5 (WSPT = 12)
3. **Sequence the jobs according to the sorted order:**
The optimal sequence based on WSPT rule (descending order):
- Job 1 (WSPT = 12)
- Job 5 (WSPT = 12)
- Job 7 (WSPT = 11)
- Job 4 (WSPT = 10)
- Job 2 (WSPT = 9)
- Job 8 (WSPT = 7)
- Job 6 (WSPT = 6)
- Job 3 (WSPT = 5)
This sequence minimizes the mean flow time because jobs with shorter processing times relative to their weights are scheduled earlier, potentially reducing idle time and improving overall efficiency.
If you need to calculate the minimum weighted mean flow time (WMFT), you would calculate the total weighted completion time (TWCT) for this sequence and divide it by the sum of weights. However, the problem did not explicitly ask for the TWCT calculation here.