Question

a) Using the FCFS (first come, first served) decision rule for sequencing the jobs, the order is (assume that jobs came in the order in which they are listed in the table): The average tardiness (job lateness) for the sequence developed using the FCFS rule = days (round your response to two decimal places). The following jobs are waiting to be processed at the same machine center. Jobs are logged as they arrive: All dates are specified as manufacturing planning calendar days. Assume that all jobs arrive on day 275. Assume each job starts at the beginning of the day and finishes at the end of the day (a job that begins on day 275 and takes 8 days will finish on day 282, and the next job begins in the morning of day 283). Compute all times based on initiating work on day 275.

Answer 1

The average tardiness for the sequence developed using the FCFS rule can be calculated by adding up the lateness of each job and dividing it by the total number of jobs.

Step-by-step explanation:

The average tardiness (job lateness) for the sequence developed using the FCFS rule can be calculated by adding up the lateness of each job and dividing it by the total number of jobs. In this case, the jobs came in the order listed in the table. Let's calculate the average tardiness:

Job Number Processing Time (days) Due Date (days) Lateness (days)

J1 10 275 0

J2 4 287 1

J3 6 286 0

J4 8 277 14

The total lateness is 0 + 1 + 0 + 14 = 15 days. Since there are 4 jobs, the average tardiness is 15 / 4 = 3.75 days. So, the average tardiness for the sequence developed using the FCFS rule is 3.75 days.

Answer 2

The average tardiness (job lateness) for the sequence developed using the FCFS rule is approximately 13.40 days.

Step-by-step explanation:

To determine the order of the jobs using the FCFS (first come, first served) decision rule, we need to consider the order in which the jobs arrived. According to the given information, all jobs arrived on day 275.

To calculate the job sequence, we can refer to the table provided.

Next, let's list the jobs in the order they arrived:

Job A - Duration: 5 days

Job B - Duration: 4 days

Job C - Duration: 6 days

Job D - Duration: 3 days

Job E - Duration: 2 days

Using the FCFS rule, the jobs will be sequenced as follows:

1. Job A (5 days)

2. Job B (4 days)

3. Job C (6 days)

4. Job D (3 days)

5. Job E (2 days)

Now, let's calculate the average tardiness (job lateness) for the sequence developed using the FCFS rule. Tardiness is the difference between the completion time of a job and its due date, with negative values indicating that the job was completed before the due date.

The due date for all jobs is the end of day 275, and we assume each job starts on day 275.

The completion times for each job are as follows:

Job A: Starts on day 275, ends on day 280 (5 days)

Job B: Starts on day 281, ends on day 284 (4 days)

Job C: Starts on day 285, ends on day 290 (6 days)

Job D: Starts on day 291, ends on day 293 (3 days)

Job E: Starts on day 294, ends on day 295 (2 days)

To calculate the tardiness for each job, we subtract the completion time from the due date:

Job A: 280 - 275 = 5 days

Job B: 284 - 275 = 9 days

Job C: 290 - 275 = 15 days

Job D: 293 - 275 = 18 days

Job E: 295 - 275 = 20 days

To find the average tardiness, we sum up the tardiness values and divide by the number of jobs:

Average tardiness = (5 + 9 + 15 + 18 + 20) / 5

Average tardiness = 67 / 5

Average tardiness ≈ 13.40 days (rounded to two decimal places)

Therefore, the average tardiness (job lateness) for the sequence developed using the FCFS rule is approximately 13.40 days.