A small parts supplier has three orders waiting to be processed. The shop will begin work today (time = 0). Orders are scheduled using the First-Come, First-Served (FCFS) rule. What are the average days past due and the average flow time for these orders?

Customer

Time Since Order Arrived (days ago)

Processing Time (days)

Due Date (days from now)

A

20

11

8

B

2

6

20

C

10

8

22

Question

A small parts supplier has three orders waiting to be processed. The shop will begin work today (time = 0). Orders are scheduled using the First-Come, First-Served (FCFS) rule. What are the average days past due and the average flow time for these orders?

Customer

Time Since Order Arrived (days ago)

Processing Time (days)

Due Date (days from now)

A

20

11

8

B

2

6

20

C

10

8

22

BlackTom AI · Accepted Answer

To tackle this FCFS scheduling question, I will first identify the processing order based on arrival times, then compute each order's completion time, its flow time, and days past due.

Option A: 4.67 days past due; 33 days flow time
- FCFS uses arrival order. All three orders have already arrived (A: 20 days ago, C: 10 days ago, B: 2 days ago), so the processing order is A, then C, then B.
- Processing timeline: A (11 days) runs 0–11, C (8 days) runs 11–19, B (6 days) runs 19–25. Completion times are A: 11, C: 19, B: 25.
- Flow time = completion time − arrival time. Using arrival times: A arrives at −20, C at −10, B at −2. So flows are A: 11 − (−20) = 31, C: 19 − (−10) = 29, B: 25 − (−2) = 27. Average flow time = (31 + 29 + 27) / 3 = 87 / 3 = 29 days, not 33.
- Days past due = max(0, completion − due). Due dates are A: 8, C: 22, B: 20. So past due values are A: max(0, 11 − 8) = 3, C: max(0, 19 − 22) = 0, B: max(0, 25 − 20) = 5. Average past due = (3 + 0 + 5) / 3 = 8/3 ≈ 2.67, which differs from 4.67 for this option and the flow time also mismatches. Therefore both figures in this option are incorrect.

Option B: 5.67 days past due; 27 days flow time
- Flow time as shown above is 29 days for FCFS with the given arrivals, not 27. This makes the flow time value incorrect.
- Days past due would be computed as 2.67 if we use the same method as in A, but even then the flow time mismatch already rules this out. So this option is incorrect for both metrics.

Option C: 2.67 days past due; 29 days flow time
- Flow time: As calculated, A finishes at 11, C at 19, B at 25. Using arrival times (A at −20, C at −10, B at −2): flows are A 31, C 29, B 27. Average flow time = (31 + 29 + 27) / 3 = 87 / 3 = 29 days, which matches the 29 days flow time in this option.
- Days past due: Due dates are A 8, C 22, B 20. Past due values are A: 11 − 8 = 3, C: 19 − 22 = −3 (not past due, so 0 when taking max), B: 25 − 20 = 5. Average past due = (3 + 0 + 5) / 3 = 8/3 ≈ 2.67 days. This aligns with the 2.67 days past due in this option. Therefore, both metrics line up with FCFS timing and the standard past-due computation.

Option D: 3.67 days past due; 31 days flow time
- As shown, the correct average flow time is 29 days, not 31, given the same FCFS schedule. The 31-day flow time here would require different completion times or arrival data, so this option misstates the flow time.
- The past-due average would not naturally become 3.67 with the same calculations, since the valid average is 2.67, making this option inconsistent with the FCFS results.

Summary across options:
- The FCFS sequence yields completion times at 11, 19, and 25 days for A, C, and B respectively, leading to flow times of 31, 29, and 27 days, and an average flow time of 29 days.
- Days past due, using max(0, completion − due), are 3 for A, 0 for C, and 5 for B, giving an average of 2.67 days past due.
- Only Option C reproduces both the 29 days flow time and the 2.67 days past due values; other options misstate one or both metrics due to incorrect calculations or assumptions.

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