Question

each day, a fedex competitor processes approximately 65,000 shipments. suppose that they use the same service quality index as fedex and identified the following number of errors during a 5-day week (see the \fedex: measuring service performance\ box). these values are hypothetical and do not reflect any real company’s actual performance.

description	weight	number of errors
damaged packages	10	20
international	1	103
invoice adjustments	1	286
late pickup stops	3	204
lost packages	10	1
missed proof of delivery	1	26
right date late	1	747
traces	3	110
wrong day late	5	20

compute the service quality indicator by finding the weighted sum of errors as a percentage of total shipments. do not round intermediate calculations. round your answer to three decimal places.

service quality indicator (sqi): %

Explanation:

Step1: Calculate weighted errors for each category

• Complaints reopened: \(3\times145 = 435\)
• Damaged packages: \(10\times20 = 200\)
• International: \(1\times103 = 103\)
• Invoice adjustments: \(1\times286 = 286\)
• Late pickup stops: \(3\times204 = 612\)
• Lost packages: \(10\times1 = 10\)
• Missed proof of delivery: \(1\times26 = 26\)
• Right date late: \(1\times747 = 747\)
• Traces: \(3\times110 = 330\)
• Wrong day late: \(5\times20 = 100\)

Step2: Sum all weighted errors

Total weighted errors \(= 435 + 200 + 103 + 286 + 612 + 10 + 26 + 747 + 330 + 100 = 2849\)

Step3: Calculate total shipments for 5 days

Daily shipments \(= 65000\), so 5 - day shipments \(= 65000\times5 = 325000\)

Step4: Compute SQI as (weighted errors / total shipments) × 100

\(SQI=\frac{2849}{325000}\times100=\frac{284900}{325000}\approx0.876615\)

Step5: Round to three decimal places

\(SQI\approx0.877\) (Wait, correction: Wait, recalculate the sum. Let's re - sum the weighted errors:

435 (complaints reopened) + 200 (damaged) = 635; 635+103 (international)=738; 738 + 286 (invoice)=1024; 1024+612 (late pickup)=1636; 1636 + 10 (lost)=1646; 1646+26 (missed proof)=1672; 1672+747 (right date late)=2419; 2419+330 (traces)=2749; 2749+100 (wrong day late)=2849. Total shipments: 65000*5 = 325000. Then \(\frac{2849}{325000}\times100=\frac{2849}{3250}\approx0.876615\), rounded to three decimal places is 0.877? Wait, no: \(2849\div325000 = 0.00876615\), multiply by 100 is \(0.876615\%\), rounded to three decimal places is \(0.877\%\)? Wait, no, 0.876615 rounded to three decimal places: the fourth decimal is 6, so we round up the third. So 0.877? Wait, no, 0.876615: first decimal 8, second 7, third 6, fourth 6. So when rounding to three decimal places, look at the fourth, which is 6 ≥ 5, so third decimal 6 becomes 7. So 0.877. Wait, but let's check the calculation again.

Wait, maybe I made a mistake in the sum of weighted errors. Let's recalculate each weighted error:

• Complaints reopened: 3 * 145 = 435
• Damaged packages: 10 * 20 = 200 (total so far: 435 + 200 = 635)
• International: 1 * 103 = 103 (635 + 103 = 738)
• Invoice adjustments: 1 * 286 = 286 (738 + 286 = 1024)
• Late pickup stops: 3 * 204 = 612 (1024 + 612 = 1636)
• Lost packages: 10 * 1 = 10 (1636 + 10 = 1646)
• Missed proof of delivery: 1 * 26 = 26 (1646 + 26 = 1672)
• Right date late: 1 * 747 = 747 (1672 + 747 = 2419)
• Traces: 3 * 110 = 330 (2419 + 330 = 2749)
• Wrong day late: 5 * 20 = 100 (2749 + 100 = 2849). So that's correct.

Total shipments: 65000 per day * 5 days = 325000.

Then weighted sum of errors is 2849.

So SQI = (2849 / 325000) 100 = (2849 100) / 325000 = 284900 / 325000 = 0.8766153846...

Rounded to three decimal places: look at the fourth decimal digit, which is 6. Since 6 ≥ 5, we round up the third decimal digit. So 0.877. Wait, but 0.876615... when rounded to three decimal places: the first decimal is 8, second 7, third 6, fourth 6. So 0.877.

Answer:

\(0.877\)