GB513 Unit 2 Data Summary Analysis Example

Same Average, Twice the Spread: A Unit 2 Data Summary Analysis of Three Suppliers' Lead Times

[Student Name]

Purdue University Global

GB513: Business Analytics

Unit 2 Data Summary Analysis

[Instructor Name]

[Date]

The manufacturer, its suppliers and every figure are composite and illustrative; the methods cited are real.

The Question

Tallgrass Equipment assembles agricultural sprayers. One purchased part, a cast pump housing, has no substitute: when it arrives late, the line stops. Purchasing wants to move from three suppliers to one, under a two-year sole-source contract, in exchange for a lower price. The question for Dana Ferris, the purchasing manager, is which supplier to choose. All three meet the price target, so the decision turns on delivery.

The data are the last thirty deliveries from each supplier, measured in days from purchase order to arrival at the dock.

How the Data Were Checked

Before summarizing, each supplier's thirty records were checked for errors. Two of Supplier B's records showed arrival dates before their order dates, a data entry problem in the receiving system; both were corrected against the packing slips. Holiday weeks were kept in, since a sole-source supplier must deliver through them. Each record counts calendar days, so a delivery ordered on a Friday and received the next Friday counts as seven days regardless of weekends.

Comparison Table

Supplier A. Mean 11.77 days; median 11.65; standard deviation 1.13; range 4.5 days, from 9.7 to 14.2; coefficient of variation 0.096.

Supplier B. Mean 11.89 days; median 11.65; standard deviation 1.98; range 9.7 days, from 7.2 to 16.9; coefficient of variation 0.166.

Supplier C. Mean 12.37 days; median 12.10; standard deviation 1.11; range 4.5 days, from 10.2 to 14.7; coefficient of variation 0.090.

Expressing spread as a share of the mean, the coefficient of variation, allows suppliers with different averages to be compared on relative spread (Anderson et al., 2020).

Side-by-Side Box Plots

Box plots for the three suppliers, drawn on the same axis, show boxes of similar position for A and C and a much wider box and whiskers for B. B's median is the same as A's, but its deliveries scatter from a week early to five days late.

Supplier B's average is no worse than the others', but its standard deviation is nearly twice theirs, and for a part that stops the line, the spread is the risk.

Translating Spread Into Days of Risk

The empirical rule says that for roughly bell-shaped data, about 95 percent of values fall within two standard deviations of the mean (Levine et al., 2021). Applied here:

Supplier A: about 95 percent of deliveries between 9.5 and 14.0 days.

Supplier B: about 95 percent between 7.9 and 15.9 days.

Supplier C: about 95 percent between 10.2 and 14.6 days.

If Tallgrass plans for a fourteen-day lead time, A and C would be late only rarely, while B would be late on a meaningful share of orders.

One Unusual Delivery

B's slowest delivery took 16.9 days. Its z-score, the number of standard deviations from B's mean, is (16.9 minus 11.89) divided by 1.98, or about 2.5. A delivery that far above the mean would be expected in well under 5 percent of orders. Under A's spread, the same 16.9 days would be a z-score of about 4.5, effectively impossible. For B, it is unusual but not surprising, which is the problem: a delivery that late will happen again.

Recommendation

Tallgrass should award the sole-source contract to Supplier A. Its average lead time is the shortest, 11.77 days, and its spread is among the smallest, with a coefficient of variation of 0.096. Supplier C is nearly as consistent but about half a day slower on average. Supplier B, despite a competitive average, is too variable for a part that stops the assembly line.

A Note on Safety Stock

Even with Supplier A, Tallgrass should hold safety stock. Sunil Chopra and Peter Meindl show that safety stock must grow with the variability of supply lead time, not only of demand (Chopra & Meindl, 2019); a simple version covers usage during a chosen number of standard deviations of lead time. With A's standard deviation of 1.13 days, two standard deviations is about 2.3 days. If the line uses about 40 housings a day, a safety stock of about 90 to 100 housings would cover A's late deliveries in nearly all cases. Under B, the same protection would need about 160.

What Purchasing Should Ask Supplier A

Before signing, purchasing should ask Supplier A three questions. Can it hold its current spread with all of Tallgrass's volume, roughly three times what it ships now? What caused its longest delivery, 14.2 days, and has that cause been fixed? And will it agree to report each shipment's order and arrival dates monthly, so the contract's performance clause can be checked against the same measure used here?

Limits

Thirty deliveries per supplier is a modest sample, and the empirical rule assumes roughly bell-shaped data, which the box plots suggest but do not prove. Lead times may also change once one supplier receives all the volume. The contract should include a delivery performance clause, reviewed every quarter.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.

Chopra, S., & Meindl, P. (2019). Supply chain management: Strategy, planning, and operation (7th ed.). Pearson.

Levine, D. M., Stephan, D. F., & Szabat, K. A. (2021). Statistics for managers using Microsoft Excel (9th ed.). Pearson.