1. Calculate the total purchase cost for each supplier.
2. Calculate the warranty replacement cost for Altman Electronics, and calculate the total cost if Altman is selected.
3. Calculate the total cost (purchase cost plus defective replacement) for each possible defect level if Crestwell is selected.
4. Based on the findings from the order of 100 bulbs from Crestwell, use Bayes’ Theorem to revise Tony’s subjective probability assessments for Crestwell’s possible defect rates.
5. Using the revised probabilities, calculate the weighted total costs for Crestwell, and compare this to the total costs calculated for Altman. Which supplier should Melinda and Tony recommend?

Melinda Wilson and Tony Green left their boss’s office, heading for the conference room to discuss the task they were given. The task is to select one of two suppliers of outdoor light bulbs. Ordinarily this would be pretty easy—just pick the one that offers the best price. But in this case, their boss is planning to provide a warranty on the bulbs that will require the company to replace all defects at no cost to the customer. Thus, product quality is an important consideration.

As Melinda and Tony settled into the plush leather conference room seats, they quickly realized that this task was more challenging than they first thought. To get started, Melinda went to the white board and began listing the information they already knew. The total purchase will be 100,000 bulbs. Regardless of which supplier is selected, the bulbs will be sold to Pittsburg customers at the same price. The first supplier, Altman Electronics, was one that Pittsburg had used for years, so they had solid quality information. Both Melinda and Tony agreed that this supplier could be counted on for a 5% defect rate. Altman’s bid was $3.00 per light. The second supplier, Crestwell Lights and Fixtures, was new to Pittsburg but offered an attractive bid of $2.70 per unit.

However, neither Melinda nor Tony had any information about Crestwell’s likely defect rate. They realized that they needed to get some more information before they could proceed.

After lunch, Tony made a few calls to other lighting companies in different parts of the country to see what their experience was with Crestwell. When Tony met Melinda back in the conference room, he went to the board and wrote his findings:

Crestwell Defect Rate ....................................... Probability
0.02 ................................................................................ 0.05
0.03 ................................................................................ 0.10
0.04 ................................................................................ 0.20
0.05 ................................................................................ 0.25
0.06 ................................................................................ 0.20
0.07 ................................................................................ 0.15
0.08 ................................................................................ 0.05

Tony explained to Melinda that Crestwell’s defect performance differed depending on which person he talked to, but these numbers summarized his findings. Thus, Crestwell’s defect rate is uncertain, and the probability of any specific defect level is really a subjective assessment made by Tony. Because customers would be refunded for defective bulbs, both Melinda and Tony were concerned that they could not determine a particular defect rate. Melinda suggested that they place a small order for 100 bulbs and see what the defect rate for those turned out to be. She figured that they could use this added information to learn more about Crestwell’s quality.

A few days later, Pittsburg received the 100 bulbs from Crestwell, and after the warehouse crew tested them, six were found to be defective. Tony did some quick calculations and found the following:

Possible Defect Rate ...........................Probability of Six Defects Given the Possible Defect Rate

0.02 ..................................................................... 0.01
0.03 ..................................................................... 0.05
0.04 ..................................................................... 0.11
0.05 ..................................................................... 0.15
0.06 ..................................................................... 0.17
0.07 ..................................................................... 0.15
0.08 ..................................................................... 0.12

Melinda and Tony returned to the conference room to consider all this information and make a decision regarding which supplier to select. They agreed that they would recommend the supplier that would provide the lowest overall cost, including purchasing and warranty replacement costs.