Question

A distributor of computer parts purchases a specific component from a supplier in lots of 1000 units. The cost of purchasing a lot is $30,000. The supplier is known to supply imperfect lots. In other words, a lot received by the distributor may contain defective units. Historical data suggest that the proportion of defective units in a lot supplied by this supplier follows the following probability distribution:

Proportion of defective units in a lot	Probability
0.05	0.50
0.10	0.25
0.25	0.15
0.50	0.10

The distributor inspects the entire lot for defective units before selling the units to PC repair shops at a price of $45 per unit. The inspection process is error-proof so all defective units in a lot are detected and replaced by the distributor. It costs $20 for the distributor to replace a defective unit. The distributor has recently learned that the supplier offers a guarantee policy through which the supplier will assume the cost of replacing defective units in excess of the first 100 faulty units found in a given lot at no cost. [This means that the first 100 defective units found in a lot are replaced by the distributor for $20 per unit; however, all additional defective unit (if any) found in a lot are replaced by the supplier at no cost to the distributor.] This guarantee policy may be purchased by the distributor prior to the receipt of a given lot at a cost of $1000 per lot. The distributor wants to determine whether it is worthwhile to purchase the supplier’s guarantee policy.

Create a complete decision tree by using PrecisionTree^®.  

Make a recommendation: What should the distributor do, using EMV as the decision-making criterion? Why?

Perform sensitivity analysis: Perform a one-way sensitivity analysis using PrecisionTree ^®  on the optimal decision by letting the cost of replacing a defective unit vary from $10 to $30 in 11 steps and the cost of purchasing the supplier's guarantee policy vary from $400 to $1600 in 7 steps. Comment on your findings.

Input Data:

Number of units in a lot 1000

Cost of purchasing a lot $30,000

Cost of repairing a defective unit in a lot $20

Cost of purchasing supplier's guarantee policy (per lot) $1,000

Selling price for a unit of the component $45

Distribution of defective units in a lot

Proportion Probability

0.05 0.50

0.10 0.25

0.25 0.15

0.50 0.10

Answer 1

Given data

a distributor of computer parts purchases a specific compnent from a supplier in lots of 1000 units. cost of purchasing a lot is $30000. the units of pc repair shops at a price of $45 per unit. it costs $20 for the distributor to repalce a defective unit. assume the cost of replacing defective units in excess of the first 100 faulty units found in a given lot at no cost.

the guarantee policy may be purchased by the distributor prior to the receipt of a given lot at a cost of $1000per lot.

The complete precision tree

Here $30000 is written as negative as it is the cost the distributor has to pay to the supplier and in case of with guarantee policy it is $1000 more so -$31000

The decision

Excel inputs

Decision node

Without guarantee policy inputs

With guarantee policy inputs

In guarantee policy after 100 units defective such as 250 defective, only 100 units replacement cost i.e. $20*100 will be incurred by the distributor so only that cost would have to be subtracted from sell revenue