Extra Problem 6 Solving Decision Trees Solution Key
EMSE 269 - Elements of Problem Solving and Decision Making
EXTRA PROBLEM 6:
SOLVING DECISION TREES
Read the following decision problem and answer the questions below.
A manufacturer produces items that have a probability p of being defective.
These items are formed into batches of 150. Past experience indicates that some (batches) are of good quality (i.e. p=0.05) and others are of bad quality
(i.e. p=0.25). Furthermore, 80% of the batches produced are of good quality and 20% of the batches are of bad quality. These items are then used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. The manufacturer can either screen each item in a batch and replace defective items at a total average cost of $10 per item or use the items directly without screening. If the latter action is chosen, the cost of rework is ultimately $100 per defective item. For these data, the costs per batch can be calculated as follows:
Screen
Do not Screen
p = 0.05
$1500
$750
p = 0.25
$1500
$3750
Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the potential
Instructor: Dr. J. R. van Dorp
1
EMSE 269 - Elements of Problem Solving and Decision Making
screening takes place. However, the manufactures may take one item taken from a batch and sent it to a laboratory, and the test results (defective or nondefective) can be reported before the screen/no-screen decision must be made. After the laboratory test, the tested item is returned to its batch. The cost of this initial inspection is $125. Also note that the probability that a random sample item is defective is
0.8 * 0.05 + 0.2 * 0.25 = 0.09, and the probability that an item in a lot is of good quality given a randomly sampled item is defective is 0.444 and the probability that an item in a lot is of good quality given a randomly sampled item is not defective is 0.835.
The manufactur wants to minimize his or
EXTRA PROBLEM 6:
SOLVING DECISION TREES
Read the following decision problem and answer the questions below.
A manufacturer produces items that have a probability p of being defective.
These items are formed into batches of 150. Past experience indicates that some (batches) are of good quality (i.e. p=0.05) and others are of bad quality
(i.e. p=0.25). Furthermore, 80% of the batches produced are of good quality and 20% of the batches are of bad quality. These items are then used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. The manufacturer can either screen each item in a batch and replace defective items at a total average cost of $10 per item or use the items directly without screening. If the latter action is chosen, the cost of rework is ultimately $100 per defective item. For these data, the costs per batch can be calculated as follows:
Screen
Do not Screen
p = 0.05
$1500
$750
p = 0.25
$1500
$3750
Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the potential
Instructor: Dr. J. R. van Dorp
1
EMSE 269 - Elements of Problem Solving and Decision Making
screening takes place. However, the manufactures may take one item taken from a batch and sent it to a laboratory, and the test results (defective or nondefective) can be reported before the screen/no-screen decision must be made. After the laboratory test, the tested item is returned to its batch. The cost of this initial inspection is $125. Also note that the probability that a random sample item is defective is
0.8 * 0.05 + 0.2 * 0.25 = 0.09, and the probability that an item in a lot is of good quality given a randomly sampled item is defective is 0.444 and the probability that an item in a lot is of good quality given a randomly sampled item is not defective is 0.835.
The manufactur wants to minimize his or