Problem #1
The following table shows the capacity required (in thousands of unspecified units) for the production of an Online service over the next 18 months.
Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Demand 25 30 32 33 32 31 30 29 28 28 29 31 30 32 33 32 34 35
- Based on MAD, which model is better, a 6 month or a 4 month moving averages? Based on your selection, what is the forecast for month 25?
- Based on MAD, which model is better, an exponential smoothing with smoothing constants of 0.7 or 0.8? Based on your selection, what is the forecast for month 25?
- Does a linear regression model is better than any of the previous (four) models? Explain.
Problem #2
A manufacturer produces items that have a probability of p 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 other 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 use in 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 If is chosen, the cost of rework is ultimately $100 per defective item. For these data, the costs per batch can be calculated as follows:
p=0.05 p=0.25
Screen $1,700 $1,700
Don't Screen $800 $4,200
Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the potential 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 manufacturer wants to minimize his/her cost. Using a decision tree, help the manager decide what he/she should do (show the decision tree, analysis, and conclusions.)