In: Economics
Sierra Mountain Bike, Inc., is a producer and
wholesaler of rugged bicycles designed for mountain touring. The
company is considering an upgrade to its current line by making
high-grade chrome alloy frames standard. Of course, the market
response to this upgrade in product quality depends on the
competitor’s reaction, if any. The company’s comptroller projects
the following annual profits (payoffs) following resolution of the
upgrade decision:
States of Nature
Sierra’s No
Decision Competitor
Competitor
Alternatives Upgrade Upgrade
Upgrade $1,000,000 $1,500,000
Do not upgrade 800,000 2,000,000
Determine the decision alternative that Sierra would
choose given a maximin criterion? Explain your choice of answer
.
Calculate the opportunity loss or regret matrix for the Competitor
Upgrade.
Calculate the opportunity loss or regret matrix for the No
Competitor Upgrade.
Which decision alternative would Sierra choose given a minimax
regret criterion?
States of nature |
No Competitor Upgrade S1 |
Competitor Upgrade S2 |
---|---|---|
Alternatives | ||
A1 | 1000000 | 1500000 |
A2 | 800000 | 2000000 |
# Maximin Criterion-----
* The course of action that maximizes the minimum possible pay- off is selected .
At first , minimum value of each row is selected
Out of these maximum value out of selected row minima is the decision criterion.
States of nature | S1 | S2 | Row Minima |
---|---|---|---|
Alternatives | |||
A1 | 1000000 | 1500000 | 1000000 |
A2 | 800000 | 2000000 | 800000 |
Out of row minima, column maxima ( maximum vale out of minima) is 800000, which belongs to A2.
So, As per Maximin criterion, decision alternative is do not upgrade
# Opportunity loss / Regret Matrix--------
* The regret table is formulated below by substracting all the elements of each column fro highest value for that column
* After that, using Minimax Regret Criterion, Minimum of these maximum regrets , corresponding to decision alternative should be selected.
States of nature | S1 | S2 | Maximum Regret |
---|---|---|---|
Alternatives | |||
A1 |
0 (1000000--1000000) |
500000 (2000000--1500000) |
500000 |
A2 |
200000 (1000000--800000) |
0 (2000000--2000000) |
200000 |
Minimum of maximum regret is 200000 in A2.
so, Decision criterion under Minimax Regret is not to upgrade.