Problem:
Decision making under uncertainty
You are a manager of Bank of America and have to decide to open new branches in Oklahoma. You have no idea about the number of new accounts that would be opened (Uncertainty). You have three choices; open 4 new branches, open 10 new branches or open 50 new branches. These choices are based on the fund available to you. As a bank manager, you would like to make as much profit for your bank. You have an estimation of the profit you can make from number of new users as shown in the payoff table below.
Payoff table:
|
Alternatives
|
No. of new accounts
|
| |
100 to 400
|
400 to 1600
|
More than 1600
|
|
Four new branches
|
$100
|
$100
|
$100
|
|
Ten new branches
|
$70
|
$130
|
$130
|
|
Fifty new branches
|
$-40
|
$60
|
$200
|
Note: Payoffs are in thousand.
Required:
Above is the payoff table that you will use to choose the best alternative based on
1. Maximin criterion
2. Maximax criterion
3. Laplace criterion
4. Minimax regret criterion
Consider the probabilities for EMV criterion only.
|
Alternatives
|
No. of new accounts
|
| |
100 to 400 (.4)
|
400 to 1600 (.35)
|
More than 1600 (.25)
|
|
Four new branches
|
$100
|
100
|
100
|
|
Ten new branches
|
70
|
130
|
130
|
|
Fifty new branches
|
-40
|
60
|
200
|
5. EMV criterion
There is 40% chance of 100 to 400 new accounts.
There is 35% chance of 400 to 1600 new accounts.
There is 25% chance of more than 1600 new accounts.
Solve the given numerical problem and illustrate step by step calculation.