Term Paper

1. List possible acts and events

i. The company can buy 18 copies and sell all with a profit of 360 since, the minimum possible event (demand) is 18. Nevertheless, this decision may regret the decision maker if the demand, incase, goes above 18.

ii. The company can buy 19 copies of the tax law book and sell all 19 and earn a profit of 380(19*20) if the demand is 19 or above. However, there is also a possibilities for the profit to go down to 360 if the demand is 18 due to the 20 penalty for the unsold item

iii. It is also possible to the company to buy 20 copies of the tax law book and able to sell all 20 if the demand is 20 /or above. But the company may also sell only 18 copies and incur penalty of 40 birr (20/each unsold item) or sell 19 copies and face the penalty of 20 birr for the single unsold copies if the demand (event) is 18 or 19 respectively.

iv. The company may also buy 21 copies and generate a profit of 420 if the demand is either exactly 21 or above. However, there is also a possibility for the event to be less than 21 in such situation the company profit will reduced by 20 birr for each unsold copy. As such it is 340,360,380 if the demand is 18, 19 or 20 respectively.

v. The company may also buy 22 copies and sell all of it and earn a profit of 440 birr if the demand is greater than or is equal to 22. But, it may also sell only 18 and face penalty of 80birr, sell 19 copies and incur 60 birr penalty, sell 20 and experience 40 birr penalty or sell 21 copies and hence, face 20 birr penalty for the unsold item.

vi. The company may also make the maximum possible decision (buy 23 copies of tax law book) and able to sell all of it with a profit of 460 birr if it is lucky enough. Or else it experience 20 birr penalty for each unsold item and as such, profit will reduced to 420,380,340,300 and 260 if demand is 22,21,20,19 or 18.

2. Construct the pay off matrix (table)

possible state of nature

18 19 20 21 22 23

E1 E2 E3 E4 E5 E6

Alternative 18 A1 360 360 360 360 360 360

decisions 19 A2 340 380 380 380 380 380

20 A3 320 360 400 400 400 400

21 A4 300 340 380 420 420 420

22 A5 280 320 360 400 440 440

23 A6 260 300 340 380 420 460

3. Choose among the various alternatives on the bases of the following criterion:

a. Maximax decision rule:

The decision maker expects that the best would happen and he/she intends to select the best from the best this can be obtained by;

 Determine the maximum pay off from each raw(Raw maxima)

18 19 20 21 22 23 Raw maxima

E1 E2 E3 E4 E5 E6

18 A1 360 360 360 360 360 360 360

19 A2 340 380 380 380 380 380 380

20 A3 320 360 400 400 400 400 400

21 A4 300 340 380 420 420 420 420

22 A5 280 320 360 400 440 440 440

23 A6 260 300 340 380 420 460 460

 Select the raw with maximum pay off ( Maximum of the raw maximum)

Therefore, the A bookstore choose strategy A6 which is buying 23 copies of tax laws as it constitutes the maximum pay off (maximax) result 460.

b. Maximin decision :

Also known as pessimist decision here, the decision maker expects that the worst could happen and intends to maximize the minimum gain. This can be done by;

 Minimum of each raw (raw minima)

 Select the maximum among the minimum

E1 E2 E3 E4 E5 E6 Raw minima

18 19 20 21 22 23

A1 18 360 360 360 360 360 360 360

A2 19 340 380 380 380 380 380 340

A3 20 320 360 400 400 400 400 320

A4 21 300 340 380 420 420 420 300

A5 22 280 320 360 400 440 440 280

A6 23 260 300 340 380 420 460 260

Thus, using maximin criteria; the bookstore selects strategy A1 which belongs to buying 18 copies of the tax laws book.

c. Savage Minimax Regret criteria :

Here, Decision maker relies on opportunity table with the intention of making the decision against maximum opportunity cost.

- Step1: Prepare opportunity cost table by selecting column maxima and deducting each elements in the respected column from the selected value.

E1 E2 E3 E4 E5 E6

18 19 20 21 22 23

A1 18 360 360 360 360 360 360

A2 19 340 380 380 380 380 380

A3 20 320 360 400 400 400 400

A4 21 300 340 380 420 420 420

A5 22 280 320 360 400 440 440

A6 23 260 300 340 380 420 460

Column maxima 360 380 400 420 440 460

E1 E2 E3 E4 E5 E6 Max opport

18 19 20 21 22 23 unity cost

A1 18 0 20 40 60 80 100 100

A2 19 20 0 20 40 60 80 80

A3 20 40 20 0 20 40 60 60

A4 21 60 40 20 0 20 40 60

A5 22 80 60 40 20 0 20 80

A6 23 100 80 60 40 20 0 100

Therefore, based on the savage minimax regret criteria the bookstores select either strategy A3 or A4 since both constitute the same minimum regret which is 60.

d. Laplace criterion

0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 expected