Production and Operation Management

Decision Making Problems 1.1

Given: Selling Price: $5Cost: $2Profit: $3

States of nature

Alternative Stocks

10 11 12 13

10 30 30 30 30

11 28 33 33 33

12 26 31 36 36

13 24 29 34 39

Answers to the given:

Solutions to the given:Alternative Stocks:

10: P30 [10 stocks multiplied by the $3 profit) in all states of nature because for every state of nature, the maximum number of stocks that you can sell are 10 stocks, so although the states of nature gives you the opportunity to sell more than 10 stocks (11, 12 and 13). Your profit would still be the same in each of them, since the available number of stocks that you can sell only is 10.

Solutions to the given:

Alternative Stocks:11: Under the state of nature 10- It means

that you have a total of 11 stocks that you can sell but you only sold 10 stocks. Hence, the computation is: (10 stocks X P3 profit) – (11 – 10 stocks X P2 cost)

And so, the answer is 28.

Solutions to the given:

Alternative Stocks:11: P33 [11 stocks multiplied by the $3 profit)

in all states of nature because for every state of nature, the maximum number of stocks that you can sell are 11 stocks, so although the states of nature gives you the opportunity to sell more than 11 stocks (12 and 13). Your profit would still be the same in each of them, since the available number of stocks that you can sell only is 11.

Solutions to the given:

Alternative Stocks:12: Under the state of nature 10- It means

that you have a total of 12 stocks that you can sell but you only sold 10 stocks. Hence, the computation is: (10 stocks X P3 profit) – (12 – 10 stocks X P2 cost)

And so, the answer is 26.

Solutions to the given:

Alternative Stocks:12: Under the state of nature 11- It means

that you have a total of 12 stocks that you can sell but you only sold 11 stocks. Hence, the computation is: (11 stocks X P3 profit) – (12 – 11 stocks X P2 cost)

And so, the answer is 31.

Solutions to the given:

Alternative Stocks:12: P36 [12 stocks multiplied by the $3 profit)

in all states of nature because for every state of nature, the maximum number of stocks that you can sell are 12 stocks, so although the states of nature gives you the opportunity to sell more than 12 stocks (13). Your profit would still be the same in each of them, since the available number of stocks that you can sell only is 12.

Solutions to the given:

Alternative Stocks:13: Under the state of nature 10- It means

that you have a total of 13 stocks that you can sell but you only sold 10 stocks. Hence, the computation is: (10 stocks X P3 profit) – (13 – 10 stocks X P2 cost)

And so, the answer is 24.

Solutions to the given:

Alternative Stocks:13: Under the state of nature 11- It means

that you have a total of 13 stocks that you can sell but you only sold 11 stocks. Hence, the computation is: (11 stocks X P3 profit) – (13 – 11 stocks X P2 cost)

And so, the answer is 29.

Solutions to the given:

Alternative Stocks:13: Under the state of nature 12- It means

that you have a total of 13 stocks that you can sell but you only sold 12 stocks. Hence, the computation is: (12 stocks X P3 profit) – (13 – 12 stocks X P2 cost)

And so, the answer is 34.

Solutions to the given:

Alternative Stocks:13: P39 [13 stocks multiplied by the $3 profit)

Decision Making 1.2

• The answers in the table can now be used to compute for the Maximax, Maximin and Minimax regret.

States of NatureAlternative

Stocks10 11 12 13 Maximax Maximin Minimax

regret

10 30 30 30 30 30 30 9

11 28 33 33 33 33 28 6

12 26 31 36 36 36 26 4

13 24 29 34 39 39 24 6

• Maximax- get the highest number per row and then get the highest maximax number. In this case is 39.

• Maximin- get the lowest number per row and then get the highest maximin number. In this case is 30.

• Minimax regret- get the highest number per column and then from that, subtract it to all the other givens in that particular column.

Minimax regret computation:States of nature

Alternative Stocks

10 11 12 13

10 30 (30 – 30) 30 (33 – 30) 30 (36 – 30) 30 (39 – 30)

11 28 (30 – 28) 33 (33 – 33) 33 (36 – 33) 33 (39 – 33)

12 26 (30 – 26) 31 (33 – 31) 36 (36 – 36) 36 (39 – 36)

13 24 (30 – 24) 29 (33 – 29) 34 (36 – 34) 39 (39 – 39)

States of nature

Alternative Stocks

10 11 12 13 Minimax regret

10 0 3 6 9 9

11 2 0 3 6 6

12 4 2 0 3 4

13 6 4 2 0 6

HerwiczFormula: Alpha(Maximax) + (1- Alpha)(Maximin)

Assuming from the same given example. The alpha is

equal to 0.70. The computation would be:

Stock

10: (0.70)(30) + (0.30)(30) = 30

11: (0.70)(33) + (0.30)(28) = 31.5

12: (0.70)(36) + (0.30)(26) = 33

13: (0.70)(39) + (0.30)(24) = 34.5

Therefore, 13 stocks will yield the highest profit.

The same computation process if you are asked to find the Minimin, Minimax and Minimax regret. The only differences are in minimin and minimax.

Minimin- get the lowest number per row and then get the lowest minimin.

Minimax- get the highest number per row and then get the lowest minimax.

Expected Value of Perfect Information

Given:Probability 0.10 0.20 0.40 0.30

10 11 12 13

Stock 10 30 30 30 30

11 28 33 33 33

12 26 31 36 36

13 24 29 34 39

• The expected value of perfect information is computed as:

Expected payoff with perfect information

-

Expected profit

• Expected payoff with perfect information can be obtained by getting the highest value for each column and then multiply it by the each given probability per stock

• Thus, the expected value of perfect information in the given would be:

10 – 0.10(30) = $3

11 – 0.20 (33) = 6.60

12 – 0.40 (36) = 14.40

13 – 0.30 (39) = 11.70

(3 + 6.60 + 14.40 + 11.70) = $35.70

• The expected profit is computed by multiplying each given in the table by the probability designated to each of that stock. Add the computed values and then get the highest value

10 11 12 13

Stock 10 30 30 30 30 30

11 28(0.10) 33(0.20) 33(0.40) 33(0.30) 32.50

12 26(0.10) 31(0.20) 36(0.40) 36(0.30) 34

13 24(0.10) 29(0.20) 34(0.40) 39(0.30) 33.50

• Expected payoff w/perfect information $35.70 - Expected profit 34.00 Expected value of perfect information $1.70