1. Decision analysis. New product and new business launch
Tomasz Brzęczek Ph.d.
Poznan University of Technology

2. Steps in decision analysis
Clearly define the problem at hand
List all possible decision alternatives
Identify the possible future outcomes / states of nature for each decision alternative
Identify the payoff for each combination of alternatives and outcomes: profit, cost, nonmonetary payoff.
Select decision analysis technique and apply it to make your decision
Payoff is also called a conditional value upon decision alternative and given outcome

3. Decision-making environment
Decision making under certainty
Decision making under uncertainty
Decision making under risk
3. The probability could be a precise measure (e.g., the probability of being dealt an ace from a deck of cards is exatly 4/52=1/13) or an estimate (e.g., the probability of high demand is 0,4)

4. Payoff table for profits (thous
Payoff table for profits (thous. €) Whether to expand business by manufacturing and marketing a new product
Alternatives
Outcomes
High demand
Moderate demand
Low demand
Build large plant
200
100
-120
Build small plant 90 50
-20
No plant
For α = 0,4 the highest weighted payoff is for decision to build a small plant
MaxiMax
MaxiMin
Criterion of realism (Hurwicz rule), α is a weight of optimism from [0, 1] Realistic value for small plant decision of slightly pesimistic John is: ,4 * 90 + (1 – 0,4) * (-20) = 24
Equally likely (Laplace) MinMax Regret

5. Expected Monetary Value of possible payoffs of decision i
EMV i ≡ E(Xi) = 𝑗=1 𝑗=𝐽 𝑃 𝑗 𝑥 𝑖𝑗
𝑃 𝑗 − probability of outcome j,
𝑥 𝑖𝑗 − payoff from decision i in outcome j.
Alternatives
Outcomes
EMV i ≡ E(Xi)
High demand
Moderate demand
Low demand
P1 = 0,3
P2 = 0,5
P3 = 0,2
Build large plant
200
100
-120 86
Build small plant 90 50
-20 48
No plant

6. Decision tree
Managerial Decision Modeling. Balakrishnan N., Render B., Stair R.M.

7. Variance S2 and standard deviation S of decision i payoffs Xi
𝑃 𝑗 − probability of outcome j,
𝑥 𝑖𝑗 − payoff from decision i in outcome j.
Alternatives
Outcomes
S(Xi)=∓ 𝑺 𝟐 (Xi)
High demand
Moderate demand
Low demand
P1 = 0,3
P2 = 0,5
P3 = 0,2
Build large plant
200
100
-120
Calculation 1.xlsx
Build small plant 90 50
-20
No plant

8. Multistage decision making
John prepared a business plan of a new product. In case of high demand for the product he makes 100. In case of lower demand he would lose -40. Probability of high demand is 0,45. He can pay 10 to conduct pilot survey of demand. Favorable survey and of unfavorable survey resulys are equally likely to occur. Given favorable survey probability of high demand is 0,8. Given unfavorable survey probability of low demand is 0,9. What should John decide? Does the best decision depend on survey result?

10. 23
100 23
-40
-10 26
-10 62 90 62 26
-50
-10
-10
-10 90
-36
-50

11. Probability and joint events probability
Conditional probabilities of High and Low demand under given survey outcome
High
Demand B
Low
Total
Fav survey A
P(B\A) = 0,8
P(B\A) = 0,2
1,0
Unfav survey A
P(B\A) = 0,1
P(B\A) = 0,9
Probability and joint events probability
High
demand
Low
P(B) = 0,45
P(B) = 0,55
Fav survey
P(A) = 0,5
P(A∩B) = 0,4
P(A∩B) = 0,1
Unfav survey
P(A∩B) = 0,05
P(A∩B) = 0,45

12. Calculate Conditional probabilities of Fav and Unfav survey under given each demand outcome
High
Demand B
Low
Fav survey A
P(A\B) =
Unfav survey A
Total
1,0
Bayes theorem
𝑃 𝐴\𝐵 = 𝑃 𝐴∩𝐵 𝑃 𝐵 𝑎𝑛𝑑 𝑃 𝐵\A = 𝑃 𝐴∩𝐵 𝑃 𝐴 that we know
1. What sense has calculated conditional probability? so
𝑃 𝐴∩𝐵 =𝑃 𝐵\A ∗𝑃 𝐴 =0,8∗0,5=0,4
𝑃 𝐴\𝐵 = 𝑃 𝐴∩𝐵 𝑃 𝐵 = 0,4 0,45 =0,89 𝑎𝑛𝑑 𝑃 𝐴 \𝐵 =0,11
𝑃 𝐴 \ 𝐵 = 𝑃 𝐴 ∩ 𝐵 𝑃 𝐵 = 0,9∗0,5 0,55 =0,82 𝑎𝑛𝑑 𝑃 𝐴\ 𝐵 =0,18

13. Can You calculate missing probabilities in each row seperately?
P(A)
P(B)
P(B|A)
P(A|B)
PA|B)
0,5
0,8
0,1
0,89
0,18
0,45
1. What sense has calculated conditional probability?