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

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

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)

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: 0,4 * 90 + (1 – 0,4) * (-20) = 24 Equally likely (Laplace) 5. MinMax Regret

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

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

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

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?

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

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

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

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?