 # Decision Analysis Steps in Decision making Decision analysis

• Slides: 29 Decision Analysis • Steps in Decision making • Decision analysis with decision tables • Types of decision environments) • Decision trees (decision modelling Steps in Decision making 1. Clearly define the problem 2. List all possible alternatives 3. Identify all possible outcomes for each alternative 4. Identify the payoff for each alternative & outcome combination 5. Use a decision modeling technique to choose an alternative Decision analysis with decision table • The quantitative data of many decision situations can be arranged in a standardized tabular form known as decision table. • Also known as payoff table • Decision table typically contains four elements. They are: • • The alternative courses of action The state of nature The probabilities of state of nature The payoffs The alternative course of action • DM involves two or more options • One, and only one of these alternatives must be selected • Alternative courses of actions are designated by a 1, a 2, a 3…… an • Number of alternative may be either finite or infinite. As for example……. The States of Nature • Also known as Events or possible futures that a decion maker can not control • A state of nature can be – – A state of economy (e. g. inflation) A weather condition A political development Or other situations • Investment example • One goal: maximize the yield after one year • Yield depends on the status of the economy (the state of nature) – Solid growth – Stagnation – Inflation Possible Situations 1. If solid growth in the economy, bonds yield 12%; stocks 15%; time deposits 6. 5% 2. If stagnation, bonds yield 6%; stocks 3%; time deposits 6. 5% 3. If inflation, bonds yield 3%; stocks lose 2%; time deposits yield 6. 5% Decision Table State of nature . 5. 3 Solid G Stagnation . 2 Inflation Alternatives A 1 Bonds 12 6 3 A 2 Stocks A 3 Time deposits 15 6. 5 3 6. 5 -2 6. 5 The probabilities of States of Nature & Payoffs • Likelihood of these states of nature • Payoff also known as outcome • Payoff can be measured in terms of money, market share or other measures. Types of decision modelling environment Type 1: Decision making under certainty Type 2: Decision making under uncertainty Type 3: Decision making under risk Decision making under certainty • The consequence of every alternative is known • Usually there is only one outcome for each alternative • This seldom occurs in reality Decision making under uncertainty • • Probabilities of the possible outcomes are not known. Choice here is made by organizational policy the attitude of the decision maker toward risk or both. Decision making methods: 1. 2. 3. 4. 5. Laplace Maximin Maximax Coefficient of Optimism(Hurwicz Criterion) The criterion of Regret(Savage’s Criterion Example • The palm tree Hotel is considering the construction of an additional wing. Mgt is evaluating the possibility of adding 30, 40, 50 rooms. The success of the addition depends on a combination of local government legislation and competition in the field, four states of nature are being considered. They are shown together with the anticipated payoff. Mgt cannot agree on the probabilities of the state of nature. The problem is : how many rooms to build in order to maximize the return on investment. Laplace (The criterion of equal probabilities Alternative/State s 1 of Nature s 2 s 3 s 4 A 1=30 10 5 4 -2 A 2=40 17 10 1 -10 A 3=50 24 15 -3 -20 E(a 1) =. 25*10+. 25*5+. 25*4+. 25*-2 =4. 25 E(a 2) =. 25*17+. 25*10+. . 25*1+25*-10 =4. 5 Largest Expected Yield E(a 3) . 25*24+. 25*15+. 25*-3+. 25*-20 =4 Criterion of Pessimism (Maximin) Alternativ s 1 e/State of Nature s 2 s 3 s 4 Worst Best of Worst A 1=30 10 5 4 -2 -2 -2* A 2=40 17 10 1 -10 A 3=50 24 15 -3 -20 Criterion of Optimism(Maximax) Alternative/St ate of Nature s 1 s 2 s 3 s 4 Best A 1=30 10 5 4 -2 10 A 2=40 17 10 1 -10 17 A 3=50 24 15 -3 -20 24 Best of Bests 24* Coefficient of Optimism(Hurwicz) Alternative/Sta s 1 te of Nature s 2 s 3 s 4 A 1=30 10 5 4 -2 A 2=40 17 10 1 -10 A 3=50 24 15 -3 -20 Hurwicz suggested that the best alternative is the one with the highest (in maximization) weighted value (WV). WV(a 1) . 7*10+(1 -. 7)*(-2)=6. 4 WV(a 2) . 7*17+(1 -. 7)*(-10)=8. 9 WV(a 3) . 7*24+(1 -. 7)*(-20)=10. 8 (Maximum)* The criterion of regret (savage’s Criterion) Alternative/Sta s 1 te of Nature s 2 s 3 s 4 A 1=30 10 5 4 -2 A 2=40 17 10 1 -10 A 3=50 24 15 -3 -20 Alternative/ s 1 State of Nature s 2 s 3 s 4 Largest regret(Worst) A 1=30 24 -10=14 15 -5=10 4 -4=0 -2 - (-2)=0 14 A 2=40 24 -17=7 15 -10=5 4 -1=3 -2 (-10)=8 8* Minimum A 3=50 24 -24=0 15 -15=0 4 -(-3)=7 -2 -(-20)=18 18 Example 2 • The manager of an advertising agency has to make decisions between three available programs (a 1, a 2, a 3)There are three possible futures that can be expected ie market rises, market falls, no change in the market. The manager can estimate the yields in each case but can not estimate the possibilities of the various future occurring. Programs s 1 s 2 s 3 a 1 3 6 -1 a 2 8 5 4 a 3 -4 7 12 Which program will the manager select if he uses the following decision approaches i. iii. iv. v. Laplace Pessimistic Otimistic Hurwicz criterion Minimax regret (Savage) Decision making under Risk • Where probabilities of outcomes are available • Expected payoff criterion: Here the Decision maker selects the alternative with the best expected(average) payoff EMV (for alternative i) = ∑(probability of outcome) x (payoff of outcome) • EOL criterion: Investment Problem Decision Table Model States of Nature Solid Stagnation Inflation Alternatives Growth Bonds 12% 6% 3% Stocks 15% 3% -2% CDs 6. 5% Table 5. 3: Decision Under Risk and Its Solution Solid Stagnation Growth Inflation Expected Value Alternatives . 5 . 3 . 2 Bonds 12% 6% 3% Stocks 15% 3% -2% 8. 0% CDs 6. 5% 8. 4% * How to find the Expected payoff • E(a 1)=12*. 5+6*. 3+3*. 2=8. 4 • E(a 2)=15*. 5+3*. 3+-2*. 2=8. 0 • E(a 3)=6. 5*. 5+6. 5*. 3+6. 5*2=6. 5 Expected Opportunity Loss • Also called regret criterion • Opportunity loss is defined as the relative loss resulting from selecting an alternative. • Minimizing expected regret. Regret is always bad and is to be avoided or minimized EOL/Regret Criterion Solid Stagnation Growth Inflation Alternatives . 5 . 3 . 2 Bonds 12% 6% 3% Stocks 15% 3% -2% CDs 6. 5% Expected Value 2. 35* Smallest EOL/Regret Criterion Solid Stagnation Inflation Expected Value Growth Alternatives . 5 . 3 Bonds 15 -12=3 6. 5 -6=. 5 Stocks 15 -15=0 6. 5 - 3=3. CDs 15 -6. 5=8. 5 6. 5 -6. 5=0 . 2 6. 5 - 3=3 =3*. 5+. 5*. 3+3*. 2=2. 35* 6. 5 -( -2) =2. 75 6. 5 -6. 5 =4. 25 Example 2 • Find the best alternative in the following decisions table: Use both an expected value and an EOL State of nature Alternative . 6 . 1 . 2 . 1 s 2 s 3 s 4 a 1 3 5 8 -1 a 2 6 5 2 0 a 3 0 5 6 4 Example 3 • A survey conducted over last 20 yrs in Hamburg Germany indicated that in 8 of them the winter was mild, in 7 of them it was cold and in remaining 5 it was very cold. A company sells 1000 heavy coats in mild year, 1300 in cold year and 2000 in very cold year. Find the yearly expected profit of the company if a coat cost 85 euro & sold to 123 euro. Decision Trees