Decision Making D.K.Sharma 1
Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision making under uncertainty, Decision making under risk, Decision Tree analysis and their Applications. 2
Decision Theory/ Decision Analysis Decisions are taken under certain degrees of knowledge like: 1. Decision Under Certainty 2. Decision Under Uncertainty 3. Decision Under Risk 3
Decision Theory/ Decision Analysis The decisions defers if we have the information about What are the course of actions / acts/ strategies are available and What are the implications of it or What the state of natures are known then decision making become easier. 4
Decision Theory/ Decision Analysis Outcomes / events or state of natures are not in the control, of decision maker. For example, Inflation, a weather condition, a political development etc. 5
Payoffs An outcome (numerical value) resulting from each possible combination of alternatives and strategies / state of nature. 6
Payoffs The payoff values are always conditional values because of the unknown state of nature. 7
Payoffs Payoffs can be measured in terms of money, market share or other measures. 8
Payoff Matrix A tabular arrangement of these conditional (payoff) values is known as payoff matrix Strategies/ State of nature Probability Alternatives / courses of actions S 1 S 2 S 3 N 1 p 1 p 11 p 12 p 13 N 2 p 2 p 21 p 22 p 23 : : : : : : : : : : N n p n p n1 p n2 p n3 9
Steps Of Decision Making Process 1. Identifying and defining the problem. 2. Listing of all possible future events, called state of nature which can occur in the context of the decision problem. Such events are not under control of decision maker because they are erratic in nature. 3. Identifying all courses of actions (alternatives or decision choices) which are available to decision maker. The decision maker has control over these courses of actions. 4. Expressing the payoffs (P ij ) resulting from each pair of course of action and state of nature. These payoffs are normally expressed in a monetary value. 5. Appling appropriate mathematical decision model to select best course of action. 10
Decision Under Certainty When the decision maker has the complete knowledge/perfect information of the consequences of every decision choice (course of action/alternative) with certainty; he will select an alternative that yields the largest return (payoff) for the future state of nature. 11
Decision Under Certainty Example: Decision to purchase either National Saving Certificate (NSC) or deposit in National Saving Scheme (NSS) is one in which it is reasonable to assume complete information about the future because there is no doubt that in India govt. will pay the interest when it is due and the principle at maturity. In this decision model only one possible state of nature exists. 12
Decision Under Risk When the decision maker has less than complete knowledge with certainty of the consequence of every decision choice (course of action) because it is not definitely known that which outcome will occur. 13
Decision Under Risk There are more than one states of nature for which he makes an assumption of the probability with which each state of nature will occur. Example: Probability of getting head in toss of a coin is 0.5 14
Decision Under Risk EMV (Expected Monitory Value) EMV = (Probability)x(Payoff) 15
Illustration: Decision Under Risk A newspaper boy buys some newspapers everyday and sells them during the day. He purchases newspapers at the rate of Rs. 3/- per newspaper and sells @ Rs. 5 per newspaper. Any unsold newspaper at the end of the day he can return to publisher for Rs. 2.50. The demand for the newspapers for he has observed over a period of 200 days is : 16
Decision Under Risk No. Of newspapers 50 55 60 65 70 75 No. Of days 20 30 50 70 20 10 If he wants to know that how many newspapers he should buy in order to maximize his profits. 17
Decision Under Risk There are two types of losses the boy may incur. If the newspaper is not sold he gets some monitory loss of Rs. 0.50 per newspaper when he returns to publisher and if he stocks less then demands there is an opportunity loss. 18
Decision Under Risk To analyse the same we construct a payoff table in case of stocking 50, 55, 60, 65, 70, 75 newspapers and calculate the EMV of random variable. (Here the gain at the end of the day) 19
Decision Under Risk Historical Demand Probability Stock 50 55 60 65 70 75 50 0.10 100 97.5 95 92.5 90 87.5 55 0.15 100 110 107.5 105 102.5 100 60 0.25 100 110 120 117.5 115 112.5 65 0.35 100 110 120 130 127.5 125 70 0.10 100 110 120 130 140 137.5 75 0.05 100 110 120 130 140 150 EMV 100 103.75 115.63 119.38 118.75 116.88 20
Decision Under Risk EMV = (Probability)x(Payoff) Highest EMV = 119.38 for 65 newspapers The table shows that the highest EMV is for stocking 65 newspapers so that the profit will be maximum. 21
Decision Under Risk If the information about the demand is known, the expected profit will be called as the expected profit with perfect information (EPPI). 22
Decision Under Risk If the information about the demand is known, the expected profit will be called as the expected profit with perfect information (EPPI). i.e. EPPI = 0.10x100 + 0.15x110 + 0.25x120 + 0.35x130 + 0.10x140 + 0.05x150 EPPI = 123.50 23
Decision Under Risk Since we do not have the perfect information about the demand we are less by = 123.50 119.37 = 4.13 We can say that the value for the perfect information is Rs. 4.13. Expected Value for Perfect Information (EVPI) EVPI = EPPI EMV 24
Decision Under Uncertainty In the absence of knowledge about the probability of any state of nature (future) occurring. The decision maker must arrive at a decision only at the actual conditional payoff values, together with a policy (attitude) The decision criteria are based on the decision maker s attitude toward life. 25
Decision Under Uncertainty The decision criteria include : Maximax Criterion - optimistic or aggressive approach. Maximin Criterion - pessimistic or conservative approach. Minimax Regret (salvage) Criterion - pessimistic or conservative approach. Equal probability (Laplace) Criterion Coefficient of optimism(hurwitz) Criterion { α(max)+(1- α)min} 26
Maximax Criterion (optimistic or aggressive approach) This criterion is based on the best possible scenario. It fits both an optimistic and an aggressive decision maker. 27
Maximax Criterion (optimistic or aggressive approach) An optimistic decision maker believes that the best possible outcome will always take place regardless of the decision made. An aggressive decision maker looks for the decision with the highest payoff (when payoff is profit). 28
Maximax Criterion (optimistic or aggressive approach) To find an optimal decision. We find the maximum payoff for each decision alternative. We select the decision alternative that has the maximum of the maximum payoff. 29
Illustration: Let s consider a problem where we have three strategies S 1, S 2, and S 3 and the states of nature are N 1, N 2 and N 3. The pay off for each combination are known or estimated. N 1 N 2 N 3 (State of nature) Strategy S 1 15 12 18 S 2 9 14 10 S 3 13 4 26 30
Maximax Criterion (optimistic or aggressive approach) State of nature N1 N2 N3 Max Strategy S1 15 12 18 18 S2 9 14 10 14 S3 13 4 26 26 31
Maximax Criterion (optimistic or aggressive approach) State of nature N1 N2 N3 Max Strategy S1 15 12 18 18 S2 9 14 10 14 S3 13 4 26 26 Maximax 26 32
Maximax Criterion (optimistic or aggressive approach) State of nature N1 N2 N3 Max Strategy S1 15 12 18 18 S2 9 14 10 14 S3 13 4 26 26 Maximax 26 33
Maxmin Criterion This criterion is based on the worst-case scenario. It fits both a pessimistic and a conservative decision maker s styles. A pessimistic decision maker believes that the worst possible result will always occur. A conservative decision maker wishes to ensure a guaranteed minimum possible payoff. 34
Maxmin Criterion To find an optimal decision We record the minimum payoff across all states of nature for each decision & Identify the decision with the maximum minimum payoff. 35
State of nature N1 N2 N3 Max Min Strategy S1 15 12 18 18 12 S2 9 14 10 14 9 S3 13 4 26 26 4 Maximax 26 Maxmin 12 36
State of nature N1 N2 N3 Max Min Laplace Strategy S1 15 12 18 18 12 15 S2 9 14 10 14 9 11 S3 13 4 26 26 4 14.3333 Maximax 26 15 Maxmin 12 37
Hurwitz Criterion Coefficient of optimism(hurwitz) Criterion { α(max)+(1- α)min} 38
State of nature N1 N2 N3 Max Min Laplace Hurwitz Strategy α = 0.9 S1 15 12 18 18 12 15 17.4 S2 9 14 10 14 9 11 13.5 S3 13 4 26 26 4 14.3333 23.8 Maximax 26 15 23.8 Maxmin 12 S3 39
Minimax (regret /Salvage) Criterion The decision maker incurs regret by failing to choose the best decision. 40
Minimax (regret /Salvage) Criterion The Minimax Regret Criterion Finds an optimal decision, for each state of nature: Determine the best payoff over all decisions. Calculate the regret for each decision alternative as the difference between its payoff value and this best payoff value. For each decision find the maximum regret over all states of nature. Select the decision alternative that has the minimum of these maximum regrets. 41
Minimax (regret /Salvage) Criterion State of nature N1 N2 N3 Strategy S1 15 12 18 S2 9 14 10 S3 13 4 26 42
Minimax (regret /Salvage) Criterion Regret N1 N2 N3 Strategy S1 0 2 8 8 S2 6 0 16 16 S3 2 10 0 10 Minimax 8 43
THANK YOU 44