Decision Making DKSharma
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.
Decision Theory/ Decision Analysis An analytical and systematic approach to depict the expected result of a situation when alternate managerial actions and outcomes are compared.
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
Decision Theory/ Decision Analysis The decision that we make are affected with the situations that are prevailing around in the organizations.
Decision Theory/ Decision Analysis The decisions defers if 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.
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.
Payoffs An outcome (numerical value) resulting from each possible combination of alternatives and strategies / state of nature.
Payoffs The payoff values are always conditional values because of the unknown state of nature.
Payoffs Payoffs can be measured in terms of money, market share or other measures.
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
Payoff Matrix Payoff table analysis can be applied when: There is a finite set of discrete decision alternatives. The outcome of a decision is a function of a single future event.
Payoff Matrix In a Payoff table - The rows correspond to the possible decision alternatives. The columns correspond to the possible future events. Events (states of nature) are mutually exclusive and collectively exhaustive. The table entries are the payoffs.
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.
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.
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.
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.
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
Decision Under Risk Knowing the probability distribution of the events the best decision is to select that alternative which has the largest expected payoff value; The expected payoff value. The expected pay off of a choice is the sum of all possible payoffs of that alternative weighted by the probabilities of those payoffs occurring and is called EMV (Expected Monitory Value) EMV = (Probability)x(Payoff)
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 :
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.
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.
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)
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
Decision Under Risk EMV Highest EMV = (Probability)x(Payoff) = 119.38 for 65 newspapers The table shows that the highest EMV is for stocking 65 newspapers so that the profit will be maximum.
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
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
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.
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}
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.
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).
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.
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.
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.
Minimax (regret /Salvage) Criterion: This criterion fits both a pessimistic and a conservative decision maker approach. The payoff table is based on lost opportunity, or regret. The decision maker incurs regret by failing to choose the best decision.
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.
Minimax (regret /Salvage) Criterion: 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
Minimax (regret /Salvage) Criterion: 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 12 15 23.8 Minimax 14 4 S3
Minimax (regret /Salvage) Criterion: Regret N1 N2 N3 Strategy S1 0 2 8 8 S2 6 0 16 16 S3 2 10 0 10 Maximax 16 Minimax 8
Decision Trees Any problem that can be presented in a decision table can also be graphically represented in a decision tree. Decision trees are most beneficial when a sequence of decisions must be made. All decision trees contain decision points or nodes, from which one of several alternatives may be chosen. All decision trees contain state-of-nature points or nodes, out of which one state of nature will occur.
Decision Trees Five Steps of Decision Tree Analysis 1. Define the problem. 2. Structure or draw the decision tree. 3. Assign probabilities to the states of nature. 4. Estimate payoffs for each possible combination of alternatives and states of nature. 5. Solve the problem by computing expected monetary values (EMVs) for each state of nature node.
Decision Trees Structure of Decision Trees Trees start from left to right. Trees represent decisions and outcomes in sequential order. Squares represent decision nodes. Circles represent states of nature nodes. Lines or branches connect the decisions nodes and the states of nature. Branches leading away from a decision node represent a course of action / strategy which can be chosen at a decision point. Branches leading away from a chance node represent a state of nature of chance event.
Decision Trees Structure of Decision Trees Since decision tree decision making under risk, the assumed probabilities of the state of nature are written alongside of respective chance branch.
Decision Trees Structure of Decision Trees Any branch that makes the end of the decision tree is called terminal branch. It can be either course of action or state of nature. These are mutually exclusive points so that exactly one course of action will be chosen. Decision tree can be deterministic or probabilistic. It can further can be divided into Single stage ( a decision under certainty) and a Multistage (a sequence of decisions).
Finding optimum sequence: Starting at the right hand side and roll backwards. At each node an expected return is calculated (i.e. position value) If the node is :- Chance Node: It is sum of the products of probabilities. EMV = (Probability)x(Payoff) Decision Node: the expected return is calculated for each of its branch and Highest Return is selected. The process continues till it reaches to initial node.
Decision Tree Illustration: Super Bazaar A company is planning to open a super bazaar in a city. The company has selected three different locations namely location A, B and C.
Decision Tree Illustration: Super Bazaar Location A is in the upper class dominated locality. Here, if the project is successful, it would give net profit of Rs. 50 Lakhs per annum, but if the project is not successful, the company would lose Rs. 65 Lakhs.
Decision Tree Illustration: Super Bazaar Location B is in middle class dominated locality. Here, if the project is successful, the company would get net profit of Rs 30 Lakhs per annum but if it fails it would have annual loss of Rs. 15 Lakhs.
Decision Tree Illustration: Super Bazaar The third location C is on the highway, little out of city. Here, if the project is successful, would yield net profit of Rs 15 Lakhs, and if it is unsuccessful, it would result in neither profit nor loss.
Decision Tree Illustration: Super Bazaar The success of a project at each location is dependent on the retail industry. If the retail industry does well, project at any location would be successful, and if the growth in the retail industry declines the project would not be so successful irrespective of location.
Decision Tree Illustration: Super Bazaar There is a 60% chance that the retail industry would grow. Given this scenario, in which location should the company open the super bazaar?
Decision Tree Solution: Super Bazaar EMV = 12 Lakh Since the EMV is highest for location B i.e. 12 Lakh. Hence company should open super bazar at Location B.
Decision Tree Solution: Super Bazaar For computing Expected profit with perfect information (EPPI) and the Expected value for Perfect information (EVPI). Location A 0 50 50 0.6 Successful Location B 1 30 0 50 0 30 Location C 0 15 15 EPPI = (0.6 X 50) + (0.4 x 0) = 30 Lakhs EVPI = EPPI EMV = 30 12 = 18 Lakhs 30 Location A 0-65 -65 0.4 Unsuccessful Location B 3-15 0 0 0-15 Location C 0 0 0
Case Illustration
Case Illustration Step 1 Define the problem. The company is considering expanding by manufacturing and marketing a new product backyard storage sheds. Step 2 List alternatives. Construct a large new plant. Construct a small new plant. Do not develop the new product line at all. Step 3 Identify possible outcomes. The market could be favorable or unfavorable.
Case Illustration Step 4 List the payoffs. Identify conditional values for the profits for large plant, small plant, and no development for the two possible market conditions. Step 5 Select the decision model. This depends on the environment and amount of risk and uncertainty. Step 6 Apply the model to the data. Solution and analysis are then used to aid in decision-making.
Case Illustration Decision Table with Conditional Values for Thompson Lumber STATE OF NATURE ALTERNATIVE FAVORABLE MARKET (Rs) UNFAVORABLE MARKET (Rs) Construct a large plant 200,000 180,000 Construct a small plant 100,000 20,000 Do nothing 0 0
Decision Making Under Uncertainty Decisions under uncertainty: 1. Maximax (optimistic) 2. Maximin (pessimistic) 3. Criterion of realism (Hurwicz) 4. Equally likely (Laplace) 5. Minimax regret
Maximax To maximizes the maximum payoff. Locate the maximum payoff for each alternative. Select the alternative with the maximum number. ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (Rs) MAXIMUM IN A ROW (Rs) Construct a large plant 200,000 180,000 200,000 Maximax Construct a small plant 100,000 20,000 100,000 Do nothing 0 0 0
Maximin To find the alternative that maximizes the minimum payoff. Locate the minimum payoff for each alternative. Select the alternative with the maximum number. ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (Rs) MINIMUM IN A ROW (Rs) Construct a large plant 200,000 180,000 180,000 Construct a small plant 100,000 20,000 20,000 Do nothing 0 0 0 Maximin
Criterion of Realism (Hurwicz) For the large plant alternative using = 0.8: (0.8)(200,000) + (1 0.8)( 180,000) = 124,000 For the small plant alternative using = 0.8: (0.8)(100,000) + (1 0.8)( 20,000) = 76,000 ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (r (Rs) CRITERION OF REALISM ( = 0.8) Rs Construct a large plant 200,000 180,000 124,000 Realism Construct a small plant 100,000 20,000 76,000 Do nothing 0 0 0
Equally Likely (Laplace) Considering all the payoffs for each alternative Find the average payoff for each alternative. Select the alternative with the highest average. ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (Rs) ROW AVERAGE (Rs) Construct a large plant 200,000 180,000 10,000 Construct a small plant 100,000 20,000 40,000 Equally likely Do nothing 0 0 0
Minimax Regret Determining Opportunity Losses for the company STATE OF NATURE FAVORABLE MARKET (Rs) UNFAVORABLE MARKET (Rs) 200,000 200,000 0 ( 180,000) 200,000 100,000 0 ( 20,000) 200,000 0 0 0
Minimax Regret Opportunity Loss Table for The company STATE OF NATURE ALTERNATIVE FAVORABLE MARKET (Rs) UNFAVORABLE MARKET (Rs) Construct a large plant 0 180,000 Construct a small plant 100,000 20,000 Do nothing 200,000 0
Minimax Regret The company s Minimax Decision Using Opportunity Loss ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (Rs) MAXIMUM IN A ROW (Rs) Construct a large plant 0 180,000 180,000 Construct a small plant 100,000 20,000 100,000 Minimax Do nothing 200,000 0 200,000
Decision Under Risk ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (Rs) EMV (Rs) Construct a large plant 200,000 180,000 10,000 Construct a small plant 100,000 20,000 40,000 Do nothing 0 0 0 Probabilities 0.50 0.50 Largest EMV
Expected Value of Perfect Information (EVPI) Suppose Scientific Marketing, Inc. offers analysis that will provide certainty about market conditions (favorable). Additional information will cost Rs 65,000. Should The company purchase the information?
Expected Value of Perfect Information (EVPI) Decision Table with Perfect Information ALTERNATIVE FAVORABLE MARKET (Rs) STATE OF NATURE UNFAVORABLE MARKET (Rs) EMV (Rs) Construct a large plant 200,000-180,000 10,000 Construct a small plant 100,000-20,000 40,000 Do nothing 0 0 0 With perfect information 200,000 0 100,000 Probabilities 0.5 0.5 EPPI
Expected Value of Perfect Information (EVPI) The maximum EMV without additional information is Rs 40,000. EVPI = EPPI Maximum EMV = Rs 100,000 Rs 40,000 = Rs 60,000 So the maximum Company should pay for the additional information is $60,000.
Expected Value of Perfect Information (EVPI) The maximum EMV without additional information is Rs 40,000. EVPI = EPPI Maximum EMV = Rs 100,000 Rs 40,000 = Rs 60,000 So the maximum The company should pay for the additional information is Rs 60,000. Therefore, The company should not pay Rs 65,000 for this information.
Decision Tree A State-of-Nature Node Favorable Market A Decision Node 1 Unfavorable Market Construct Small Plant 2 Favorable Market Unfavorable Market
Decision Tree Alternative with best EMV is selected EMV for Node 1 = Rs 10,000 1 = (0.5)(Rs 200,000) + (0.5)( Rs 180,000) Favorable Market (0.5) Payoffs Rs 200,000 Unfavorable Market (0.5) Rs 180,000 Construct Small Plant 2 Favorable Market Unfavorable Market (0.5) (0.5) Rs 100,000 Rs 20,000 EMV for Node 2 = Rs 40,000 = (0.5)(Rs 100,000) + (0.5)( Rs 20,000) Rs 0
The Company s Decision Tree First Decision Point Second Decision Point Payoffs Small Plant 2 3 Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.78) Unfavorable Market (0.22) Rs 190,000 Rs 190,000 Rs 90,000 Rs 30,000 No Plant Rs 10,000 1 Small Plant 4 5 Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.27) Unfavorable Market (0.73) Rs 190,000 Rs 190,000 Rs 90,000 Rs 30,000 No Plant Rs 10,000 Small Plant 6 7 Favorable Market (0.50) Unfavorable Market (0.50) Favorable Market (0.50) Unfavorable Market (0.50) Rs 200,000 Rs 180,000 Rs 100,000 Rs 20,000 No Plant Rs 0
The Company s Decision Tree 1. Given favorable survey results, EMV(node 2) EMV(node 3) = EMV(large plant positive survey) = (0.78)(Rs 190,000) + (0.22)( Rs 190,000) = Rs 106,400 = EMV(small plant positive survey) = (0.78)(Rs 90,000) + (0.22)( Rs 30,000) = Rs 63,600 EMV for no plant = Rs 10,000 2. Given negative survey results, EMV(node 4) = EMV(large plant negative survey) = (0.27)(Rs 190,000) + (0.73)( Rs 190,000) = Rs 87,400 EMV(node 5) = EMV(small plant negative survey) = (0.27)(Rs 90,000) + (0.73)( Rs 30,000) = Rs 2,400 EMV for no plant = Rs 10,000
The Company s Decision Tree 3. Compute the expected value of the market survey, EMV(node 1) = EMV(conduct survey) = (0.45)(Rs 106,400) + (0.55)(Rs 2,400) = Rs 47,880 + Rs 1,320 = Rs 49,200 4. If the market survey is not conducted, EMV(node 6) EMV(node 7) = EMV(large plant) = (0.50)(Rs 200,000) + (0.50)( Rs 180,000) = Rs 10,000 = EMV(small plant) = (0.50)(Rs 100,000) + (0.50)( Rs 20,000) = Rs 40,000 EMV for no plant = Rs 0 5. The best choice is to seek marketing information.
Rs 49,200 The Company s Decision Tree First Decision Point Second Decision Point Payoffs Rs 40,000 Rs 2,400 Rs 106,400 Small Plant Small Plant Rs 106,400 Rs 63,600 Rs 87,400 Rs 2,400 Rs 10,000 Rs 40,000 Small Plant Favorable Market (0.78) Unfavorable Market (0.22) Favorable Market (0.78) Unfavorable Market (0.22) No Plant Favorable Market (0.27) Unfavorable Market (0.73) Favorable Market (0.27) Unfavorable Market (0.73) No Plant Favorable Market (0.50) Unfavorable Market (0.50) Favorable Market (0.50) Unfavorable Market (0.50) No Plant Rs 190,000 Rs 190,000 Rs 90,000 Rs 30,000 Rs 10,000 Rs 190,000 Rs 190,000 Rs 90,000 Rs 30,000 Rs 10,000 Rs 200,000 Rs 180,000 Rs 100,000 Rs 20,000 $0
Expected Value of Sample Information Suppose The company wants to know the actual value of doing the survey. Expected value with sample information, assuming no cost to gather it EVSI = Expected value of best decision without sample information = (EV with sample information + cost) (EV without sample information) EVSI = (Rs 49,200 + Rs 10,000) Rs 40,000 = Rs 19,200
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