Decision analysis: part 1 BSAD 30 Dave Novak Source: Anderson et al., 2013 Quantitative Methods for Business 12 th edition – some slides are directly from J. Loucks © 2013 Cengage Learning 1

Overview What is decision analysis? Problem Formulation Decision alternative States of nature Payoff Decision Making without Probabilities Optimistic (maximax) Conservative (maximin) Minimum regret (minimax) 2

Overview Decision Making with Probabilities Decision tress Calculating the expected value OF perfect information 3

Decision analysis Decision analysis can be used to develop an optimal strategy when a decision maker is faced with a number of alternatives and an uncertain or risk-filled pattern of future events Even when a careful decision analysis has been conducted, the uncertain future events make the final consequence uncertain 4

Decision analysis The risk (exposure to some type of negative outcome) associated with any decision alternative is a direct result of the uncertainty associated with the final consequence Good decision analysis includes risk analysis that provides probability information about the favorable as well as the unfavorable consequences that may occur 5

Problem formulation A decision problem is characterized by: 1. decision alternatives 2. states of nature 3. resulting payoffs 6

Problem formulation The decision alternatives are the different possible strategies the decision maker can employ The states of nature refer to future events, not under the control of the decision maker, which may occur States of nature should be defined so that they are mutually exclusive and collectively exhaustive 7

Development corp. example Pittsburgh Development Corporation (PDC) purchased land that will be the site of a new luxury condominium complex. PDC commissioned preliminary architectural drawings for three different project alternatives: 1) 30 condos, 2) 60 condos, and 3) 90 condos The financial success of the project depends upon the size of the condominium complex and the uncertainty concerning the demand for the condominiums The PDC decision problem is to select the project alternative that will lead to the largest profit given the uncertainty concerning the demand for the condominiums 8

Influence diagram An influence diagram is a graphical device showing the relationships among the decisions, the chance events, and the consequences Squares or rectangles depict decision nodes Circles or ovals depict chance nodes Diamonds depict consequence nodes Lines connecting the nodes show the direction of influence 9

Influence diagram ComplexSizeComplexSize ProfitProfit Demand for the Condominiums Condominiums Decision Chance Consequence 10

Payoff table The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate quantifiable measure 11

Development corp. example Consider the following problem with: 3 decision alternatives and 2 states of nature with the following payoff table representing profits (in millions): PAYOFF TABLE States of Nature Strong Demand Weak Demand Decision Alternative s 1 s 2 Small complex, d Medium complex, d Large complex, d

Decision making without probabilities Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are: 1. The optimistic approach 2. The conservative approach 3. The minimax regret approach 13

Optimistic approach The decision with the largest possible payoff is chosen If the payoff table was in terms of costs, the decision with the lowest cost would be chosen If the payoff table was in terms of profit, the decision with the greatest profit would be chosen 14

Optimistic approach Also referred to as maximax approach Choose the decision that has the largest profit value in the entire payoff table (largest profit of strong demand scenarios) Maximum Decision Payoff d 1 8 d 2 14 d 3 20 Maximum Decision Payoff d 1 8 d 2 14 d 3 20 Maximax payoff Maximax payoff Maximax decision Maximax decision 15

Conservative approach For each decision the minimum payoff is listed and then the decision corresponding to the maximum of the minimum payoffs is selected If the payoff was in terms of costs, the maximum cost would be determined for each decision and then the decision corresponding to the smallest of the maximum costs is selected (the maximum possible cost is minimized 16

Conservative approach Also referred to as maximin approach Choose the decision with the maximum of the minimum payoffs (largest profit of the weak demand scenarios) Minimum Decision Payoff d 1 7 d 2 5 d 3 -9 Minimum Decision Payoff d 1 7 d 2 5 d 3 -9 Maximin payoff Maximin payoff Maximin decision Maximin decision 17

Minimum regret approach The minimax regret approach requires the construction of a regret table or an opportunity loss table Calculate the difference between each payoff and the largest payoff for each state of nature Then, using the regret table, the maximum regret for each possible decision is listed Select decision corresponding to the minimum of the maximum regrets 18

Minimum regret approach Also referred to as minimax approach Subtract each payoff in a column from the largest payoff in the column REGRET TABLE States of Nature Strong Demand Weak Demand Decision Alternative s 1 s 2 Small complex, d Medium complex, d Large complex, d

Minimum regret approach 20

Minimum regret approach Also referred to as minimax approach For each decision list the maximum regret and choose the decision with the minimum of these values Maximum Decision Regret d 1 12 d 2 6 d 3 16 Maximum Decision Regret d 1 12 d 2 6 d 3 16 Minimax regret Minimax regret Minimax decision Minimax decision 21

Incorporating probabilities Expected Value Approach If probabilistic information regarding the states of nature is available, we can use the expected value (EV) approach The expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature The decision yielding the best expected return is chosen 22

Expected value approach The expected value of a decision alternative is the sum of weighted payoffs for the decision alternative: where: N = the number of states of nature P(s j ) = the probability of state of nature s j V ij = the payoff corresponding to decision alternative d i and state of nature s j 23

Expected value approach Calculate the expected value for each decision using the decision tree on slide 27 d 1, d 2, and d 3 represent the decision alternatives of building a small, medium, and large condo complex s 1 and s 2 represent the states of nature for strong demand and weak demand 24

Decision trees A decision tree can help with the representation of the problem and the solution for the problem A decision tree is a chronological representation of the decision problem Each decision tree has two types of nodes: round nodes correspond to the states of nature square nodes correspond to the decision alternatives 25

Decision trees The branches leaving each round node represent the different states of nature The branches leaving each square node represent the different decision At the end of each limb of a tree are the payoffs attained from the series of branches making up that limb 26

Decision trees d1d1 d2d2 d3d3 s1s1 s1s1 s1s1 s2s2 s2s2 s2s2 Payoffs $8 mil $7 mil $14 mil $5 mil $20 mil -$9 mil

Decision trees 1 1 small d 1 medium d 2 large d

Expected value of perfect information Often information is available which can improve the probability estimates for the states of nature The expected value of perfect information (EVPI) is the increase in the expected profit that would result if one knew with certainty which state of nature would occur The EVPI provides an upper bound (or maximum) on the expected value of any sample or survey information 29

Expected value of perfect information EVPI calculation 1. Determine the optimal return corresponding to each state of nature 2. Compute the expected value of the optimal returns 3. Subtract the EV of the optimal decision from the amount determined in Step 2 30

Expected value of perfect information Expected value with perfect information (EVwPI) Expected value without perfect information (EVwoPI) 31

Expected value of perfect information Expected value OF perfect information (EVPI) 32

Summary What is decision analysis? Problem Formulation Decision alternative States of nature Payoff Decision Making without Probabilities Optimistic (maximax) Conservative (maximin) Minimum regret (minimax) 33

Summary Decision Making with Probabilities Decision tress Calculating the expected value OF perfect information 34