4Advantages of using models less expensive and disruptive than real world experimentationpermits “what if” type of questions and scenariosbuilt for management problems and encourage management inputforce a consistent and systematic approach to problem solvingrequire managers to be specific about constraints and goalshelp to reduce the time needed in decision making
5Disadvantages of using models may be expensive and time consuming to develop and testoften misused and feared because of their mathematical complexitytend to downplay the role and value of non-quantifiable information and qualitative reasoningassumptions sometime not realistic
62. The Decision ProcessDefine the problem and the factors that influence itEstablish decision criteria and goalsFormulate a model or relationship between goals and variablesIdentify and evaluate alternativesSelect the best alternativeImplement the decisionEvaluate the results
73. Decision TheoryAn example problem: Your T-shirt business makes a $10 profit for each shirt ordered and sold, but loses $5 for each unsold shirt.
8Fundamental terms in decision theory alternative - course of action that must be chosen by the decision makerstate of nature - an occurrence over which the decision maker has little or no control
9Types of decisions Decision making under certainty: The decision maker knows the outcome for an alternative/decision with certainty (probability = 1)
10Decision making under uncertainty The decision maker knows possible outcomes but not the probability associated with each outcome (know possible states of natures, but not probabilities)
11Decision Making Under Uncertainty Step 1. Create a decision table (payoff table)List alternatives along one axis and states of nature along the other axisWrite or calculate outcomes (payoffs) in the body of the table
12Decision Making Under Uncertainty States of Nature (Demand)Demand Decision 10 shirts20 shirts30 shirtsOrder 10$100Order 20$50$200Order 30$0$150$300
13Decision Making Under Uncertainty Step 2. Make the decision based on a criterionmaximax – choose the alternative that has the best outcome in the best case scenario, a very optimistic criterionFind the maximum payoff for each alternativeChoose the alternative with the largest maximum
14Decision Making Under Uncertainty States of Nature (Demand)Demand Decision 10 shirts20 shirts30 shirtsRow MaxRow MinRow AveOrder 10$100Order 20$50$200Order 30$0$150$300
15Decision Making Under Uncertainty maximin - choose the alternative that has the best outcome in the worst case scenario, a very pessimistic criterion1) Find the minimum payoff for each alternative2) Choose the alternative with the largest minimum
16Decision Making Under Uncertainty equally likely - choose the alternative with the highest average outcome1) Find the average payoff for each alternative2) Choose the alternative with the highest average
17Decision Making Under Uncertainty minimax regret – choose the alternative with the least opportunity cost (the largest regret), another pessimistic criterionCalculate Regret by using the maximum of the state of Nature subtracts the payoffFor each alternative, find the maximum regretChoose the alternative with the smallest maximum regret as the decision
18Decision Making Under Uncertainty -- Minimax Regret Regret TableStates of Nature (Demand)Demand Decision 10 shirts20 shirts30 shirtsOrder 10$0$100$200Order 20$50Order 30
193. Decision making under risk The decision maker knows not only the possible outcomes but also the probability of occurrence for each outcome (know the possible states of natures with the associated probabilities)--Choose the alternative with the largest MEAN payoff (EMV)
20Decision Making Under Risk Demand Decision 10 shirtsProb(.3)20 shirtsProb(.4)30 shirtsEMV ForDecisionOrder 10$100Order 20$50$200$155Order 30$0$150$300
21QuestionAmong the three decision making situations (decision making under certainty, decision making under uncertainty, decision making under risk), which one has the least available information?
22Decision Making Under Risk Expected value of perfect information (EVPI)EVPI = EMV under certainty - highest EMV under riskEMV under certainty =(best outcome for SON1) x (prob. of SON1)+ (best outcome for SON2) x (prob. of SON2)(best outcome for last SON) x (prob. of last SON)
23Decision Making Under Risk Calculate EVPI Example continuous Demand Decision 10 shirtsProb(.3)20 shirtsProb(.4)30 shirtsOrder 10$100Order 20$50$200Order 30$0$150$300
24Decision Making Under Risk Calculate EVPI Example continuous EMV under certainty =EVPI =
25Decision TreeDecision tree - used to systematically represent problems that involve sequential decision making
26Decision Tree represents a decision node, after which are all alternatives the decision maker may chooseO represents a state of nature node, after which are all outcomes (states of nature) may occur
27Decision TreeSteps to represent a sequential decision problem by decision treeDefine the problemStructure (draw) the decision treeAssign probabilities to each state of natureIdentify payoffs for each possible combination of alternatives and states of natureCompute the EMV for each state of nature node by working backward
28Decision TreeExample: Represent the T-shirt example by a decision tree
29Problem 2Bakery Products is considering the introduction of a new line of products. In order to produce the new line, the bakery is considering either a major or minor renovation of the current plant. The market for the new line of products could be either favorable or unfavorable. Bakery Products has the option of not developing the new product line at all. The following payoff table has been developed for each alternative under various market conditions.
31Problem 2 continuousThe marketing department has estimated that the chance of having a favorable market is about 60%.1. Represent the problem by a decision tree2. Which alternative maximizes the expected return (EMV)?
32Problem 2 continuousAdditional information: Before making the final decision, Bakery Products would like to consider a marketing research survey at a cost of $5,000. Past experience indicates that the survey is positive 80% of the time when the market is favorable and the survey in negative 60% of the time when the market is unfavorable.3. Redraw the decision tree to take the survey option into consideration.4. Should the company conduct the survey before making the final decision? How should the decision be made if it is based on the survey results (assuming now that the survey is done)?
33Homework for Decision-Making Tools Problem 1A small building contractor has recently experienced successive years in which demand for services exceeded the firm’s capacity. The contractor must now make a decision concerning future capacity. To address this capacity problem he could expand his business, subcontract the extra work, or do nothing. He has estimated his future profits under each of three states of nature he believes could occur (below).
34Homework for Decision-Making Tools (Problem 1 continuous)Future Demand (states of nature)AlternativeLowAverageLargeRow MaxRow MinRow AveMaxRegretExpand$15,000$35,000$65,000Subcontract$40,000$45,000Do nothing$25,000
35Homework for Decision-Making Tools (Problem 1 continuous)1. Which alternative should he choose if the decision criterion is:maximax?maximin?equally likely?minimax regret?2. For the problem above, consider the additional information. Suppose after a certain amount of discussion with others, the contractor thinks (subjectively) that the probabilities of low, average, and high demands are 0.5, 0.3, and 0.2, respectively.Determine the expected profit (EMV) for each decision alternative. Which alternative is the best?Compute the expected value of perfect information (EVPI).
36Homework for Decision-Making Tools Problem 2For the above problem, the subcontractor has enlisted the help from his old POM teacher to make his decision. His teacher offers to do some market research in the subcontractor’s market. Since the teacher has done this sort of things before, he tells the contractor that historically, the research is positive 90%, 50%, and 15% of the time when the market demand is high, average, and low, respectively. The POM teacher tells the contractor that he will do the market research for $1,500. So now the contractor has two decisions to make: 1) whether to hire his POM teacher to have the research done, and 2) the original capacity problem, i.e., whether to expand, subcontract, or do nothing.
37Homework for Decision-Making Tools (Problem 2 continuous)1. Draw a decision tree taking into account both decisions that need to be made. Make sure to include all probabilities for the states of nature, and the EMV’s for each node2. What should the contractor do? (write down the course of action and expected payoff)3. Assuming the decision is made to do the market research, has the contractor paid the POM teacher too much or too little? What should be the fair value of the market research by his POM teacher?