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**Topic 2. DECISION-MAKING TOOLS**

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**1. Models for decision making**

Real life experiments Iconic models Simulation models Quantitative models Algebraic - B/E analysis, cost/benefit analysis Statistical analysis – forecasting, quality control, decision theory Linear programming - a variety of POM applications Queuing theory Inventory models Network models - PERT and CPM

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Which model to use?

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**Advantages of using models**

less expensive and disruptive than real world experimentation permits “what if” type of questions and scenarios built for management problems and encourage management input force a consistent and systematic approach to problem solving require managers to be specific about constraints and goals help to reduce the time needed in decision making

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**Disadvantages of using models**

may be expensive and time consuming to develop and test often misused and feared because of their mathematical complexity tend to downplay the role and value of non-quantifiable information and qualitative reasoning assumptions sometime not realistic

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2. The Decision Process Define the problem and the factors that influence it Establish decision criteria and goals Formulate a model or relationship between goals and variables Identify and evaluate alternatives Select the best alternative Implement the decision Evaluate the results

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3. Decision Theory An example problem: Your T-shirt business makes a $10 profit for each shirt ordered and sold, but loses $5 for each unsold shirt.

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**Fundamental terms in decision theory**

alternative - course of action that must be chosen by the decision maker state of nature - an occurrence over which the decision maker has little or no control

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**Types of decisions Decision making under certainty:**

The decision maker knows the outcome for an alternative/decision with certainty (probability = 1)

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**Decision 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)

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**Decision Making Under Uncertainty**

Step 1. Create a decision table (payoff table) List alternatives along one axis and states of nature along the other axis Write or calculate outcomes (payoffs) in the body of the table

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**Decision Making Under Uncertainty**

States of Nature (Demand) Demand Decision 10 shirts 20 shirts 30 shirts Order 10 $100 Order 20 $50 $200 Order 30 $0 $150 $300

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**Decision Making Under Uncertainty**

Step 2. Make the decision based on a criterion maximax – choose the alternative that has the best outcome in the best case scenario, a very optimistic criterion Find the maximum payoff for each alternative Choose the alternative with the largest maximum

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**Decision Making Under Uncertainty**

States of Nature (Demand) Demand Decision 10 shirts 20 shirts 30 shirts Row Max Row Min Row Ave Order 10 $100 Order 20 $50 $200 Order 30 $0 $150 $300

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**Decision Making Under Uncertainty**

maximin - choose the alternative that has the best outcome in the worst case scenario, a very pessimistic criterion 1) Find the minimum payoff for each alternative 2) Choose the alternative with the largest minimum

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**Decision Making Under Uncertainty**

equally likely - choose the alternative with the highest average outcome 1) Find the average payoff for each alternative 2) Choose the alternative with the highest average

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**Decision Making Under Uncertainty**

minimax regret – choose the alternative with the least opportunity cost (the largest regret), another pessimistic criterion Calculate Regret by using the maximum of the state of Nature subtracts the payoff For each alternative, find the maximum regret Choose the alternative with the smallest maximum regret as the decision

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**Decision Making Under Uncertainty -- Minimax Regret**

Regret Table States of Nature (Demand) Demand Decision 10 shirts 20 shirts 30 shirts Order 10 $0 $100 $200 Order 20 $50 Order 30

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**3. 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)

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**Decision Making Under Risk**

Demand Decision 10 shirts Prob(.3) 20 shirts Prob(.4) 30 shirts EMV For Decision Order 10 $100 Order 20 $50 $200 $155 Order 30 $0 $150 $300

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Question Among the three decision making situations (decision making under certainty, decision making under uncertainty, decision making under risk), which one has the least available information?

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**Decision Making Under Risk**

Expected value of perfect information (EVPI) EVPI = EMV under certainty - highest EMV under risk EMV 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)

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**Decision Making Under Risk Calculate EVPI Example continuous**

Demand Decision 10 shirts Prob(.3) 20 shirts Prob(.4) 30 shirts Order 10 $100 Order 20 $50 $200 Order 30 $0 $150 $300

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**Decision Making Under Risk Calculate EVPI Example continuous**

EMV under certainty = EVPI =

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Decision Tree Decision tree - used to systematically represent problems that involve sequential decision making

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Decision Tree represents a decision node, after which are all alternatives the decision maker may choose O represents a state of nature node, after which are all outcomes (states of nature) may occur

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Decision Tree Steps to represent a sequential decision problem by decision tree Define the problem Structure (draw) the decision tree Assign probabilities to each state of nature Identify payoffs for each possible combination of alternatives and states of nature Compute the EMV for each state of nature node by working backward

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Decision Tree Example: Represent the T-shirt example by a decision tree

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Problem 2 Bakery 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.

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**Problem 2 continuous Alternatives Favorable Market Unfavorable Market**

Major Renovation $100,000 -$90,000 Minor Renovation $40,000 -$20,000 Do Nothing $0

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Problem 2 continuous The marketing department has estimated that the chance of having a favorable market is about 60%. 1. Represent the problem by a decision tree 2. Which alternative maximizes the expected return (EMV)?

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Problem 2 continuous Additional 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)?

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**Homework for Decision-Making Tools**

Problem 1 A 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).

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**Homework for Decision-Making Tools**

(Problem 1 continuous) Future Demand (states of nature) Alternative Low Average Large Row Max Row Min Row Ave Max Regret Expand $15,000 $35,000 $65,000 Subcontract $40,000 $45,000 Do nothing $25,000

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**Homework 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).

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**Homework for Decision-Making Tools**

Problem 2 For 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.

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**Homework 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 node 2. 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?

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An Introduction to Decision Theory

An Introduction to Decision Theory

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