Topic 2. DECISION-MAKING TOOLS

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

Which model to use?

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

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

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

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.

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

Types of decisions

1. Decision making under certainty:

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

2. 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)

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

Decision Making Under Uncertainty

States of Nature (Demand)

Demand Decision

10 shirts 20 shirts 30 shirts

Order 10 $100 $100 $100

Order 20 $50 $200 $200

Order 30 $0 $150 $300

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

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 $100 $100

Order 20 $50 $200 $200

Order 30 $0 $150 $300

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

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

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

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 $0 $100

Order 30 $100 $50 $0

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)

Decision Making Under Risk

Demand Decision

10 shirtsProb(.3)

20 shirtsProb(.4)

30 shirtsProb(.3)

EMV ForDecision

Order 10 $100 $100 $100 $100

Order 20 $50 $200 $200 $155

Order 30 $0 $150 $300 $150

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?

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)

Decision Making Under RiskCalculate EVPI Example

continuousDemand Decision

10 shirtsProb(.3)

20 shirtsProb(.4)

30 shirtsProb(.3)

Order 10 $100 $100 $100

Order 20 $50 $200 $200

Order 30 $0 $150 $300

Decision Making Under RiskCalculate EVPI Example

continuous

EMV under certainty =

EVPI =

Decision Tree

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

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

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

Decision Tree

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

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.

Problem 2 continuous

Alternatives Favorable Market

Unfavorable Market

Major Renovation $100,000 -$90,000

Minor Renovation $40,000 -$20,000

Do Nothing $0 $0

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)?

Problem 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)?

Homework 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).

Homework for Decision-Making Tools

(Problem 1 continuous)

Future Demand (states of nature)  

Alternative Low Average Large Row Max

Row Min

Row Ave

MaxRegret

Expand $15,000 $35,000 $65,000

Subcontract $35,000 $40,000 $45,000

Do nothing $45,000 $35,000 $25,000

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).

Homework 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.

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 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?