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Chapter 9 - Decision Analysis - Part I

• Decision Analysis Examples • Problem Formulation• Decision Table • Decision Making under Uncertainty without Probabilities

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Decision Analysis Examples• Managers often must make decisions in environments that

are fraught with uncertainty.

• Examples

– A manufacturer introducing a new product into the marketplace

• What will be the reaction of potential customers?• How much should be produced?• Should the product be test-marketed?• How much advertising is needed?

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Decision Analysis Examples– A government contractor bidding on a new contract

• What will be the actual costs of the project?• Which other companies might be bidding?• What are their likely bids?

– A financial firm investing in securities• Which are the market sectors and individual securities

with the best prospects?• Where is the economy headed?• How about interest rates?• How should these factors affect the investment

decisions?

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Problem Formulation

• A decision problem is characterized by objective, decision alternatives, states of nature, and resulting payoffs.

• The decision alternatives are the different possible strategies that the decision maker can employ.

• The states of nature refer to future events, not under the control of the decision maker that may occur. States of nature should be defined so that they are mutually exclusive and collectively exhaustive.

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Decision Table

• A table showing all combinations of decision alternatives, states of nature, and all payoffs is a decision table.

• The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff.

• Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate measure.

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Example: Burger PrinceBurger Prince Restaurant is planning to open a new restaurant on Main Street. It has three different models under consideration, each with a different seating capacity.

Three decisions: d1: Model A: Small capacityd2: Model B: Medium capacity, andd3: Model C: Large capacity

Burger Prince estimates that the average number of customers per hour will be 80, 100, or 120.

Three states of nature:s1 = 80s2 = 100, and s3 = 120

Example: Burger Prince

The profit payoff table for the three models is as follows:

Question: Which model should Burger Prince choose in order to maximize the profit payoff?

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Decision Making Under Uncertainty (Without Probabilities)

• Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is unavailable are:

– the optimistic approach– the conservative approach– the minimax regret approach.

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Optimistic Approach

• The optimistic approach would be used by an optimistic decision maker. It focuses only on the best that can happen.

• The maximax criterion is the decision criterion for the eternal optimist. The decision with the largest possible payoff is chosen.

• Procedure:– Identify the maximum payoff from any state of nature for

each alternative.– Find the maximum of these maximum payoffs and choose

this alternative.

• If the payoff table is in terms of costs, the decision with the lowest cost (minimin) will be chosen.

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Example: Burger Prince

Optimistic Approach (Maximax)If Burger Prince is optimistic to the future demand, then the optimistic approach should be used to make the decision. Burger Prince should list the maximum profit payoff for each decision and then choose the decision with the maximum of these maximum profit payoffs.

Decision Maximum RecommendedAlternative Profit Payoff Decisiond1: Model A $15,000 d2: Model B $18,000 d3: Model C $21,000 d3: Model C

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Conservative Approach

• The conservative approach would be used by a conservative decision maker. It focuses only on the worst that can happen. A maximin approach is used.

• Procedure:– Identify the minimum payoff from any state of nature for

each alternative.– Find the maximum of these minimum payoffs and choose

this alternative.

• If the payoff is in terms of costs, the maximum costs will be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected. (Hence, the maximum possible cost is minimized – Minimax approach.)

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Example: Burger Prince

Conservative Approach (Maximin)If Burger Prince is conservative to the future demand, then the conservative approach should be used to make the decision. Burger Prince should list the minimum profit payoff for each decision and then choose the decision with the maximum of these minimum profit payoffs.

Decision Minimum RecommendedAlternative Profit payoff Decisiond1: Model A $10,000 d1: Model Ad2: Model B $8,000 d3: Model C $6,000

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Minimax Regret Approach

• The minimax regret criterion is the decision criterion for the decision maker to minimize the regret for not choosing the best decision.

• It focuses only on the regret level (opportunity cost).• The minimax regret approach requires the construction of a

regret table or an opportunity loss table. • This is done by calculating for each state of nature the

difference between each payoff and the best payoff for that state of nature.

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Minimax Regret Approach

• Procedure:– Identify the maximum regret from any state of nature for

each alternative.– Find the minimum of these maximum regrets and choose

this alternative.

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Example: Burger Prince

Minimax Regret ApproachIf Burger Prince wishes to minimize the regret (opportunity cost) in case the chosen decision is not the best, then the minimax regret approach should be used to make the decision.Burger Prince should construct a regret table by subtracting each profit payoff in a column from the largest profit payoff in that column. For each decision list the maximum regret. Choose the decision with the minimum of these values.

The resulting regret table is on next slide.

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Example: Burger Prince

Decision Maximum RecommendedAlternative s1 = 80 s2 = 100 s3 = 120 Regret Decisiond1: Model A $0 $3,000 $7,000 $7,000 d2: Model B $2,000 $0 $9,000 $9,000 d3: Model C $4,000 $2,000 $0 $4,000 d3: Model C

Average Number of Customers Per Hr

REGRET TABLEState of Nature

S1 S2 S3 Minima MaximaD1 100 250 180D2 70 190 250D3 85 170 200

Regret Table

S1 S2 S3 MaximaD1D2D3

Classroom Exercise 1: Numbers are cost values

Find the best decision for

1. Optimistic approach

2. Conservative approach

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Classroom Exercise 1: Solution

The best decision for

1. Optimistic approach: D2

2. Conservative approach: D3

3. Mini-max regret approach: D3 18 - Chap 09

S1 S2 S3 Minima MaximaD1 100 250 180 100 250D2 70 190 250 70 250D3 85 170 200 85 200

Regret TableS1 S2 S3 Maxima

D1 30 80 0 80D2 0 20 70 70D3 15 0 20 20

Classroom Exercise 2:Mr. Chung is the manager of Lingnan Grocery Store. He now needs to replenish his supply of strawberries. His regular supplier can provide as many cases as he wants. However, because these strawberries already are very ripe, he will need to sell them tomorrow and then discard any that remain unsold. Mr. Chung estimates that he will be able to sell 10, 11, 12, or 13 cases tomorrow. He can purchase the strawberries for $30 per case and sell them for $80 per case. If there is any unsatisfied demand, the penalty is $5 per case. Mr. Chung now needs to decide how many cases to stock today.•Develop a decision problem by identifying the objective, the decision alternative, the states of nature and the payoff table.•How many cases of strawberry should be stocked today if optimistic, conservative or minimax regret approach is used?

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Classroom Exercise 2: Solution

• Objective: to determine the optimal stock level to maximize the profit payoff.

• Decisions: – d1 stock 10 cases of strawberry– d2 stock 11 cases of strawberry– d3 stock 12 cases of strawberry and– d4 stock 13 cases of strawberry

• States of nature– s1 10 cases of strawberry will be sold– s2 11 cases of strawberry will be sold– s3 12 cases of strawberry will be sold and– s4 13 cases of strawberry will be sold

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Classroom Exercise 2: Solution

• Selling price per case of strawberry = $80• Unit cost = $30• Penalty of each case of unsatisfied demand = $5 per case• Profit payoff table

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s1 s2 s3 s410 11 12 13

Decision d1 10 $500 $495 $490 $485d2 11 $470 $550 $545 $540d3 12 $440 $520 $600 $595d4 13 $410 $490 $570 $650

State of nature

Classroom Exercise 2: Solution

Optimistic Approach (Maximax)

Conservative Approach (Maximin)

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s1 s2 s3 s410 11 12 13 Maxima Best

Decision d1 10 $500 $495 $490 $485 $500d2 11 $470 $550 $545 $540 $550d3 12 $440 $520 $600 $595 $600d4 13 $410 $490 $570 $650 $650 d4

State of nature

s1 s2 s3 s410 11 12 13 Minima Best

Decision d1 10 $500 $495 $490 $485 $485 d1d2 11 $470 $550 $545 $540 $470d3 12 $440 $520 $600 $595 $440d4 13 $410 $490 $570 $650 $410

State of nature

Classroom Exercise 2: Solution

Minimax Regret Approach

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s1 s2 s3 s410 11 12 13

Decision d1 10 $500 $495 $490 $485d2 11 $470 $550 $545 $540d3 12 $440 $520 $600 $595d4 13 $410 $490 $570 $650

Regret Tables1 s2 s3 s410 11 12 13 Maxima Best

Decision d1 10 $0 $55 $110 $165 $165d2 11 $30 $0 $55 $110 $110d3 12 $60 $30 $0 $55 $60 d3d4 13 $90 $60 $30 $0 $90

State of nature

State of nature