Chapter 9 - Decision Analysis - Part I Decision Analysis Examples Problem Formulation Decision Table Decision Making under Uncertainty without Probabilities

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?

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?

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.

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.

Example: Burger Prince Burger 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 capacity d2: Model B: Medium capacity, and d3: 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 = 80 s2 = 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?

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.

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.

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.

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.)

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.

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.

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.

Example: Burger Prince Minimax Regret Approach If 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.

Example: Burger Prince

Classroom Exercise 1: Numbers are cost values Find the best decision for Optimistic approach Conservative approach Mini-max regret approach 17 - Chap 09

Classroom Exercise 1: Solution The best decision for Optimistic approach: D2 Conservative approach: D3 Mini-max regret approach: D3 18 - Chap 09

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?

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

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

Classroom Exercise 2: Solution Optimistic Approach (Maximax) Conservative Approach (Maximin)

Classroom Exercise 2: Solution Minimax Regret Approach