Lesson Slides MODULE A: DECISION-MAKING TOOLS 4 OCT 2018 Module A:Decision-Making Tools • Break-even analysis (Chapter 7) – Analysis to compare processes by finding the volume at which two pro cesses have equal total costs. • Preference matrix – Table that allows managers to rate alternatives based on several perfor mance criteria. • Decision theory – Approach when outcomes associated with alternatives are in doubt. • Decision Tree – Model to compare alternatives and their possible consequences. Decision Theory • • Decision theory is a general approach to decision making when the outcomes associated with alternatives are in doubt A manager makes choices using the following process: 1. List a reasonable number of feasible alternatives 2. List the events (states of nature) 3. Calculate the payoff table showing the payoff for each alternativ e in each event 4. Estimate the probability of occurrence for each event 5. Select the decision rule to evaluate the alternatives Decision making under uncertainty Decision making under uncertainty. The manager can list the possible events but cannot estimate probabilities. 1.Four decision rules a.Maximin – (“best of the best”) For those pessimists who tend to believe that the “worst case” event will certainly occur, this decision rule chooses the alternative that has the best result, given the worst event will occur. b.Maximax – (“best of the best”) For those optimists who tend to believe that the best possible event will certainly occur, this decision rule chooses the alternative that has the best result, given the best event will occur. c.Equally Likely – (“the best weighted payoff”) For realists who tend to believe that events tend to even out in the long run, this decision rule places equal weight, or assumes equal probability, for each of the possible events. d.Minimax Regret – (“best worst regret”) This decision rule looks to minimize the worst possible negative effect (regrets) associated with making a wrong decision (and ignoring the positive effects of a good decision). Decision Making Under Certainty • • The simplest solution is when the manager knows which e vent will occur Here the decision rule is to pick the alternative with the b est payoff for the known event IN CLASS EXAMPLES MODULE A DECISION MAKING TOOLS 4-oct-2018 Decisions Under Certainty IN CLASS EXAMPLE 1 A manager is deciding whether to hire vendor A or vendor B. The decision much de pends on the future demand. The demand may be small or large. Assume that pay offs for each alternative are known with certainty. What is the best choice if future demand will be low? Possible Future Demand Alternative Low High Vendor A 200 270 Vendor B 160 800 0 0 Do nothing Decision Making Under Uncertainty Can list the possible events but can not estimate the probabilities 1. Maximin: The best of the worst, a pessimistic approach 2. Maximax: The best of the best, an optimistic approach 3. Equally Likely: The alternative with the best weighted pay off assuming equal probabilities 4. Minimax Regret: Minimizing your regret (also pessimistic) Decisions Under Uncertainty IN CLASS EXAMPLE 2 Reconsider the payoff matrix in Example 1. What is the best alternative for each decision rule? SOLUTION a. Maximin. An alternative’s worst payoff is the lowest number in its row of the payoff matrix, because the payoffs are profits. The worst payoffs ($000) are: Alternative Worst Payoff Vendor A 200 Vendor B 160 Decisions Under Uncertainty b. Maximax. An alternative’s best payoff ($000) is the highest number in its row of the payoff matrix, or Alternative Best Payoff Vendor A 270 Vendor B 800 c. Equally Likely. With two events, we assign each a probability of 0.5. Thus, the weighted payoffs ($000) are Alternative Vendor A Vendor B Weighted Payoff Decisions Under Uncertainty d. Minimax Regret. If demand turns out to be low, the best alternative is Vendor A and its regret is Vendor B is hire when demand turns out to be low, the regret is Regret Alternative Low Demand High Demand Maximum Regret Vendor A 200 – 200 = 0 800 – 270 = 530 530 Vendor B 200 – 160 = 40 800 – 800 = 0 40 The column on the right shows the worst regret for each alternative. To minimize the maximum regret, pick a Vendor B. The biggest regret is associated with having only Vendor A and high demand. IN CLASS EXAMPLE 3 Cheng (a realist), Mala (a pessimist), and Wani (an optimist) are joint owners in a hotelier company. They must decide whether to build medium-sized hotel, homestay-based hotel or budget hotel in Kundasang. The government is about to issue a policy and recommendation on pioneer hoteliers that depends on geographical nature and certain treaties are obtained. The policy is expected to affect demand for the accommodations; however it is impossible at this time to assess the probability of these policy “events.” The following data are available: Payoffs (Profits) Alternative Hill-side Heavily hilly Non-Hilly Medium-size $840,000 $440,000 $190,000 Homestay $370,000 $220,000 $670,000 $25,000 $1,150,000 ($25,000) Budget Solutions ICE3 Payoffs (Profits) Alternative Hill-side Heavily hilly Non-Hilly Medium-size $840,000 840-840=0 $440,000 $190,000 670-190=480 Homestay $370,000 840-370=470 $220,000 $670,000 670-670=0 $25,000 $1,150,000 1150-1150=0 Budget ($25,000) 670-(-25)=695 Cheng (realist – Equally Likely) would choose Medium-size hotel. Mala (pessimist – Maximin) would choose Homestay-based hostel Wani (optimist – Maximax) would choose Budget hotel The Minimax Regret solution is Medium-size hotel (Smallest biggest regret $710,000) Decisions Under Risk • The manager can list the possible events and estimate their probabilities • The manager has less information than decision making under certainty, but more information than with decision making under uncertainty • The expected value rule is widely used • This rule is similar to the Equally Likely decision rule, except th at the events are no longer assumed to be equally likely Decisions Under Risk IN CLASS EXAMPLE 4 Reconsider the payoff matrix in Example 1 & Example 2. For the expected value decision rule, which is the best alternative if the probability of small demand is estimated to be 0.4 and the probability of large demand is estimated to be 0.6? SOLUTION Possible Future Demand The expected value for each alternative is as follows: Alternative Vendor A Vendor B Alternative Small (0.4) Large (0.6) Vendor A 200 270 Vendor B 160 800 Expected Value IN CLASS EXAMPLE 5 For Cheng (a realist), Mala (a pessimist), and Wani (an optimist), find the best decision using the expected value rule. The probabilities for the events are given below. What alternative has the best expected results? Payoffs (Profits) Alternative Medium-size Homestay Budget Heavily hilly Non-Hilly Medium-size $840,000 $440,000 $190,000 Homestay $370,000 $220,000 $670,000 $25,000 $1,150,000 ($25,000) Budget Alternative Hill-side Hill-side (0.50) Heavily hilly (0.30) Non-hilly (0.20) Expected Value Decision Trees • Are schematic models of available alternatives and possible consequences • Are useful with probabilistic events and sequential decisions Square nodes represent decisions Circular nodes represent events Events leaving a chance node are collectively exhaustive • Conditional payoffs for each possible alternative-event combination sh own at the end of each combination • Draw the decision tree from left to right • Calculate expected payoff to solve the decision tree from right to left Decision Trees E1 & Probability E2 & Probability E3 & Probability Payoff 1 Payoff 2 Payoff 3 Alternative 3 1 1st decision 2 Alternative 5 Possible 2nd decision E2 & Probability = Event node Alternative 4 E3 & Probability Payoff 1 Payoff 2 Payoff 3 Payoff 1 Payoff 2 = Decision node Ei = Event i P(Ei) = Probability of event i FIGURE A.2 – A Decision Tree Model Decision Tree: ICE 6 A firm is deciding between two alternatives: to introduce a new product or to keep the existing product. Introducing a new product has uncertain outcomes in dependence on the demand. If the demand is high, the resulting profit of the firm will be 140. The low demand will be result in the profit 80. The firm estimates the probabilities of a high and low demand 0.7 and 0.3, respectively. If the firm keeps the existing product, its profit will be 110. SOLUTION • For the chance node 2, we calculate the expected value of the profit (0.7*140 + 0.3*80 = 122) and write this value over the node 2. • At the decision node 1, we select the decision alternative with the higher expected profit. Because max (122;110) = 122, introducing the new product is profitable. We write the maximum expected profit over the node 1 and draw double lines through the branch representing the inferior (worse) decision alternative. DECISION TREE: ICE7 A company faces a decision with respect to a product (codenamed M997) developed by one of its research laboratories. It has to decide whether to proceed to test market M997 or whether to drop it completely. It is estimated that test marketing will cost £100K. Past experience indicates that only 30% of products are successful in test market. If m997 is successful at the test market stage then the company faces a further decision relating to the size of plant to set up to produce m997. A small plant will cost £150K to build and produce 2000 units a year whilst a large plant will cost £250K to build but produce 4000 units a year. The marketing department have estimated that there is a 40% chance that the competition will respond with a similar product and that the price per unit sold (in £) will be as follows (assuming all production sold): Large Plant Small Plant Respond to competition 20 35 Not respond to competition 50 65 Assuming that the life of the market for M997 is estimated to be 7 years and that the yearly plant running costs are £50K (both sizes of plant - to make the numbers easier!) should the company go ahead and test market M997? ICE8 A developer must decide how large a luxury sports complex to build – small, medium, or large. The Profitability of this complex depends upon the future level of demand for the complex • States of nature: the states of nature could be defined as low demand and high demand • Alternatives: could decide to build a small, medium, or large complex • Payoffs: the profit for each alternative under each Potential state of nature is going to be determined Payoff in Millions of Dollars Alternative Low (0.3) High (0.7) Small 8 8 Medium 5 15 -11 22 Large