Chapter 1 business mathematics for .pptx

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1. Introduction to Decision Analysis

2. What is Decision Analysis? Definition : Decision making is a cognitive process that results in the selection of a belief or course of action from several possible alternatives , based on available information and the values of the decision-maker ( Simon , 1955) It involves : Systematic approach to making decisions uner uncertainty. Involves various models and tools to evaluate different decision alternatives & potential outcomes Helping decision-makers chooese the best course of action Goal To optimize decison-making by assessing risks, benefits, and uncertainties, enabling rational and informed choices.

3. Importance of Decision Making Why It Matters? Decision making underpins strategic business operations, organizational behavior, and leadership effectiveness. Applications: Corporate Settings: Strategic planning, mergers, crisis management. Personal Contexts: Career development, ethical dilemmas.

4. The Six Step in Decision Theory Clearly define the problem at hand List the possible alternatives Identify all the possible outcomes List the pay-off or profit of each combination of alternatives and outcomes Select one of the mathematical decision theory models Apply the model and make your decision.

5. Key Concepts in Decision Analysis DECISON ALTERNATIVE: different possible actions that the decision-maker can choose from in a given situation STATE OF NATURE: Different conditions or events that could occur in the future, affecting the outcomes of the decision alternatives (e.g., high demand, low demand). PAYOFF TABLE: table that shows the outcome (payoff) of each decision alternative for each possible state of nature. It helps visualize potential gains or losses. EXPECTED MONETARY VALUE(EMV): A weighted average of payoffs, where the weights are the probabilities of the different states of nature.

6. Decision Alternatives: Examples Launching a new product Alt.1: Introduce the product to the local market first Alt.2: Launch the product globally at the same time to capture a larger market share. Alt 3: Delay the launch until market conditions improve Alt 4: Focus on digital marketing and e-commerce platforms for the product launch. Choosing a Marketing Strategy Alt1: Focus on digital marketing and e-commerce platforms for the product launch. Alt 2: Allocate resources to traditional advertising, like TV and radio ads, to reach an older demographic. Alt 3 : Implement a content marketing strategy through blogs and educational videos. Pricing Strategy Alt1: Offer premium pricing to position the product as a luxury item Alt2: Implement competitive pricing to match or undercut competitors. Alt3: Use a penetration pricing strategy to attract early customers with lower prices, then gradually increase. Alt 4: Offer bundle pricing to incentivize larger purchases. Expanding Business Operations Investment in Technology

7. State of Nature Market Demand High Demand:  Consumers are eager to buy a product, and sales are strong. Moderate Demand:  Consumers show average interest, leading to steady but unspectacular sales. Low Demand:  Consumer interest is minimal, leading to poor sales Pricing Price goes up Price remain unchanged Price goes down

8. Certainty The outcome of each decision alternatives in known with certainty Select alternative that provide the best known result Uncertainty The outcomes and probabilities are unkown Rely on subjective judgement and available information to make decisions Under Risk The outcome of decision alternatives are not certain, but the probabilities of different outcomes are known use probabilitic apoproaches of for decision-making Type of Decision-Making Environment

9. Decision-making Under Certainty The DM knows each alternatives the result or consequence certainty The choice should be chosen are the alternatives with the highest payoff Example Invest in fixed deposit of Bank A with interest of RM250 per annum Invest in fixed deposit of Bank B with interest of RM260 per annum Invest in fixed deposit of Bank C with interest of RM300 per annum ** the obvious decision to invest is Bank C as it yields the highest interest of RM300.

10. Decision-making Under Uncertainty DM cannot estimate the outcome’s probabilities. DM will make decisions using following criteria maximax (optimistic) Maximin (Pessimistic) Hurwicz’s criterion of realism Laplace’s equally likely criterion Minimax regret

11. Example Fauziah Company is going to introduce one of the three new products: Keropok , Satay, or Chips. As the market condition (favourable, stable, or unfavourable) effect the payoffs of th products, the company estimates the following payoff (RM): Product Market Condition (RM) Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 Satay 12,000 7,000 2,000 Chips 11,000 10,000 -6,000

12. Maximax (Optimistic Decision) Product Market Condition (RM) Maximum in a Row (RM) Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 18,000 Satay 12,000 7,000 2,000 12,000 Chips 11,000 10,000 -6,000 11,000 Since the best of max column is RM18,000, the decision is to produce Keropok .

13. Maximin (Pessimistic) Product Market Condition (RM) Minimum in a Row (RM) Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 -5,000 Satay 12,000 7,000 2,000 2,000 Chips 11,000 10,000 -6,000 -6,000 Since the best values in minimum row is RM2,000, the decision is to produce Satay. DM look for the worst possible payoff of each alternatives and select the highest value of the worst payoff of alternatives.

14. Criteria of Realism ( Hurwicz ) Requires a coefficient of realism,k which represent the degree of optimism K lies between 0 and 1. Weighted average = k (Max in row)+(1- k )(Min in row) Then select the highest weighted average. So, we will choose Keropok as the highest value among the three alternatives Product Market Condition (RM) Maximum in a Row Minimum in a Row (RM) Weighted Average k=0.7 Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 18 , 000 -5,000 11,100 Satay 12,000 7,000 2,000 12,000 2,000 9,000 Chips 11,000 10,000 -6,000 11,000 -6,000 5,900

15. Laplace’s Equally Likely Criterion The mean value is calculated for each alternatives, and choose the highest mean value. The Keropok alternatives will be chosen as it is the largest mean. Product Market Condition (RM) Row Mean Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 (18000+9000-5000)/3 = 7333.33 Satay 12,000 7,000 2,000 7000 Chips 11,000 10,000 -6,000 5000

16. Minimax Regret Regret = Opportunity loss Opportunity Loss = optimal payoff state nature – payoff for the alternative Satay alternatives is chosen Product Market Condition (RM) Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 Satay 12,000 7,000 2,000 Chips 11,000 10,000 -6,000 Product Market Condition (RM) Maximum in a Row (RM) Favourable Stable Unfavourable Keropok 18000-18000=0 10,000-9,000=1000 2,000-(-5,000)=7000 7,000 Satay 18000-12000=6000 10000-7000=3000 2000-2000=0 6,000 Chips 18000-11000=7000 10000-10000=0 2000-(-6000)=8000 8,000

17. Decision-making under risk The probabilities of information is given DM will make decision based on Expected Monetary Value (EMV) Expected Value of Perfect Information(EVPI) Expected Opportunity Loss (EOL)

18. Expected Monetary Value EMV = (Payoff)(Probability) Keropok is the higest (RM8900), the best alternative is to produce Keropok . Product Market Condition (RM) Expected Monetary Value(EMV) Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 18000(0.3)+9000(0.5)+(-5000)(0.2)=8900 Satay 12,000 7,000 2,000 7500 Chips 11,000 10,000 -6,000 7100 Not introducing Probability 0.3 0.5 0.2

19. Expected Value of Perfect Information (EVPI) EVPI is difference between expected value with perfect information (EVWPI) and the maximum EMV without perfect information. EVPI = EVWPI –max EMV EVWPI =. (Best payoff)(probability) Shafie Market Research Company has approach Fauziah Company so that he can help Fauziah make decision about which product to produce. This will prevent Fauziah from making an expensive mistake by choosing the wrong product to produce. Thus the maximum amount of money that Fauziah is willing to pay Shafie to carry out market research is called EVPI. EVWPI = 18000(0.3)+10000(0.5) +2000(0.3) = 10800 Then, EVPI= EVWPI – maximum EMV = 10800-8900 =RM1900 Hence, the most that Fauziah willing to pay for the information is RM1900.

20. Expected Opportunity Loss (EOL) The alternative method to maximise EMV is to minimise expected opportunity loss OL = Maximum payoff - payoff alternatives The minimum value of EOL is equal to EVPI. The best alternative is the minimum opportunity loss = Ker opok Product Market Condition (RM) Favourable Stable Unfavourable Keropok 18,000 9,000 -5,000 Satay 12,000 7,000 2,000 Chips 11,000 10,000 -6,000 Not introducing Probability 0.3 0.5 0.2 Product Market Condition (RM) Expected Opportunity Loss (EOL) Favourable Stable Unfavourable Keropok 18000-18000=0 10000-9,000=1000 2000-(-5000)=7000 0(0.3)+1000(0.5)+(7000)(0.2)=1900 Satay 6000 3,000 2,000 3300 Chips 7000 10,000 -6,000 3700 Do nothing 18000 10000 2000 10800 Probability 0.3 0.5 0.2

21. Try it Yourself Jo Company is considering several alternatives development projects. The financial success of these projects depends on three market conditions. The projects and their four-year financial returns (RM in millions) with the given market conditions are shown in the following table. Which investment should be chosen using each of the following decision criteria? Maximax =bungalow Criterion of realism, k=0.6 = bungalow Minimax regret criterion= bungalow Project Good Market Average Market Poor Market Max in row Min in row Weighted Average Shop 49 22 10 49 10 Bungalow 53 39 21 53 21 40.2 Condominium 36 20 14 36 14 27.2 Apartment 26 16 13 26 13 20.8

22. Project Good Market Average Market Poor Market Max in row Max in row Min in row Weighted Average Shop 53-49 39-22 21-10 32 49 10 Bungalow 53-53 39-39 21-21 53 21 40.2 Condominium 53-36 39-20 21-14 43 36 14 27.2 Apartment 53-26 39-16 21-13 58 26 13 20.8

23. Try Yourself Shima is considering opening a beauty salon in Puchong . She has identified a location near a shopping centre. Her option is to open a small shop, medium-sized shop, or no shop at all. The market for a beauty salon can be good, average, or bad. The probabilities, for these option are 0.3, 0.6, and 0.1 respectively.The profit are shown in the table below. Building no shop at all results in no loss or no gain. What is the best decision under this situation? Alternatives Good Market (RM) Average Market (RM) Poor Market (RM) Small Shop 2000 1000 -500 Medium-size shop 5000 3000 -2000 No shop

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