Decision making models


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Decision making models

  1. 1. ADDITIONAL NOTES BM014-3-3-DMKGDECISION MAKING MODELSIntroduction-Organizations and individuals are faced almost daily with the problems of having tomake decisions. The decision-making process is made difficult by the presence ofuncertainty concerning the surrounding environment.-For example, a company in the process of formulating an advertising strategy isuncertain not only of its competitors’ responses but also of the market demand for itsproduct. Yet, a decision must be made on product pricing, the choice of markets, theadvertising media, and the size of the advertising budget.-Prior to these decisions, the same company must decide on the scale of its productivefacilities. What machines should be purchased to manufacture the product? Should thecompany start out on a small production scale and later expand, or should it remainsmall? Should it start out with a large production capacity on the premise that the marketdemand will be great?-In this chapter we shall present the basic concepts of decision theory and illustratevarious methods that have been employed to solve management decision problems.-Note: Problem formulation or model development need to be completed before solvingand making decisions.Problem Formulation-The first step involved identifying: -Decision alternatives / choices -Uncertain/chance events /state of nature -consequences/objectives- e.g max profit/ min cost-Use technique: -Payoff tables -Shows consequences of various combination of decision alternatives & state of nature/uncertainties -consequences are known as payoffs (profit, costs, time)-Example: making investment decision: deciding to purchase a real estate…..Payoff tablesE.g .1 Mr Azlan deciding to purchase 1 of 3 types of real estate: d1 = apartment building d2 = office building d3 = warehouseTo choose the best 1, depends on the future economic condition(state of nature): 1
  2. 2. ADDITIONAL NOTES BM014-3-3-DMKG s1 = Good Economic Condition (GEC) s2 = Poor Economic Condition (PEC)Alternatives/Choices GEC(s1) PEC(s2)Apartment (d1) 15 7Office (d2) 22 -4Warehouse (d3) 12 9His objective is to maximize profit.Types of Decision Problems 1. Decision making under certainty In this class of problems, the decision maker (by some means) knows for certain which event will occur. In the context of the types of problems presented in this chapter, decision making under certainty is reduced to the trivial task of selecting the action yielding the highest payoff once we know what event to expect. For example, referring to example 1 above, if Mr.Azlan has the reliable information that the economic condition this year will be in a good condition, he would definitely purchase office building, because it gives the highest payoff. As you might guess, such decision problems rarely occur. 2. Decision making under uncertainty Decision making under uncertainty refers to problems in which the decision maker does not know for certain which event will occur. There are two types of such problems- probabilistic and non-probabilistic decision problems. 2.a.Nonprobabilistic decision problems It occurs when management does not have reasonable estimates of the likelihoods of the occurrence of various events. Thus, certain management may not have adequate information to assign probabilities to the four possible events. 2.b.Probabilistic decision problem The decision maker is able to assign probabilities to the various events that may occur. 2.a.Non-probabilistic decision rules -When decision maker has less ability in assessing the probabilities ( no information on the future events), -or desire a simple best-case and worse-case analysis -There are 4 approaches to use: 1) Maximax (optimistic) approach- for the risk taker person 2
  3. 3. ADDITIONAL NOTES BM014-3-3-DMKG -Choose the best possible pay off (profit). Step 1 : Identify and List the maximum payoff of each alternative (row-wise) Step 2: find & select the best possible payoff (e.g. largest profit)- (column-wise) Note: “minimin” if the payoff are costsalternatives GEC PEC Maximum p/offd1 15 7 15d2 22 -4 22d3 12 9 12 maximax So, choose d2 (office) which gives the highest payoff 2) Maximin(conservative) approach-for the risk averse person -Choose the best from the worst possible payoff (profit) Step 1: List the minimum payoffs of each alternative (row-wise) Step 2:Choose alternative that provide overall maximum payoff (column-wise) Note: “minimax” if the payoff are costs.alternatives GEC PEC Minimum p/offd1 15 7 7d2 22 -4 -4d3 12 9 9 MaximinSo, choose d3(warehouse) which gives the highest payoff. 3) Minimax Regret Approach/rule -Minimizing the regrets for not making the best decision Step 1: Subtract each entry in a column from the largest entry in that column. opportunity loss (regret) = difference between payoff of the best decision alternative and the payoff of alternative chose. Regret / Opportunity loss tablealternative GEC PECd1 15 22 - 15 = 7 7 9–7=2d2 22 22 - 22 = 0 -4 9 – (-4) = 13d3 12 22 – 12 = 10 9 9–9=0Choose the highest value 3
  4. 4. ADDITIONAL NOTES BM014-3-3-DMKG Regret/opportunity loss tablealternatives GEC PEC Minimaxd1 7 2 7d2 0 13 13d3 10 0 10 Minimum regret So, the best decision is to choose d1 ( apartment) 4) Criterion of Realism ( Hurwicz Criterion) -Balance, neither purely optimistic, nor pessimistic -Pay off are weighted by a coefficient of optimism : ( α ) ( max in row) + ( 1 – α) (min in row)alternatives GEC PEC Criterion of realism (α =0.75)d1 7 2 (0.75) ( 7) + ( 0.25) (2) = 5.75d2 0 13 (0.75) (13) + (0.25) ( 0) = 9.75d3 10 0 (0.75) (10) + (0.25) (0) = 7.5 Best alternative So, the best alternative will be purchasing office building (d2). 2.b.Probabilistic decision problems -When the decision maker is able to assign probabilities to the various events, it is then possible to employ a probabilistic decision rule called the Bayes criterion. -The Bayes criterion selects the decision alternative having the maximum expected payoff. -Some of the textbook referring this Bayes decision to Expected value (EV) approach which indicates the same interpretation. -However, EV approach might have slight different in terms of calculation technique. -If the decision maker is working with a loss table, the Bayes criterion selects the decision alternatives having the minimum expected loss. -The Bayes decision rule (maximizing expected payoffs ) is implemented as follows: Step1: For each decision alternative, compute the expected payoff. This is done by weighting each payoff in the row corresponding to the decision alternative by the probability of the corresponding event and then summing these terms. 4
  5. 5. ADDITIONAL NOTES BM014-3-3-DMKG Step2: Select the decision alternatives having the maximum expected payoff. This decision is called a Bayes Decision. Notationally, we shall let R denote payoff (reward) and L denote loss. Also, the expected payoff if we choose action a will be written ER (a). Example: Suppose you are given the payoff table shown in the table below. You are also told that the probabilities of occurance for the three events, s1, s2, s2 are 0.2, 0.7 and 0.1, respectively. So, P(s1) = 0.2, P (s2) = 0.7, P(s3) = 0.1, where the P denotes “probability.” s1 s2 s3a1 10 15 13a2 7 20 15a3 8 20 10Determine the Bayes decision rules using the maximum expected payoff rule.Solution:The expected payoff if we select a1 is computed as follows:ER(a1) = (0.20) (10) + (0.70) (15) + (0.10) (13) = 13.8ER(a2) = (0.20) (7) + (0.70) (20) + (0.10) (15) = 16.9ER(a3) = (0.20) ( 8) + (0.70) (20) + (0.10) (10) = 16.6The maximum payoff is a2. Thus the Bayes decision is a2.Expected Value (EV) ApproachBy means of EV principle, we find out the expected value of an alternative. This isrepeated for all the alternatives. The formula of this principle is the following:EV (alternatives d1) = (payoff of first state of nature) × (Probability of first state of nature) +(payoff of second state of nature) ×(probability of second state of nature) +…………………………………………………………………………... +(payoff of last state of nature) × (probability of last state of nature) 5
  6. 6. ADDITIONAL NOTES BM014-3-3-DMKGMathematically: nEV (d1) = ∑ V ij P (Sj) J=1Where n = total number of states of nature Sj = jth state of nature Vij = Payoff of d1 with respect to Sj P (Sj) = probability of SjThe best alternative is that one which will entail highest expected value. The working isshown in the following table: GEC PEC(1-p =0.4) EV (p=0.6)Apartment(d1) 15 7 15 × 0.6 + 7 × 0.4 = 11.8Office Building(d2) 22 -4 22 × 0.6 + (-4) × 0.4 = 11.6Warehouse(d3) 12 9 12 × 0.6 + 9 × 0.4 =10.8 Best alternativeRemark: The expected value of 11.8 (highest in the present case) does not mean that thechosen alternative, i.e, apartment building will result the profit $11.8miilion; rather it isone of 15 million and 7 million will result. The expected value means that if the samedecision situation arises a large number of times, then on the average payoff of $11.8million will result.Expected Opportunity Loss (EOL) ApproachFirstly we need to from opportunity loss table (the procedure is the same with theminimax regret approach above), Subtract each entry in a column from the largest entryin that column.That alternative is the best which gives the least EOL. GEC(p=0.6) PEC(1-p=0.4) EOLApartment(d1) 22-15 =7 9-7=2 7 × 0.6 + 2 × 0.4 = 5Office 22-22 =0 9-(-4) =13 0 × 0.6 + 13 × 0.4 = 5.2Building(d2)Warehouse(d3) 22-12 =10 9-9 = 0 10 × 0.6 + 0 × 0.4 = 6 Best alternativeNote: the best alternative is d1; Apartment, same as given by EV principle. This is notcoincidence. The best alternative given by both the methods will always be the same.Expected value of perfect Information (EVPI) 6
  7. 7. ADDITIONAL NOTES BM014-3-3-DMKG-Given a probabilistic decision problem, what would it be worth to the decision maker tohave access to an information source that would indicate for certain which of the eventswill occur?-Such an information source would offer perfect information to the decision maker.-The expected value of such information is referred to as the expected value of perfectinformation (EVPI).-In general, the formula to calculate for EVPI is:EVPI = (EVwPI – EVwoPI)Example:-Suppose Azlan purchase additional information regarding the occurrence of future statesof nature. Azlan hires an economic forecaster to do the analysis.-Assume that any findings given by the forecaster is completely perfect/correct.-Assume : study provide “perfect” information, thus company is certain which state ofnature is going to happen.alternatives GEC PECApartment (d1) 15 7Office (d2) 22 -4Warehouse (d3) 12 9 Choose the best-In GEC, select d2 & gain pay off of $22m-In PEC, select d3 & gain payoff of 9m What is the EV?If P (s1) = 0.6 There is a 60% probability that the perfect information will indicategood economic condition & d2 will provide $22m profit.If P(s2) = 0.4 There is a 40% probability that the perfect information will indicatepoor economic condition & d3 will provide $9m profit.EV with perfect info (EVwPI0 = 22 × 0.6 + 9 × 0.4 = $16.8EV without perfect info (EVwoPI) = $ 11.8 because we choose the highest value.alternatives GEC(p=0.6) PEC(p=0.4) Expected Value (EV)Apartment (d1) 15 7 (15)(0.6) + ( 7 ) (0.4) = 11.8Office (d2) 22 -4 (22) (0.6) + (-4) ( 0.4) = 11.6Warehouse (d3) 12 9 (12) (0.6) + (9) (0.4) =10.8 7
  8. 8. ADDITIONAL NOTES BM014-3-3-DMKGEVPI = EVwPI – EVwoPIEVPI = $16.8 - $ 11.8 = $5m Additional EV that can be obtained if perfect info available Maximum amount that the company should be willing to pay to purchase the info. 8