© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-1 Decision Trees and Tables; LP Modeling Turban, Aronson, and Liang Decision Support Systems and Intelligent Systems, Seventh Edition

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-2 Decision-Making The act of choosing from a set of alternatives to obtain a goal

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-3 Decision-Making Certainty –Assume complete knowledge –All potential outcomes known –Easy to develop –Resolution determined easily –Can be very complex –example: the amount returned on an investment with a constant rate (CD)

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-4 Decision-Making Uncertainty –Several outcomes for each decision –Probability of occurrence of each outcome unknown –Insufficient information –Assess risk and willingness to take it –Pessimistic/optimistic approaches

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-5 DM under uncertainty for a maximization problem Optimistic – look at the best outcome for each alternative, then choose the “best of the best” Pessimistic – look at the worst outcome for each alternative, then choose the “best of the worst”

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-6 DM under uncertainty for a minimization problem Optimistic – look at the smallest payoff for each alternative, then choose the “lowest of the lows” Pessimistic – look at the largest payoff for each alternative, then choose the “lowest of the highs”

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-7 Decision Tables Multiple criteria decision analysis Features include: –Decision variables (alternatives) –Uncontrollable variables –Result variables Applies principles of certainty, uncertainty, and risk

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-8 DM under uncertainty example 1 – Driving to school To save on gasoline, Janet and Joe agree to form a carpool for traveling to and from school. After limiting the travel routes to two alternatives, the students cannot agree on the best way to get to school. The students do not know the condition of the freeway ahead of time. If Janet is an optimist, which route does she prefer? If Joe is a pessimist, which does he prefer?

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-9 Janet and Joe Decision table Decision Alternatives States of Nature s1= light freeway traffic s2 = heavy freeway traffic a1 = take freeway 10 minutes40 minutes a2 = take Walnut Ave. 20 minutes

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-10 Results of Janet and Joe Janet is optimisitic, therefore choose the best of the best –a 1 : 10 minutes***** –a 2 : 20 minutes Joe is pessimistic, therefore choose the best of the worst –a 1 : 40 minutes –a 2 : 20 minutes*****

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-11 Naddol Toy Company Plant Construction See handout for problem Set up the decision table Why can we eliminate option 4? Is the problem a maximization or minimization problem? What alternative would you choose is you were optimistic? Pessimistic?

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-12 NADDOL Decision Table Decision Alternatives States of Nature s 1 = low demand s 2 = medium demand s 3 = high demand a 1 = build small plant $250,000-$40,000$0 a 2 = build moderate plant -$50,000$350,000$60,000 a 3 = build large plant -$100,000$80,000$400,000 a 4 = build very large plant -$120,000$75,000$400,000

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-13 Decision-Making Probabilistic Decision-Making –Decision under risk –Probability of each of several possible outcomes occurring –Risk analysis Calculate value of each alternative Select best expected value (For each alternative, mult. prob. of each SoN by the expected outcome and add)

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-14 Naddol revisited under risk! Now look at the Naddol problem using the following probabilities of each state of nature: P(s 1 ) =.3 = P(low demand) P(s 2 ) =.6 = P(medium demand) P(s 3 ) =.1 = P(high demand) Find the expected value for each alternative and choose the best one

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-15 Decision Alternatives States of Nature s 1 = low demand;.3 s 2 = medium demand;.6 s 3 = high demand;.1 a 1 = build small plant $250,000 $75,000 -$40,000 -$24,000 $0 a 2 = build moderate plant -$50,000 -$15,000 $350,000 $210,000 $60,000 $6,000 a 3 = build large plant -$100,000 $30,000 $80,000 $48,000 $400,000 $40,000 a 4 = build very large plant -$120,000$75,000$400,000 Decision Making Under Risk

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-16 Decision Tree Graphical representation of relationships Multiple criteria approach Demonstrates complex relationships Cumbersome, if many alternatives

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-17

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-18 Modeling with Spreadsheets Flexible and easy to use End-user modeling tool Allows linear programming and regression analysis Features what-if analysis, data management, macros Seamless and transparent Incorporates both static and dynamic models

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-19

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-20 MSS Mathematical Models Link decision variables, uncontrollable variables, parameters, and result variables together –Decision variables describe alternative choices. –Uncontrollable variables are outside decision- maker’s control. –Fixed factors are parameters. –Intermediate outcomes produce intermediate result variables. –Result variables are dependent on chosen solution and uncontrollable variables.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-21 MSS Mathematical Models Nonquantitative models –Symbolic relationship –Qualitative relationship –Results based upon Decision selected Factors beyond control of decision maker Relationships amongst variables

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-22

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-23 Mathematical Programming Tools for solving managerial problems Decision-maker must allocate resources amongst competing activities Optimization of specific goals Linear programming –Consists of decision variables, objective function and coefficients, uncontrollable variables (constraints), capacities, input and output coefficients

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-24 Sungold Paint LP problem In preparing Sungold paint, it is required that the paint have a brilliance rating of at least 300 degrees and a hue level of at least 250 degrees. Brilliance and hue levels are determined by two ingredients, Alpha and Beta. Both Alpha and Beta contribute equally to the brilliance rating; one ounce (dry weight) of either produces one degree of brilliance in one drum of paint. However, the hue is controlled entirely by the amount of Alpha; one ounce of it producing 3 degrees of hue in one drum of paint. The cost of Alpha is 45 cents per ounce, and the cost of Beta is 12 cents per ounce. Assuming that the objective is to minimize the cost of the resources, then the problem is to find the quantity of Alpha and Beta to be included in the preparation of each drum of paint.

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-25 Set-up of Sungold Paint LP problem Decision variables –A = quantity of Alpha to be included, in ounces, per drum –B = quantity of Beta to be included, in ounces, per drum

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-26 Set-up of Sungold Paint LP problem, 2 Objective = to minimize cost of ingredients for one drum Uncontrollable variables = price per ounce of each ingredient –Cost of Alpha =.45 per ounce (cents) –Cost of Beta =.12 per ounce (cents)

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-27 Set-up of Sungold Paint LP problem, 3 S0, the objective function is displayed as:.45A +.12B with the goal of minimizing the cost!

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-28 Set-up of Sungold Paint LP problem, 4 Constraints – usually decided by the situation 1.To supply brilliance rating of at least 300 degrees per drum, each ounce of alpha or beta increases the brilliance by 1 degree, so… A + B >= 300

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-29 Set-up of Sungold Paint LP problem, 5 2.To provide hue level of at least 250 degrees, the effect of alpha alone on hue is… 3A + 0B >= 250

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-30 Set-up of Sungold Paint LP problem, 6 3.Non-negativity constraints (neither value can be 0 or less), so A >= 0 B >= 0

© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition, Turban, Aronson, and Liang 4-31 Rapido Sports – try to set up for HW The advertising agency promoting the new Rapido sports car wants to get the best possible exposure for the product within the available $200,000 budget. To do so, the agency must decide how much to spend on its two most effective media: evening television spots and large magazine ads. Each television spot costs $20,000 and a magazine ad involves a $5000 expenditure. Fractional spots and ads can be purchase from the media. By processing industry’s ratings through the company’s media evaluation information system, research staff have estimated that 400,000people will be reached with each television spot and 150,000 people will be reached with a magazine ad. Dawn Shaw, the agency director, knows from experience that it is important to use both media. In this way, the advertising will reach the broadest spectrum of potential Rapido customers. As a result, she decides to contract for at least 4, but no more than 12, television spots and a minimum of 6 magazine ads.