Problem Solving And Decision Decision Analysis
21/10/2014Problem Solving and DecisionMaking 7 Steps of Problem SolvingSistem Pendukung KeputusanDecision AnalysisSesi 05-07Dosen Pembina: Danang Junaedi(First 5 steps are the process of decision making)– Define the problem.– Identify the set of alternative solutions.– Determine the criteria for evaluating alternatives.– Evaluate the alternatives.– Choose an alternative (make a ----------------------------– Implement the chosen alternative.– Evaluate the results.1Teknik Informatika - UTAMA2 The field of decision analysis provides frameworkfor making important decisions. Decision analysis allows us to select a decisionfrom a set of possible decision alternatives whenuncertainties regarding the future exist. The goal is to optimized the resulting payoff interms of a decision criterion. Maximizing expected profit is a common criterionwhen probabilities can be assessed. When risk should be factored into the decisionmaking process, Utility Theory provides amechanism for analyzing decisions in light of risks.Sistem Pendukung KeputusanTeknik Informatika - UTAMASistem Pendukung Keputusan Decision theory and decision analysis help people(including business people) make better decisions.– They identify the best decision to take.– They assume an ideal decision maker: Fully informed about possible decisions and their consequences. Able to compute with perfect accuracy. Fully rational. Decisions can be difficult in two different ways:– The need to use game theory to predict how other people willrespond to your decisions.– The consequence of decisions, good and bad, are stochastic. That is, consequences depend on decisions of nature.3Teknik Informatika - UTAMADecision Analysis DefinitionsDecision Analysis Definitions Actions – alternative choices for a courseof action Events –possible outcomes of chancehappenings Payoffs – a value associated with theresult of each event Decision criteria – rule for selecting anaction Decision analysis explicit, quantitative methodto make (or think about) decisions in the face ofuncertainty.Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung KeputusanIntroduction to Decision Analysis54Portray options and their consequencesQuantify uncertainty using probabilitiesQuantify the desirability of outcomes using utilitiesCalculate the expected utility of each option(alternative course of action)– Choose the option that on average leads tomost desirable outcomes––––Teknik Informatika - UTAMA61
21/10/2014Decision Analysis Definitions A set of alternative actions– Only one will be correct, but we don’t know inadvance A set of outcomes and a value for each– Each is a combination of an alternative action and astate of nature– Value can be monetary or otherwiseTeknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung Keputusan A set of possible states of nature7 – States of nature should be defined sothat they are mutually exclusive (one orthe other) and collectively exhaustive(one will happen). There will be either rain or sun, but notboth.Indications for Decision AnalysisDecision Making Criteria CertaintyUncertainty about outcomes of alternative courses ofaction.1.2.3.4.5.9 Ignorance– Decision Maker knows all possible states of nature,but does not know probability of occurrence Risk– Decision Maker knows all possible states of nature,and can assign probability of occurrence for eachstateTeknik Informatika - UTAMA10Problem FormulationCriteria for decision makingSistem Pendukung Keputusan Maximize expected monetary value Minimize expected monetary opportunity loss Maximize return to risk ratio– E monetary V/σ Maximize maximum monetary value (maximax) – bestbest case monetary value Maximize minimum monetary value (maximin) – bestworst case monetary value Minimize maximum opportunity loss (minimax) – bestworst case for opportunity lossTeknik Informatika - UTAMA8– Decision Maker knows with certainty what the stateof nature will be - only one possible state of natureDeveloping policies, treatment guidelines, etc.At the bedside (i.e. helping patients make decisions)Focus discussion and identify important research needsIn your life outside of medicineAs teaching tool to discourage dogmatism and to demonstraterigorously the need to involve patients in decisionsTeknik Informatika - UTAMASistem Pendukung Keputusan A decision problem is characterized bydecision alternatives, states of nature(decisions of nature), and resultingpayoffs.The decision alternatives are thedifferent possible actions or strategiesthe decision maker can employ.The states of nature refer to possiblefuture events (rain or sun) not under thecontrol of the decision maker.Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung Keputusan– We may chose whichever we please11 A decision problem is characterized by decisionalternatives, states of nature, and resulting payoffs. The decision alternatives are the different possiblestrategies the decision maker can employ. The states of nature refer to future events, not underthe control of the decision maker, which willultimately affect decision results. States of natureshould be defined so that they are mutually exclusiveand contain all possible future events that could affectthe results of all potential decisions.Teknik Informatika - UTAMA122
21/10/2014Decision Theory ModelsSistem Pendukung Keputusan Decision theory problems are generallyrepresented as one of the following:Influence Diagram– Influence Diagram– Payoff Table/Decision Table– Decision Tree– Game Theory14Teknik Informatika - UTAMA13Sistem Pendukung KeputusanInfluence Diagrams An influence diagram is a graphical deviceshowing the relationships among the decisions,the chance events, and the consequences. Squares or rectangles depict decision nodes. Circles or ovals depict chance nodes. Diamonds depict consequence nodes. Lines or arcs connecting the nodes show thedirection of influence.Pay-Off Table1615Payoff TablesPayoff Table Analysis The consequence resulting from a specificcombination of a decision alternative and a stateof nature is a payoff. A table showing payoffs for all combinations ofdecision alternatives and states of nature is apayoff table. Payoffs can be expressed in terms of profit, cost,time, distance or any other appropriate measure. Payoff TablesTeknik Informatika - UTAMA– Payoff Table analysis can be applied when Sistem Pendukung KeputusanSistem Pendukung KeputusanTeknik Informatika - UTAMA17 There is a finite set of discrete decision alternatives. The outcome of a decision is a function of a single futureevent.– In a Payoff Table The rows correspond to the possible decision alternatives. The columns correspond to the possible future events. Events (States of Nature) are mutually exclusive andcollectively exhaustive. The body of the table contains the payoffs.Teknik Informatika - UTAMA3
21/10/2014Decision Making ModelEvent iMarket A1Do not market A2SuccessFailure 45.00- 36- 3- 3Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung KeputusanPayoff Table19Teknik Informatika - UTAMASistem Pendukung KeputusanEx: Decision Making UnderUncertaintySistem Pendukung KeputusanDecision Making UnderUncertaintyTeknik Informatika - UTAMA21Teknik Informatika - UTAMAEx: SI KASEP INVESTMENTDECISION Si Kasep has inherited 1000. He has decided to invest the money for one year. A broker has suggested five potentialinvestments.–––––Gold.Company ACompany BCompany CCompany D Si Kasep has to decide how much to invest ineach investment.Teknik Informatika - UTAMA22SOLUTIONSistem Pendukung KeputusanSistem Pendukung Keputusan20 Construct a Payoff Table.Select a Decision Making Criterion.Apply the Criterion to the Payoff table.Identify the Optimal DecisionTeknik Informatika - UTAMA4
21/10/2014Construct a Payoff TableThe Payoff Table Construct a Payoff Table for Kasep this is the set of five investment opportunities.– Defined the states of nature. Kasep considers several stock market states (expressed bychanges in the DJA)State of NatureS.1: A large rise in the stock marketS.2: A small rise in the stock marketS.3: No change in the stock marketS.4: A small fall in stock marketS5: A large fall in the stock marketDJA CorrespondenceIncrease over 1000 pointsIncrease between 300 and 1000Change between -300 and 300Decrease between 300 and 800Decrease of more than 800Sistem Pendukung KeputusanSistem Pendukung Keputusan– Determine the set of possible decision alternatives.The Stock Option Alternative is dominatedby theBondAlternativeTeknik Informatika- UTAMATeknik Informatika - UTAMASistem Pendukung KeputusanThe Payoff TableDecision Making UnderUncertainty28Decision Making UnderUncertaintyThe Maximin Criterion The decision criteria are based on the decisionmaker’s attitude toward life. This criterion is based on the worst-casescenario. It fits both a pessimistic and a conservativedecision maker. These include an individual being pessimistic oroptimistic, conservative or aggressive. Criteria– Maximin Criterion - pessimistic or conservativeapproach.– Minimax Regret Criterion - pessimistic orconservative approach.– Maximax criterion - optimistic or aggressiveapproach.– Principle of Insufficient Reasoning.Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung KeputusanTeknik Informatika - UTAMA– A pessimistic decision maker believes that the worstpossible result will always occur.– A conservative decision maker wishes to ensure aguaranteed minimum possible payoff.Teknik Informatika - UTAMA5
The Maximin CriterionThe Minimax Regret Criterion To find an optimal decision This criterion fits both a pessimistic and a conservativedecision maker. The payoff table is based on “lost opportunity,” or“regret”. The decision maker incurs regret by failing to choose the“best” decision. To find an optimal decision– Record the minimum payoff across all states of naturefor each decision.– Identify the decision with the maximum “minimumpayoff”.Sistem Pendukung KeputusanSistem Pendukung Keputusan21/10/2014Teknik Informatika - UTAMA Determine the best payoff over all decisions. Calculate the regret for each decision alternative as the differencebetween its payoff value and this best payoff value.– For each decision find the maximum regret over all states ofnature.– Select the decision alternative that has the minimum of these“maximum regrets”.Teknik Informatika - UTAMAThe Minimax Regret CriterionSistem Pendukung KeputusanThe Minimax Regret CriterionSistem Pendukung Keputusan– For each state of nature.Teknik Informatika - UTAMATeknik Informatika - UTAMAThe Maximax CriterionThe Maximax Criterion– An optimistic decision maker believes that the best possibleoutcome will always take place regardless of the decision made.– An aggressive decision maker looks for the decision with thehighest payoff (when payoff is profit) To find an optimal decision.– Find the maximum payoff for each decision alternative.– Select the decision alternative that has the maximum of the“maximum” payoff.Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung Keputusan This criterion is based on the best possible scenario. It fits both an optimistic and an aggressive decisionmaker.Teknik Informatika - UTAMA6
The Principle of InsufficientReasonThe Principle of InsufficientReason This criterion might appeal to a decision makerwho is neither pessimistic nor optimistic. Sum of PayoffsSistem Pendukung KeputusanSistem Pendukung Keputusan21/10/2014 It assumes all the states of nature are equallylikely to occur. The procedure to find an optimal decision.– For each decision add all the payoffs.– Select the decision with the largest sum (for profits).Teknik Informatika - UTAMA37– Gold500– Company A 350– Company B 50– Company C 300 Based on this criterion the optimaldecision alternative is to invest in gold.38Teknik Informatika - UTAMASistem Pendukung KeputusanThe Principle of InsufficientReasonDecision Making Under Risk40Teknik Informatika - UTAMA39Sistem Pendukung KeputusanThe Expected Value CriterionSistem Pendukung KeputusanDecision Making Under RiskTeknik Informatika - UTAMA41 When to Use the Expected Value Approach– The Expected Value Criterion is useful in cases wherelong run planning is appropriate, and decisionsituations repeat themselves.– One problem with this criterion is that it does notconsider attitude toward possible losses.Teknik Informatika - UTAMA427
21/10/2014Sistem Pendukung KeputusanThe Expected Value CriterionDecision Making With PerfectInformation44Teknik Informatika - UTAMA43 The Gain in Expected Return obtained fromknowing with certainty the future state of natureis called:Expected Value of Perfect InformationTherefore, the EVPI is the expected regretcorresponding to the decision selectedusing the expected value criterion(EVPI) It is also the Smallest Expect Regret of anydecision alternative.Teknik Informatika - UTAMAExpected Value of PerfectInformationSistem Pendukung KeputusanSistem Pendukung KeputusanExpected Value of PerfectInformationTeknik Informatika - UTAMASistem Pendukung KeputusanExpected Value of PerfectInformationDecision Making With PerfectImperfect Information48Teknik Informatika - UTAMA8
21/10/2014Decision Making with ImperfectInformation (Bayesian Analysis )Ex: SI KASEP INVESTMENTDECISION (continued)Sistem Pendukung KeputusanSistem Pendukung KeputusanShould Kasep purchase the Forecast ?Teknik Informatika - UTAMA Kasep can purchase econometric forecast resultsfor 50. The forecast predicts “negative” or “positive”econometric growth. Statistics regarding the forecast.49Teknik Informatika - UTAMA Kasep needs to know the following probabilities Kasep should determine his optimaldecisions when the forecast is “positive”and “negative”. If his decisions change because of theforecast, he should compare the expectedpayoff with and without the forecast. If the expected gain resulting from thedecisions made with the forecast exceeds 50, he should purchase the forecast.Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung (Large rise The forecast predicted “Positive”)P(Small rise The forecast predicted “Positive”)P(No change The forecast predicted “Positive ”)P(Small fall The forecast predicted “Positive”)P(Large Fall The forecast predicted “Positive”)P(Large rise The forecast predicted “Negative ”)P(Small rise The forecast predicted “Negative”)P(No change The forecast predicted “Negative”)P(Small fall The forecast predicted “Negative”)P(Large Fall) The forecast predicted “Negative”) Bayes’ Theorem provides a procedure to calculate theseprobabilitiesTeknik Informatika - UTAMASistem Pendukung KeputusanBayes TheoremSistem Pendukung KeputusanBayes Theorem52Teknik Informatika - UTAMA53Teknik Informatika - UTAMA549
21/10/2014Sistem Pendukung KeputusanBayes TheoremSistem Pendukung KeputusanBayes TheoremTeknik Informatika - UTAMA5556Teknik Informatika - UTAMA58Teknik Informatika - UTAMA60Sistem Pendukung KeputusanEx:Sistem Pendukung KeputusanEx:Teknik Informatika - UTAMATeknik Informatika - UTAMA57Teknik Informatika - UTAMA59Sistem Pendukung KeputusanSistem Pendukung KeputusanEx:10
21/10/2014Expected Value of SampleInformationThe Reversed Expected Value With the forecast available, the Expected Value ofReturn is revised. Calculate Revised Expected Values for a givenforecast as follows.EV(Invest in .Gold A “Positive” forecast) Comp .286( -100250 ) .375( 200150 ) .071(-100100 ) .268( 200300 ) 0(-1500 ) 180 84Gold A “Negative” forecast) EV(Invest in Comp .250 ) .205( 100200 ) .341( 150200 ) .136( -100300 ) .227( -1500) .091( -100 120 65Sistem Pendukung KeputusanSistem Pendukung Keputusan The expected gain from making decisions basedon Sample Information.Teknik Informatika - UTAMA62Teknik Informatika - UTAMAEREV ExpectedWithout SamplingInformation 130in a– Therest ofValuethe revisedEV s arecalculated EVSI Expected Value of SamplingInformationsimilar manner.Expected Value of Sample InformationSistem Pendukung KeputusanSistem Pendukung Keputusan ERSI - EREV 193 - 130 63.So,Should Kasep purchase the Forecast ?Invest inExpectedStock whenthe withForecastis “Positive”ERSIReturnsampleInformation (0.56)(250) (0.44)(120) 193 is “Negative”Invest in Goldwhen the forecastTeknik Informatika - UTAMAYes, Kasep should purchase the Forecast.His expected return is greater than theForecast cost.( 63 50) Efficiency EVSI / EVPI 63 / 141 0.45Teknik Informatika - UTAMASistem Pendukung KeputusanDecision Tree66Teknik Informatika - UTAMA6511
21/10/2014Sistem Pendukung KeputusanDecision TreesSistem Pendukung KeputusanDecision TreesTeknik Informatika - UTAMA67Teknik Informatika - UTAMAMs. Brooks is a 50 year old woman with anincidental cerebral aneurysm. She presented withnew vertigo 3 weeks ago and her primary MDordered a head MRI. Her vertigo has subsequentlyresolved and has been attributed to labyrinthitis.Sistem Pendukung KeputusanTeknik Informatika - UTAMA68Motivating Case:Sistem Pendukung KeputusanDecision TreeHer MRI suggested a left posterior communicatingartery aneurysm, and a catheter angiogramconfirmed a 6 mm berry aneurysm.69Teknik Informatika - UTAMA70Alternative ways of dealing withuncertaintyCase Presentation (cont’d) Dogmatism. All aneurysms should be surgicallyPast medical history is remarkable only for 35pack-years of cigarette smoking.Exam is normal.Ms. Brooks: “I don’t want to die before my time.”clipped.Sistem Pendukung KeputusanSistem Pendukung Keputusan A decision tree is a chronologicalrepresentation of the decisionproblem. Each decision tree has two types ofnodes; round nodes correspond tothe states of nature while squarenodes correspond to the decisionalternatives. The branches leaving each roundnode represent the different states ofnature while the branches leavingeach square node represent thedifferent decision alternatives. At the end of each limb of a tree arethe payoffs attained from the seriesof branches making up that limb.Question is: Do we recommend surgical clippingof the aneurysm or no treatment? Policy. At UCSF we clip all aneurysms. Experience. I’veORreferred a number of aneurysmpatients for surgery and they have done well. Whim. Let’s clip this one.Decision AnalysisNihilism. It really doesn't matter.Defer to experts. Vascular neurosurgeons say clip.Defer to patients. Would you rather have surgery orlive with your aneurysm untreated?Teknik Informatika - UTAMA71Teknik Informatika - UTAMA7212
21/10/20141. FORMULATE AN EXPLICITQUESTION- Formulate explicit, answerable question.- May require modification as analysis progresses.- The simpler the question, without losing importantdetail, the easier and better the decision analysis.1. Formulate an explicit question2. Make a decision tree.(squares decision nodes, circles chance nodes)a) Alternative actions branches of the decision node.b) Possible outcomes of each branches of chance nodes.3. Estimate probabilities of outcomes at each chance node.4. Estimate utilities numerical preference for outcomes.5. Compute the expected utility of each possible action6. Perform sensitivity analysisTeknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung KeputusanOverview of DA Steps7374Decision Trees: Simple to Creating a decision tree structuring the problem Provide a reasonably complete depiction of the problem. Best is one decision node (on the left, at the beginning ofthe tree). Branches of each chance node -- exhaustive andmutually exclusive. Proceed incrementally. Begin simple.Sistem Pendukung KeputusanSistem Pendukung KeputusanWhich treatment strategy, surgical clipping or notreatment, is better for Ms. Brooks considering her primaryconcern about living a normal life span?Teknik Informatika - UTAMA2. MAKE A DECISION TREETeknik Informatika - UTAMAIn the aneurysm example, our interest is in determining what’s bestfor Ms. Brooks so we'll take her perspective. We will begin withthe following question:75Teknik Informatika - UTAMASistem Pendukung Keputusan to ComplexSistem Pendukung Keputusan to Less Simple 76Teknik Informatika - UTAMA77Teknik Informatika - UTAMA7813
21/10/20143. ESTIMATE PROBABILITIESFigure 1Sistem Pendukung KeputusanSistem Pendukung Keputusan Teknik Informatika - UTAMA79 From the most reliable results applicable tothe patient or scenario of interest.Standard hierarchies of data qualityDefinitive trials Meta-analysis of trials Systematic review Smaller trials Large cohortstudies Small cohort studies Case-controlstudies Case series Expert opinionTeknik Informatika - UTAMA3. Fill in the probabilities:No treatment node803. Fill in the probabilities Prob rupture exp life span x rupture/yrSistem Pendukung KeputusanSistem Pendukung Keputusan– Expected life span: From US mortality figures: 35 years– Probability of untreated aneurysm rupture.– Cohort study 0.05%/yr for 10 mm– Lifetime prob rupture 0.05%/y x 35 y 1.75% Case fatality of rupture Meta-analysis: 45%Teknik Informatika - UTAMA81Teknik Informatika - UTAMA3. Fill in the probabilities:Surgery node823. Fill in the probabilities– rupture.– No data: probably very small 0 (Opinion)Sistem Pendukung KeputusanSistem Pendukung Keputusan Probability of treated aneurysm Surgical mortality. Options: Meta-analysis of case series: 2.6% Clinical databases: 2.3% The numbers at UCSF: 2.3%Teknik Informatika - UTAMA83Teknik Informatika - UTAMA8414
21/10/20144. Fill in the utilities Valuation of an outcome (more restrictive use inthe next lecture). Best 1 Worst 0 In this case, she wants to avoid early death:Sistem Pendukung KeputusanSistem Pendukung Keputusan4. Estimate utilities– Normal survival 1– Early death 085Teknik Informatika - UTAMATeknik Informatika - UTAMA5. Compute expected utility ofeach branchCalled "folding back" the tree.Expected utility of action each possibleoutcome weighted by its probability.Simple arithmetic calculationsSistem Pendukung KeputusanSistem Pendukung Keputusan5. COMPUTE THE EXPECTEDUTILITY OF EACH BRANCH87Teknik Informatika - UTAMATeknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung Keputusan.865 vs .977886. Perform sensitivityanalysis5. Compute expected utility ofeach branchTeknik Informatika - UTAMA8689 How certain are we of our recommendation? Change the input parameters to see how theyaffect the final result.– What if her life expectancy were shorter?– What if the rupture rate of untreated aneurysms werehigher?– How good a neurosurgeon is required for a toss up?Teknik Informatika - UTAMA9015
21/10/2014Point at which the two lines cross treatment threshold.Sistem Pendukung KeputusanSistem Pendukung KeputusanFigure 4Base CaseTeknik Informatika - UTAMA91Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung KeputusanSTEP BACK AND REVIEW THEANALYSISTeknik Informatika - UTAMAAs each iteration is completed, step back Have we answered the question?Did we ask the right question?Are there other details that might be important?Consider adding complexity to improve accuracy.Teknik Informatika - UTAMAMs. Brooks94Improve the AnalysisSistem Pendukung KeputusanSistem Pendukung KeputusanWe recommend NO surgery. “Thanks But I meant I wanted to livethe most years possible. Dying at age 80isn’t as bad as dying tomorrow ”Teknik Informatika - UTAMA95Add layers of complexity toproduce a more realistic analysis.Teknik Informatika - UTAMA9616
21/10/2014Game TheorySistem Pendukung KeputusanGame Theory Game theory can be used to determineoptimal decision in face of other decisionmaking players. All the players are seeking to maximizetheir return. The payoff is based on the actions takenby all the decision making players.97Teknik Informatika - UTAMAClassification of GamesIGA SUPERMARKET Number of Players The town of Gold Beach is served by twosupermarkets: IGA and Sentry. Market share can be influenced by theiradvertising policies. The manager of each supermarket mustdecide weekly which area of operations todiscount and emphasize in the store’snewspaper flyer. Total return– Zero Sum - The amount won and amount lost by all competitorsare equal (Poker among friends)– Nonzero Sum -The amount won and the amount lost by allcompetitors are not equal (Poker In A Casino) Sequence of Moves– Sequential - Each player gets a play in a given sequence.– Simultaneous - All players play simultaneously.Sistem Pendukung KeputusanSistem Pendukung Keputusan– Two players - Chess– Multiplayer - More than two competitors (Poker)Teknik Informatika - UTAMATeknik Informatika - UTAMAData A gain in market share to IGA results inequivalent loss for Sentry, and vice versa (i.e. azero sum game)Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung Keputusan The weekly percentage gain in market share forIGA, as a function of advertising emphasis.IGA needs to determine an advertising emphasis thatwill maximize its expected change in market shareregardless of Sentry’s action.Teknik Informatika - UTAMA17
21/10/2014SOLUTION– Constraints IGA’s market share increase for any givenadvertising focus selected by Sentry, must be at leastV.– Decision variables X1 the probability IGA’s advertising focus is on meat. X 2 the probability IGA’s advertising focus is on produce. X 3 the probability IGA’s advertising focus is ongroceries.– Objective Function For IGA Maximize expected market change (in its own favor)regardless of Sentry’s advertising policy. Define the actual change in market share as V.– The ModelSistem Pendukung KeputusanSistem Pendukung Keputusan IGA’s Perspective - A Linear ProgrammingmodelTeknik Informatika - UTAMATeknik Informatika - UTAMASentry’s Perspective - A LinearProgramming model– The Model– Y1 the probability that Sentry’s– Y2 the probability that Sentry’sproduce.– Y3 the probability that Sentry’sgroceries.– Y4 the probability that Sentry’sadvertising focus is on meat.advertising focus is onadvertising focus is onadvertising focus is on bakery. Objective function– Minimize changes in market share in favor of IGA ConstraintsSistem Pendukung KeputusanSistem Pendukung Keputusan Decision variables– Sentry’s market share decrease for any given advertising focusselected by IGA, must not exceed V.Teknik Informatika - UTAMATeknik Informatika - UTAMAOptimal SolutionReferensi For IGA1. For Sentry– Y1 0.6; Y2 0.2; Y3 0.2; Y4 0 For both players V 0 (a fair game).Teknik Informatika - UTAMASistem Pendukung KeputusanSistem Pendukung Keputusan– X1 0.3889; X2 0.5; X3 0.1112.3.4.5.Dr. Mourad YKHLEF,2009,Decision Support System,King Saud UniversityJames G. Kahn, MD, MPH,2010, Decision Analysis,UCSF Department of Epidemiology and BiostatisticsRoberta Russell & Bernard W. Taylor, III,2006,Decision Analysis, Operations Management - 5thEditionm John Wiley & SonDr. C. Lightner,2010,Decision Theory, FayettevilleState UniversityZvi Goldstein,2010,Chapter 8-Decision Analysis,-Teknik Informatika - UTAMA10818
Oct 18, 2014 · A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs. The decision alternatives are the different possible strategies the decision maker can employ. The states of nature refer to future events, not under the control of the decision maker, which
3.3 Problem solving strategies 26 3.4 Theory-informed field problem solving 28 3.5 The application domain of design-oriented and theory-informed problem solving 30 3.6 The nature of field problem solving projects 31 3.7 The basic set-up of a field problem solving project 37 3.8 Characteristics o
can use problem solving to teach the skills of mathematics, and how prob-lem solving should be presented to their students. They must understand that problem solving can be thought of in three different ways: 1. Problem solving is a subject for study in and of itself. 2. Problem solving is
Combating Problem Solving that Avoids Physics 27 How Context-rich Problems Help Students Engage in Real Problem Solving 28 The Relationship Between Students' Problem Solving Difficulties and the Design of Context-Rich Problems 31 . are solving problems. Part 4. Personalizing a Problem solving Framework and Problems.
The Problem Solving Inventory (PSI) [8] is a 35-item instrument (3 filler items) that measures the individual's perceptions regarding one's problem-solving abilities and problem-solving style in the everyday life. As such, it measures a person's appraisals of one's problem-solving abilities rather than the person's actual problem .
THREE PERSPECTIVES Problem solving as a goal: Learn about how to problem solve. Problem solving as a process: Extend and learn math concepts through solving selected problems. Problem solving as a tool for applications and modelling: Apply math to real-world or word problems, and use mathematics to model the situations in these problems.
What is Problem Solving? 2(1)(B) The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. What is Problem Solving?
Problem Solving Methods There is no perfect method for solving all problems. There is no problem-solving computer to which we could simply describe a given problem and wait for it to provide the solution. Problem solving is a creative act and cannot be completely explained. However, we can still use certain accepted procedures
understanding in problem-solving is needed to improve their problem-solving skill. The previous research showed that map meetings learning including summary lecture, problem-solving session, and the plenary could help the novice students in understanding the physics concept and develop the problem-solving skill [11]. Therefore, this
