管理科学12-决策分析.ppt

Click to edit Master title style,Chapter 12-Decision Analysis,*,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Chapter 12,Decision Analysis,Introduction to Management Science,8th Edition,by,Bernard W.Taylor III,1,Chapter 12-Decision Analysis,Components of Decision Making,Decision Making without Probabilities,Decision Making with Probabilities,Decision Analysis with Additional Information,Utility,Chapter Topics,2,Chapter 12-Decision Analysis,Table 12.1,Payoff Table,A,state of nature,is an actual event that may occur in the future.,A,payoff table,is a means of organizing a decision situation,presenting the payoffs from different decisions given the various states of nature.,Decision Analysis,Components of Decision Making,3,Chapter 12-Decision Analysis,Decision situation:,Decision-Making Criteria:,maximax,maximin,minimax,minimax regret,Hurwicz,and equal likelihood,Table 12.2,Payoff Table for the Real Estate Investments,Decision Analysis,Decision Making without Probabilities,4,Chapter 12-Decision Analysis,Table 12.3,Payoff Table Illustrating a Maximax Decision,In the,maximax,criterion the decision maker selects the decision that will result in the,maximum of maximum,payoffs;an optimistic criterion.,Decision Making without Probabilities,Maximax Criterion,5,Chapter 12-Decision Analysis,Table 12.4,Payoff Table Illustrating a Maximin Decision,In the,maximin,criterion the decision maker selects the decision that will reflect the,maximum of the minimum,payoffs;a pessimistic criterion.,Decision Making without Probabilities,Maximin Criterion,6,Chapter 12-Decision Analysis,Table 12.6,Regret Table Illustrating the Minimax Regret Decision,Regret,is the difference between the payoff from the best decision and all other decision payoffs.,The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.,Decision Making without Probabilities,Minimax Regret Criterion,7,Chapter 12-Decision Analysis,The,Hurwicz,criterion is a compromise between the maximax and maximin criterion.,A coefficient of optimism,is a measure of the decision makers optimism.,The Hurwicz criterion multiplies the best payoff by and the worst payoff by 1-.,for each decision,and the best result is selected.,Decision,Values,Apartment building$50,000(.4)+30,000(.6)=38,000,Office building$100,000(.4)-40,000(.6)=16,000,Warehouse$30,000(.4)+10,000(.6)=18,000,Decision Making without Probabilities,Hurwicz Criterion,8,Chapter 12-Decision Analysis,The,equal likelihood,(or,Laplace,)criterion multiplies the decision payoff for each state of nature by an equal weight,thus assuming that the states of nature are equally likely to occur.,Decision,Values,Apartment building$50,000(.5)+30,000(.5)=40,000,Office building$100,000(.5)-40,000(.5)=30,000,Warehouse$30,000(.5)+10,000(.5)=20,000,Decision Making without Probabilities,Equal Likelihood Criterion,9,Chapter 12-Decision Analysis,A,dominant,decision is one that has a better payoff than another decision under each state of nature.,The appropriate criterion is dependent on the“risk”personality and philosophy of the decision maker.,Criterion,Decision(Purchase),MaximaxOffice building,MaximinApartment building,Minimax regretApartment building,HurwiczApartment building,Equal likelihoodApartment building,Decision Making without Probabilities,Summary of Criteria Results,10,Chapter 12-Decision Analysis,Exhibit 12.1,Decision Making without Probabilities,Solution with QM for Windows(1 of 3),11,Chapter 12-Decision Analysis,Exhibit 12.2,Decision Making without Probabilities,Solution with QM for Windows(2 of 3),12,Chapter 12-Decision Analysis,Exhibit 12.3,Decision Making without Probabilities,Solution with QM for Windows(3 of 3),13,Chapter 12-Decision Analysis,Expected value,is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.,EV(Apartment)=$50,000(.6)+30,000(.4)=42,000,EV(Office)=$100,000(.6)-40,000(.4)=44,000,EV(Warehouse)=$30,000(.6)+10,000(.4)=22,000,Table 12.7,Payoff table with Probabilities for States of Nature,Decision Making with Probabilities,Expected Value,14,Chapter 12-Decision Analysis,The,expected opportunity loss,is the expected value of the regret for each decision.,The expected value and expected opportunity loss criterion result in the same decision.,EOL(Apartment)=$50,000(.6)+0(.4)=30,000,EOL(Office)=$0(.6)+70,000(.4)=28,000,EOL(Warehouse)=$70,000(.6)+20,000(.4)=50,000,Table 12.8,Regret(Opportunity Loss)Table with Probabilities for States of Nature,Decision Making with Probabilities,Expected Opportunity Loss,15,Chapter 12-Decision Analysis,Exhibit 12.4,Expected Value Problems,Solution with QM for Windows,16,Chapter 12-Decision Analysis,Exhibit 12.5,Expected Value Problems,Solution with Excel and Excel QM(1 of 2),17,Chapter 12-Decision Analysis,Exhibit 12.6,Expected Value Problems,Solution with Excel and Excel QM(2 of 2),18,Chapter 12-Decision Analysis,The expected value of perfect information(EVPI)is the maximum amount a decision maker would pay for additional information.,EVPI equals the expected value given perfect information minus the expected value without perfect information.,EVPI equals the,expected opportunity loss,(EOL)for the best decision.,Decision Making with Probabilities,Expected Value of Perfect Information,19,Chapter 12-Decision Analysis,Table 12.9,Payoff Table with Decisions,Given Perfect Information,Decision Making with Probabilities,EVPI Example(1 of 2),20,Chapter 12-Decision Analysis,Decision with perfect information:,$100,000(.60)+30,000(.40)=$72,000,Decision without perfect information:,EV(office)=$100,000(.60)-40,000(.40)=$44,000,EVPI=$72,000-44,000=$28,000,EOL(office)=$0(.60)+70,000(.4)=$28,000,Decision Making with Probabilities,EVPI Example(2 of 2),21,Chapter 12-Decision Analysis,Exhibit 12.7,Decision Making with Probabilities,EVPI with QM for Windows,22,Chapter 12-Decision Analysis,A decision tree is a diagram consisting of decision nodes(represented as squares),probability nodes(circles),and decision alternatives(branches).,Table 12.10,Payoff Table for Real Estate Investment Example,Decision Making with Probabilities,Decision Trees(1 of 4),23,Chapter 12-Decision Analysis,Figure 12.1,Decision Tree for Real Estate Investment Example,Decision Making with Probabilities,Decision Trees(2 of 4),24,Chapter 12-Decision Analysis,The expected value is computed at each probability node:,EV(node 2)=.60($50,000)+.40(30,000)=$42,000,EV(node 3)=.60($100,000)+.40(-40,000)=$44,000,EV(node 4)=.60($30,000)+.40(10,000)=$22,000,Branches with the greatest expected value are selected.,Decision Making with Probabilities,Decision Trees(3 of 4),25,Chapter 12-Decision Analysis,Figure 12.2,Decision Tree with Expected Value at Probability Nodes,Decision Making with Probabilities,Decision Trees(4 of 4),26,Chapter 12-Decision Analysis,Exhibit 12.8,Decision Making with Probabilities,Decision Trees with QM for Windows,27,Chapter 12-Decision Analysis,Exhibit 12.9,Decision Making with Probabilities,Decision Trees with Excel and,TreePlan,(1 of 4),28,Chapter 12-Decision Analysis,Exhibit 12.10,Decision Making with Probabilities,Decision Trees with Excel and,TreePlan,(2 of 4),29,Chapter 12-Decision Analysis,Exhibit 12.11,Decision Making with Probabilities,Decision Trees with Excel and,TreePlan,(3 of 4),30,Chapter 12-Decision Analysis,Exhibit 12.12,Decision Making with Probabilities,Decision Trees with Excel and TreePlan(4 of 4),31,Chapter 12-Decision Analysis,Decision Making with Probabilities,Sequential Decision Trees(1 of 4),A,sequential decision tree,is used to illustrate a situation requiring a,series of decisions,.,Used where a payoff table,limited to a single decision,cannot be used.,Real estate investment example modified to encompass a ten-year period in which several decisions must be made:,32,Chapter 12-Decision Analysis,Figure 12.3,Sequential Decision Tree,Decision Making with Probabilities,Sequential Decision Trees(2 of 4),33,Chapter 12-Decision Analysis,Decision Making with Probabilities,Sequential Decision Trees(3 of 4),Decision is to purchase land;highest net expected value($1,160,000).,Payoff of the decision is$1,160,000.,34,Chapter 12-Decision Analysis,Figure 12.4,Sequential Decision Tree with Nodal Expected Values,Decision Making with Probabilities,Sequential Decision Trees(4 of 4),35,Chapter 12-Decision Analysis,Exhibit 12.13,Sequential Decision Tree Analysis,Solution with QM for Windows,36,Chapter 12-Decision Analysis,Exhibit 12.14,Sequential Decision Tree Analysis,Solution with Excel and TreePlan,37,Chapter 12-Decision Analysis,Bayesian analysis uses additional information to alter the marginal probability of the occurrence of an event.,In real estate investment example,using expected value criterion,best decision was to purchase office building with expected value of$444,000,and EVPI of$28,000.,Table 12.11,Payoff Table for the Real Estate Investment Example,Decision Analysis with Additional Information,Bayesian Analysis(1 of 3),38,Chapter 12-Decision Analysis,A,conditional probability,is the probability that an event will occur given that another event has already occurred.,Economic analyst provides additional information for real estate investment decision,forming conditional probabilities:,g=good economic conditions,p=poor economic conditions,P=positive economic report,N=negative economic report,P(P,g)=.80P(N,G)=.20,P(P,p)=.10P(N,p)=.90,Decision Analysis with Additional Information,Bayesian Analysis(2 of 3),39,Chapter 12-Decision Analysis,A,posteria probability,is the altered marginal probability of an event based on additional information.,Prior probabilities for good or poor economic conditions in real estate decision:,P(g)=.60;P(p)=.40,Posteria probabilities by,Bayes rule:,(g,P)=P(P,G)P(g)/P(P,g,)P(g)+P(P,p)P(p),=(.80)(.60)/(.80)(.60)+(.10)(.40)=.923,Posteria(revised)probabilities for decision:,P(g,N)=.250P(p,P)=.077P(p,N)=.750,Decision Analysis with Additional Information,Bayesian Analysis(3 of 3),40,Chapter 12-Decision Analysis,Decision Analysis with Additional Information,Decision Trees with Posterior Probabilities(1 of 4),Decision tree with posterior probabilities differ from earlier versions in that:,Two new branches at beginning of tree represent report outcomes.,Probabilities of each state of nature are posterior probabilities from Bayes rule.,41,Chapter 12-Decision Analysis,Figure 12.5,Decision Tree with Posterior Probabilities,Decision Analysis with Additional Information,Decision Trees with Posterior Probabilities(2 of 4),42,Chapter 12-Decision Analysis,Decision Analysis with Additional Information,Decision Trees with Posterior Probabilities(3 of 4),EV(apartment building)=$50,000(.923)+30,000(.077),=$48,460,EV(strategy)=$89,220(.52)+35,000(.48)=$63,194,43,Chapter 12-Decision Analysis,Figure 12.6,Decision Tree Analysis,Decision Analysis with Additional Information,Decision Trees with Posterior Probabilities(4 of 4),44,Chapter 12-Decision Analysis,Table 12.12,Computation of Posterior Probabilities,Decision Analysis with Additional Information,Computing Posterior Probabilities with Tables,45,Chapter 12-Decision Analysis,The,expected value of sample information,(EVSI)is the difference between the expected value with and without information:,For example problem,EVSI=$63,194-44,000=$19,194,The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information:,efficiency=EVSI/EVPI=$19,194/28,000=.68,Decision Analysis with Additional Information,Expected Value of Sample Information,46,Chapter 12-Decision Analysis,Table 12.13,Payoff Table for Auto Insurance Example,Decision Analysis with Additional Information,Utility(1 of 2),47,Chapter 12-Decision Analysis,Expected Cost(insurance)=.992($500)+.008(500)=$500,Expected Cost(no insurance)=.992($0)+.008(10,000)=$80,Decision should be,do not,purchase insurance,but people almost always,do,purchase insurance.,Utility,is a measure of personal satisfaction derived from money.,Utiles,are units of subjective measures of utility.,Risk averters,forgo a high expected value to avoid a low-probability disaster.,Risk takers,take a chance for a bonanza on a very low-probability event in lieu of a sure thing.,Decision Analysis with Additional Information,Utility(2 of 2),48,Chapter 12-Decision Analysis,Decision Analysis,Example Problem Solution(1 of 9),49,Chapter 12-Decision Analysis,Decision Analysis,Example Problem Solution(2 of 9),Determine the best decision without probabilities using the 5 criteria of the chapter.,Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions.Use expected value and expected opportunity loss criteria.,Compute expected value of perfect information.,Develop a decision tree with expected value at the nodes.,Given following,P(P,g)=.70,P(N,g)=.30,P(P,p)=20,P(N,p)=.80,determine posteria probabilities using Bayes rule.,Perform a decision tree analysis using the posterior probability obtained in part e.,50,Chapter 12-Decision Analysis,Step 1(part a):Determine decisions without probabilities.,Maximax Decision:Maintain status quo,Decisions,Maximum Payoffs,Expand$800,000,Status quo1,300,000(maximum),Sell 320,000,Maximin Decision:Expand,Decisions,Minimum Payoffs,Expand$500,000(maximum),Status quo-150,000,Sell 320,000,Decision Analysis,Example Problem Solution(3 of 9),51,Chapter 12-Decision Analysis,Minimax Regret Decision:Expand,Decisions,Maximum Regrets,Expand$500,000(minimum),Status quo 650,000,Sell 980,000,Hurwicz(,=.3)Decision:Expand,Expand$800,000(.3)+500,000(.7)=$590,000,Status quo$1,300,000(.3)-150,000(.7)=$285,000,Sell$320,000(.3)+320,000(.7)=$320,000,Decision Analysis,Example Problem Solution(4 of 9),52,Chapter 12-Decision Analysis,Equal Likelihood Decision:Expand,Expand$800,000(.5)+500,000(.5)=$650,000,Status quo,$1,300,000(.5)-150,000(.5)=$575,000,Sell$320,000(.5)+320,000(.5)=$320,000,Step 2(part b):Determine Decisions with EV and EOL.,Expected value decision:Maintain status quo,Expand$800,000(.7)+500,000(.3)=$710,000,Status quo$1,300,000(.7)-150,000(.3)=$865,000,Sell$320,000(.7)+320,000(.3)=$320,000,Decision Analysis,Example Problem Solution(5 of 9),53,Chapter 12-Decision Analysis,Expected opportunity loss decision:Maintain status quo,Expand$500,000(.7)+0(.3)=$350,000,Status quo 0(.7)+650,000(.3)=$195,000,Sell$980,000(.7)+180,000(.3)=$740,000,Step 3(part c):Compute EVPI.,EV given perfect information=1,300,000(.7)+500,000(.3)=$1,060,000,EV without perfect information=$1,300,000(.7)-150,000(.3)=$865,000,EVPI=$1.060,000-865,000=$195,000,Decision Analysis,Example Problem Solution(6 of 9),54,Chapter 12-Decision Analysis,Step 4(part d):Develop a decision tree.,Decision Analysis,Example Problem Solution(7 of 9),55,Chapter 12-Decision Analysis,Step 5(part e):Determine posterior probabilities.,P(g,P)=P(P,G)P(g)/P(P,g,)P(g)+P(P,p)P(p),=(.70)(.70)/(.70)(.70)+(.20)(.30)=.891,P(p,P)=.109,P(g,N)=P(N