IOE 202: lecture 14 outline

Transcription

1 IOE 202: lecture 14 outline Announcements Last time... Value of information (perfect and imperfect) in decision analysis Course wrap-up: topics covered and where to go from here IOE 202: Operations Modeling, Fall 2009 Page 1 Last time: Making decisions under uncertainty Sequencing of the decisions and outcomes of uncertain events Decision trees: Lay out the model visually Display sequences of decisions and outcomes Parse a complex decision into its constituents, show how to piece together an overall strategy Using Bayes Decision rule (maximize expected payoff, based on best available estimates of likelihoods, or probabilities, of all possible outcomes of uncertain events) Value of obtaining additional information: holding/canceling an outdoor event with or without a weather forecast With an imperfect weather forecast, expected return of the optimal strategy $6,200 Without a weather forecast, expected return of the best available strategy is $5,550 Value of the forecast is $650. IOE 202: Operations Modeling, Fall 2009 Page 2

2 Weather information for scheduling an outdoor event in mid-june Part I of the problem: Historically, the likelihood of it raining on any given day in mid-june is 27%. Part II of the problem According to station records, the station s next-day forecast in mid-june is sunny 90% of the time When the weather forecast was sunny, the next day turned out to actually be sunny 80% of the time When the weather forecast was rain, it actually rained 90% of the time Are these probabilities and frequencies consistent with each other? Two ways of measuring reliability of the forecast: How frequently are the station s forecasts of sunny days/rainy days correct? How frequently is a sunny day/rainy day correctly forecast? IOE 202: Operations Modeling, Fall 2009 Page 3 Forecast reliability What fraction of June days are sunny? What fraction of sunny days are correctly forecast? What fraction of sunny days are forecast as rainy? What fraction of June days are rainy? What fraction of rainy days are correctly forecast? What fraction of rainy days are forecast as sunny? IOE 202: Operations Modeling, Fall 2009 Page 4

3 Medical decision making and quality of testing 2 It is estimated that 1.1 million adults and adolescents people were living with diagnosed or undiagnosed HIV infection in the United States. 1 This translates into prevalence rate of per 100,000 population Should CDC recommend regular screenings of patients in health care settings? What would be the pros and cons? The standard blood test for HIV is fairly accurate: The probability that someone infected with HIV will test positive is 0.99 The probability that someone not infected with HIV will test negative is also 0.99 A randomly selected person tests positive. What is the probability that this person is infected with HIV? 1 This data comes from a 2006 CDC assessment. 2 See also the article Mammogram Math in the New York Times Magazine, 12/12/09 IOE 202: Operations Modeling, Fall 2009 Page 5 Diagram for HIV testing accuracy HIV negative HIV pos. # of persons in the population who would test positive: # of HIV positive persons who would test positive: # of HIV negative persons who would test positive: Fraction of positive tests coming from HIV negative persons: IOE 202: Operations Modeling, Fall 2009 Page 6

4 Value of perfect information in decision analysis A major movie studio has just completed production of an upcoming summer release, and is trying to decide whether to invest an extra $30 million into an aggressive advertising campaign, or to proceed with a normal campaign 1/4 of the movies made by this studio turn out to be hits, the rest flop at the box office If the movie is a hit, it will bring in $100M in tickets sales and merchandise without aggressive marketing and $110M with aggressive marketing The movie is a flop, it will only bring in $40M without aggressive marketing, but $80M with aggressive marketing What type of an advertising campaign should the studio undertake? (To answer this, build a small decision tree) What is the Expected Value of Perfect Information? I.e., what would it be worth to the studio to know ahead of time if the movie is a hit or a flop? (A different small decision tree) IOE 202: Operations Modeling, Fall 2009 Page 7 Best decision without additional information IOE 202: Operations Modeling, Fall 2009 Page 8

5 Best decision with perfect information IOE 202: Operations Modeling, Fall 2009 Page 9 Value of imperfect information, or experimentation The studio is considering hiring an industry consultant to conduct preview screenings to try to predict whether the movie is going to be a hit or a flop. If a movie is destined to be a hit, there is a 80% chance that the preview feedback will be positive If a movie is destined to be a flop, there is still a 40% change that the preview feedback will be positive (preview audiences tend to be overly enthusiastic...) What is the value to the studio of this preview? I.e., how much would the studio be willing to pay the consultant to conduct this preview? IOE 202: Operations Modeling, Fall 2009 Page 10

6 Decision tree w. previews IOE 202: Operations Modeling, Fall 2009 Page 11 Necessary calculations What fraction of all movies this studio makes get positive reviews? What fraction of movies that get positive reviews are hits? What fraction of movies that get positive reviews are flops? What fraction of all movies this studio makes get negative reviews? What fraction of movies that get negative reviews are hits? What fraction of movies that get negative reviews are flops? IOE 202: Operations Modeling, Fall 2009 Page 12

7 The goals of IOE 202 The goals set forth for IOE 202 are, in part, to let you appreciate role of operations in a firm, appreciate complexities of optimal decisions under constraints, appreciate complexities of design and analysis of operations under uncertainty, appreciate complexities of integrating various levels of operations, appreciate complexities of collection and analysis of data and its role in decision problems, appreciate role of uncertainty in operations decisions. IOE 202: Operations Modeling, Fall 2009 Page 13 IOE 202: the big picture Examples of a broad range of problems that can be approached by IOE methodology A variety of IOE methods to approach a broad range of problems Importance of expressing and formulating decisions, constraints, and performance measures in real-life problems Importance of considering the uncertainty involved in analyzing and modeling operations Some of modern software capabilities for formulating and solving problems IOE 202: Operations Modeling, Fall 2009 Page 14

8 Topics and further courses IOE 441 Production and inventory control IOE 310 Linear and integer programming models IOE 265 Probability and statistics (also, IOE 366), understanding uncertainty IOE 316 Stochastic models, including queueing models IOE 460 Decision analysis IOE 373 Software from engineering and managerial perspectives Not covered in 202: IOE 333 Ergonomics IOE 202: Operations Modeling, Fall 2009 Page 15