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Unformatted text preview: Space 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 Space 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.
Page 2 IOE 202: Operations Modeling, Fall 2009 Space 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%. 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 Part II of the problem
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?
Page 3 IOE 202: Operations Modeling, Fall 2009 Space Forecast reliability What What What What What What fraction fraction fraction fraction fraction fraction of of of of of of June days are sunny? sunny days are correctly forecast? sunny days are forecast as rainy? June days are rainy? rainy days are correctly forecast? rainy days are forecast as sunny?
Page 4 IOE 202: Operations Modeling, Fall 2009 Space Medical decision making and quality of testing2
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 447.8 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
1 2 A randomly selected person tests positive. What is the probability that this person is infected with HIV? This data comes from a 2006 CDC assessment. See also the article “Mammogram Math” in the New York Times’ Magazine, 12/12/09
IOE 202: Operations Modeling, Fall 2009 Page 5 Space 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:
Page 6 IOE 202: Operations Modeling, Fall 2009 Space 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)
Page 7 IOE 202: Operations Modeling, Fall 2009 Space Best decision without additional information IOE 202: Operations Modeling, Fall 2009 Page 8 Space Best decision with perfect information IOE 202: Operations Modeling, Fall 2009 Page 9 Space 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 Space Decision tree w. previews IOE 202: Operations Modeling, Fall 2009 Page 11 Space Necessary calculations What What What What What What fraction fraction fraction fraction fraction fraction of all movies this studio makes get positive reviews? of movies that get positive reviews are hits? of movies that get positive reviews are ﬂops? of all movies this studio makes get negative reviews? of movies that get negative reviews are hits? of movies that get negative reviews are ﬂops?
Page 12 IOE 202: Operations Modeling, Fall 2009 Space 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 Space 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 Space 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 ...
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This note was uploaded on 03/17/2010 for the course IOE 202 taught by Professor Marinaepelman during the Fall '09 term at University of Michigan-Dearborn.
- Fall '09