Space IOE 202: lecture 14 outline trianglerightsld Announcements trianglerightsld Last time... trianglerightsld Value of info rmation (p erfect and imp erfect) in decision analysis trianglerightsld Course wrap-up: topics covered and where to go from here trianglerightsld Project Q&A IOE 202: Op erations Mo del ing, Fall 2008 Page 1 Space Last time: trianglerightsld Making decisions under uncertaint y trianglerightsld Sequencing of the decisions and outcomes of uncertain events trianglerightsld Decision trees: trianglerightsld Lay out the mo del visually trianglerightsld Displa y sequences of decisions and outcomes trianglerightsld Parse a complex de cision into its constituents, sho w how to piece togethe r an overall strategy trianglerightsld Using Ba yes? Decision rule (maximize exp ected payoff, based on best available estimates of likeliho ods, or probabilities, of all possible outcomes of uncertain events ) trianglerightsld Value of obtaining additional info rmation: holding/cance ling an outdo or event with or without a weather forecast trianglerightsld With an im perfect weather forec ast, exp ected return of the optimal strategy $6,200 trianglerightsld Without a weather forecast, exp ected return of the best available strategy is $5,550 trianglerightsld Value of the forecast is $650. IOE 202: Op erations Mo del ing, Fall 2008 Page 2 Space Weather info rmation for scheduling an outdo or event in mid-June trianglerightsld Acco rding to station reco rds, the station?s next-da y forecast in mid-June is ?sunny? 90% of the time trianglerightsld When the weather forec ast was ?sunny ,? the next day turne d out to actually be sunny 80% of the time trianglerightsld When the weather forec ast was ?rain,? it actually rained 90% of the time trianglerightsld Histo rically , the likeliho od of it raining on any given day in mid-June is 27%. Are these probabilities and frequencies consistent with each other? Tw o ways of measuring reliabilit y of the forecast: trianglerightsld Ho w frequently are the station?s forecasts of a sunny days are correct? What ab out rainy days? trianglerightsld Ho w frequently is a sunny day corre ctly forecast by the station? What ab out rainy days? IOE 202: Op erations Mo del ing, Fall 2008 Page 3 Space Forecast reliabilit y What fraction of June days are sunny? What fraction of sunny days are correc tly 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: Op erations Mo del ing, Fall 2008 Page 4 Space Medical decision making and qualit y of testing trianglerightsld 550,000 people in the US are infected with HIV out of the total population of 250 million 1 trianglerightsld The standa rd blo od test for HIV is fairly accurate: trianglerightsld The probabilit y that someone infected with HIV will test positive is 0.99 trianglerightsld The probabilit y that someone not infected with HIV will test negative is also 0.99 trianglerightsld A randomly selected person tests positive. What is the probabilit y that this person is infected with HIV? 1 This data is a bit outdated, but still gives an ?o rder of magnitude? assessment IOE 202: Op erations Mo del ing, Fall 2008 Page 5 Space Diagram for HIV testing accuracy HIV negative HIV pos. trianglerightsld # of persons in the population who would test positive: trianglerightsld # of HIV positive persons who would test positive: trianglerightsld # of HIV negative persons who would test positive: trianglerightsld Fraction of positive tests com ing from HIV negative persons: IOE 202: Op erations Mo del ing, Fall 2008 Page 6 Space Value of perfect info rmation in decision analysis trianglerightsld A majo r movie studio has just completed pro duction of an up coming summer release, and is trying to decide whether to invest an extra $30 million into an aggressive adve rtising campaign, or to pro ceed with a normal campaign trianglerightsld 1/4 of the movies made by this studio turn out to be hits, the rest flop at the box office trianglerightsld If the movie is a hit, it will bring in $100M in tick ets sales and merchandise without aggressive ma rketing and $110M with aggressive ma rketing trianglerightsld The movie is a flop, it will only bring in $40M without aggressive ma rketing, but $80M with aggressive ma rketing trianglerightsld What typ e of an advertising cam paign should the studio undertak e? (To answ er this, build a small decision tree) trianglerightsld What is the Exp ected Value of Perf ect Info rmation ? I.e ., what would it be worth to the studio to kno w ahead of time if the movie is a hit or a flop? (A different small decision tree) IOE 202: Op erations Mo del ing, Fall 2008 Page 7 Space Best decision without additional info rmation IOE 202: Op erations Mo del ing, Fall 2008 Page 8 Space Best decision with perfe ct info rmation IOE 202: Op erations Mo del ing, Fall 2008 Page 9 Space Value of imp erfect info rmation, or exp erimentation trianglerightsld 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. trianglerightsld If a movie is destined to be a hit, there is a 80% chance that the preview feedback will be positive trianglerightsld 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...) trianglerightsld 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: Op erations Mo del ing, Fall 2008 Page 10 Space Decision tree w. previews IOE 202: Op erations Mo del ing, Fall 2008 Page 11 Space Necessa ry calculations What fraction of all movies this studio mak es 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 mak es 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: Op erations Mo del ing, Fall 2008 Page 12 Space The goals of IOE 202 The goals set forth for IOE 202 are, in part, to let you trianglerightsld app reciate role of op erations in a firm, trianglerightsld app reciate complexities of optimal decisions under constraints, trianglerightsld app reciate complexities of design and analysis of op erations under uncertaint y, trianglerightsld app reciate complexities of integrating various levels of op erations, trianglerightsld app reciate complexities of collection and analysis of data and its role in decision problem s, trianglerightsld app reciate role of uncertaint y in op erations decisions. IOE 202: Op erations Mo del ing, Fall 2008 Page 13 Space IOE 202: the big picture trianglerightsld Examples of a broad range of problems that can be app roached by IOE metho dology trianglerightsld A variet y of IOE metho ds to app roach a broad range of problems trianglerightsld Imp ortance of exp ressing and formulating decisions, constraints, and perfo rmance measures in real- life problems trianglerightsld Imp ortance of considering the uncertaint y involved in analyzing and mo deling op erations trianglerightsld Some of mo dern soft ware capabilities for formulating and solving problem s IOE 202: Op erations Mo del ing, Fall 2008 Page 14 Space Topics and further courses IOE 441 Pro duction and invento ry control IOE 310 Linea r and integer programm ing mo dels IOE 265 Probabilit y and statistics (also, IOE 366), understanding uncertaint y IOE 316 Sto chastic mo dels, including queueing mo dels IOE 460 Decision analysis IOE 373 Soft ware ? from engineering and managerial persp ectives Not cove red in 202: IOE 333 Ergonomics IOE 202: Op erations Mo del ing, Fall 2008 Page 15 Marina Epelman L14
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