A1 45730 15sep08

A1 45730 15sep08 - 45 730 Probability & Decision Making...

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45 730 Probability & Decision Making (9/15/08) Topics for today’s class: • Decision Theory Examples • Examples of Binomial and Poisson models
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Example: ICI product development Situation: • ICI has developed new (unpatentable) use for anthraquinone (AQ) in paper production • Needs to decide whether to continue research and whether to introduce product in commercial market • Final success of research process is uncertain • Success of market for product is uncertain Note: Example is taken from “Swinging on the Branch of a Tree: Project Selection Applications,” Interfaces , Nov/Dec 1993
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Two levels of uncertainty: • Success or failure of research P (Research successful) = 0.6 P (Research unsuccessful) = 0.4 • Success or failure of market for product P (Mkt successful) = 0.4 P (Mkt unsuccessful) = 0.6 Note: Uncertainty associated with research precedes market uncertainty
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Possible actions: • Research decision: Continue or halt research • Introduction decision: Introduce or do not introduce product Note: Research decision precedes introduction decision
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Payoffs: • Research cost = $ 0.8 mil • Product introduction cost = $3.5 mil • Product profits if successful = $25 mil • Product profits if unsuccessful = $0
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Decision tree: Reflects timing, probabilities, payoffs
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Decision tree: Reflects timing, probabilities, payoffs 0.4 Mkt successful 20.7 Commercial develop 25 20.7 -3.5 5.7 0.6 0.6 Mkt unsuccessful Research successful -4.3 10 - 4 . 3 05 . 7 Continue research No commercial develop -0.8 -0.8 3.1 0 -0.8 0.4 Research unsuccessful 1 -0.8 3.1 0 -0.8 Halt research 0 00
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A multistage decision problem • Actions • Followed by uncertain event • Followed by action • Followed by final uncertain event Strategy will be a contingency plan: “If event X occurs, take action Y”
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Solution method: “Rolling back” the tree • Begin with last decision involving uncertainty • Treat last decision as single stage decision problem and find action that maximizes expected payoff • Move to previous decision taking into account implications of acting optimally at later decision • Determine optimal action for that decision • Continue working backward until initial decision is reached
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A1 45730 15sep08 - 45 730 Probability & Decision Making...

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