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Decision Trees

Decision Trees. Used for complex decision problems characterized by uncertainities Two main symbols: Box = Decision Circle = Random event Expected profit values calculated Select decision with highest exp. profit. An Example.

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Decision Trees

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  1. Decision Trees • Used for complex decision problems • characterized by uncertainities • Two main symbols: • Box = Decision • Circle = Random event • Expected profit values calculated • Select decision with highest exp. profit

  2. An Example A glass factory specializing in crystal is experiencing a substantial backlog, and the firm's management is considering three courses of action: A) Arrange for subcontracting, B) Construct new facilities. C) Do nothing (no change) The correct choice depends largely upon demand, which may be low, medium, or high. By consensus, management estimates the respective demand probabilities as .10, .50, and .40.

  3. The Payoff Table The management also estimates the profits when choosing from the three alternatives (A, B, and C) under the differing probable levels of demand. These costs, in thousands of dollars are presented in the table below:

  4. A B C Step 1: Draw the decisions

  5. $90k High demand (.4) $50k Medium demand (.5) $10k Low demand (.1) A $200k High demand (.4) $25k B Medium demand (.5) -$120k Low demand (.1) C $60k High demand (.4) $40k Medium demand (.5) $20k Low demand (.1) Step 2: Draw the random events

  6. $90k High demand (.4) $50k Medium demand (.5) $62k $10k Low demand (.1) A EVA=.4(90)+.5(50)+.1(10)=$62k Step 3: Calculate exp. values

  7. $90k High demand (.4) $50k Medium demand (.5) $10k Low demand (.1) A $200k High demand (.4) $25k B Medium demand (.5) -$120k Low demand (.1) C $60k High demand (.4) $40k Medium demand (.5) $20k Low demand (.1) Step 4: Select best alternative $62k $80.5k $46k Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility.

  8. Other views and criteria • Sensitivity analysis for the estimated probabilities • Can we “buy” better information? EVPI • Risk Aversion, Utilities

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