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Decision Trees in Risky Business Scenarios

Decision trees are used to map complex decisions characterized by uncertainty and risk, aiding in selecting the highest expected value choice. Explore an example of decision tree analysis in a crystal factory's management dilemma. Learn steps involved in decision tree analysis and evaluating the highest expected profit alternative.

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Decision Trees in Risky Business Scenarios

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  1. Ákvarðanatré (Decision Trees) • Notuð til að kortleggja flóknar ákvarðanir • sem einkennast af óvissu / áhættu • Tvö tákn notuð: • Kassi merkir ákvarðanataka • Bolla merkir hendingu / atburði með líkindum • Væntigildi reiknuð, ákvörðun með hæsta væntigildið valin

  2. Dæmi um ákvarðanatré 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. Dæmi um ákvarðanatré : Hagnaðartaflan (“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 Dæmi um ákvarðanatré : Þrep 1. Teikna ákvarðanirnar

  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) Dæmi um ákvarðanatré : Þrep 2. Bæta við mögulegum atburðum, líkum á þeim og hagnaði.

  6. $90k High demand (.4) $50k Medium demand (.5) $62k $10k Low demand (.1) A EVA=.4(90)+.5(50)+.1(10)=$62k Dæmi um ákvarðanatré : Þrep 3. Ákvarða væntigildi hverrar ákvörðunar

  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) Dæmi um ákvarðanatré : Þrep 4. Hæsta væntigildi => bestu ákvörðun $62k $80.5k $46k Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility.

  8. Önnur sjónarmið • Eru líkur rétt metnar? Næmnigreining! • Er hægt að “kaupa” meiri fullvissu (t.d. afla öruggari upplýsinga um eftirspurn)? • Áhættufælni (“Risk Aversion”)

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