Ákvarðanatré (Decision Trees)

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Presentation transcript:

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

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. 20

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: 21

Dæmi um ákvarðanatré : Þrep 1. Teikna ákvarðanirnar B C 22

Dæmi um ákvarðanatré : Þrep 2 Dæmi um ákvarðanatré : Þrep 2. Bæta við mögulegum atburðum, líkum á þeim og hagnaði. A B C High demand (.4) Medium demand (.5) Low demand (.1) $90k $50k $10k $200k $25k -$120k $60k $40k $20k 23

Dæmi um ákvarðanatré : Þrep 3. Ákvarða væntigildi hverrar ákvörðunar High demand (.4) Medium demand (.5) Low demand (.1) A $90k $50k $10k EVA=.4(90)+.5(50)+.1(10)=$62k $62k 24

Dæmi um ákvarðanatré : Þrep 4. Hæsta væntigildi => bestu ákvörðun High demand (.4) Medium demand (.5) Low demand (.1) A B C $90k $50k $10k $200k $25k -$120k $60k $40k $20k $62k $80.5k $46k Alternative B generates the greatest expected profit, so our choice is B or to construct a new facility. 25

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