Construction Problem: Introduction Construction Problem: Introduction The follow

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Construction Problem: Introduction

Construction Problem: Introduction The following questions refer to this problem: The manager of a construction company must decide whether to build single family homes, apartments, or condominiums. Profit:s (in thousands of dollars) are given in the following table and depend on various possible population trends. The probability of a declining population is 0.4, the probability for a stable population is 0.5 and the probability of a growing population is 0.1 Payoff Table (in thousands of dollars): Single Family Homes Apartments Condominiums Declining Population Stable Population Growing Population 90 170 1020 70 70 20 220

Explanation / Answer

Part 1: If the manager uses the maximum likelihood criterion, what kind of dwellings will he decide to build?

Maximum likelihood criterion chooses highest probability scenario, in this case it is stable population, where the most demandes dwellings are APARTMENTS.

Part 2: If he uses Bayes' decision rule, which kind of dwellings will he decide to build?

Bayes' decision rule recommends to build the dwellings with highest expected results, it means to multiply payoffs by probability of occurrence, and to choose the dwellings with maximum expected value.
Single family home: 200,000x0.4+90,000x0.5+70,000x0.1=132,000
Apartments: 70,000x0.4+170,000x0.5+90,000x0.1=122,000
Condominiums: -20,000x0.4+100,000x0.5+220,000x0.1=64,000
The maximum value is 132,000 (Single Family Homes)

Part 3: What is the expected value of perfect information for this problem?

If the statement refers to Part 2, the expected value of perfect information to build Single Family Homes
EVPI=200,000x0.4+90,000x0.5+70,000x0.1=132,000

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