Decision Science Following is the payoff table for the Pittsburgh Development Co

Question

Decision Science

Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S_1) and a corresponding probability of 0.2 that demand will be weak (S_2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.5 million and as long as the payoff for the weak demand was greater than or equal to -$19 million. a. Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d_3 the optimal solution? If required, The payoff for the medium complex under strong demand remains less than or equal to $ million, the large complex remains the best decision. b. Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative d_3 the optimal solution? If required, The payoff for the small complex under strong demand remains less than or equal to $ million, the large complex remains the best decision.

Explanation / Answer

a) Expected value of Large complex decision, d3 = 20*0.8 + (-9)*0.2 = $ 14.20 m

Therefore large complex will remain the best decision, as long as the expected value for medium complex decision is less than or equal to $ 14.20 m.

a) Let X be the maximum possible payoff under strong demand of medium complex decision.

So, X*0.8 + 5*0.2 = 14.20

or, X = (14.20-5*0.2)/0.8 = $ 16.50 m

The payoff for the medium complex under strong demand remains less than or equal to $ 16.50 million, the large complex remains the best decision.

b) Using the same approach as above,

X = (14.20 - 7*0.2)/0.8 = 16.00

The payoff for the small complex under strong demand remains less than or equal to $ 16.00 million, the large complex remains the best decision.

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