2. A real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has two acceptable alternatives: residential proposal or commercial proposal. The main factor or state of nature that will influence the profitability of the development is whether or not a shopping center is built close by and the size of the shopping center. There is a 20% chance of no center being built, a 50% chance of a medium shopping center built, and a 30% chance of a large shopping center. If the developer selects the residential proposal and no center is built, he has a further set of options: do nothing $400,000 payoff; build a small shopping center himself $700,000 payoff; or put in a park resulting in $800,000 payoff. Should a medium shopping center be built nearby, his payoff for residential would be $1,600,000 and large shopping center results in a $1,200,000 payoff. If the developer selects the commercial proposal and no center is built, he also has the set of options: do nothing but payoff would be $-50,000; build a small shopping center himself for $1,400,000 payoff; or put in a park resulting in $1,000,000 payoff. Should a medium shopping center be built nearby, his payoff for commercial would be $400,000 and large shopping center results in a $1,500,000 payoff. a. Draw a decision tree for this problem. b.Determine the EMV for the problem and identify the best decision.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 46P

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2. A real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has two acceptable alternatives: residential proposal or commercial proposal. The main factor or state of nature that will influence the profitability of the development is whether or not a shopping center is built close by and the size of the shopping center. There is a 20% chance of no center being built, a 50% chance of a medium shopping center built, and a 30% chance of a large shopping center.

If the developer selects the residential proposal and no center is built, he has a further set of options: do nothing $400,000 payoff; build a small shopping center himself $700,000 payoff; or put in a park resulting in $800,000 payoff. Should a medium shopping center be built nearby, his payoff for residential would be $1,600,000 and large shopping center results in a $1,200,000 payoff.
If the developer selects the commercial proposal and no center is built, he also has the set of options: do nothing but payoff would be $-50,000; build a small shopping center himself for $1,400,000 payoff; or put in a park resulting in $1,000,000 payoff. Should a medium shopping center be built nearby, his payoff for commercial would be $400,000 and large shopping center results in a $1,500,000 payoff.

a. Draw a decision tree for this problem.

b.Determine the EMV for the problem and identify the best decision.

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$E x p e c t e d m o n e t a r y v a l u e (E M V) i n s t r u c t s e x p e r t o p i n i o n s t o d r i v e d e c i s i o n s c o n c e r n i n g p r o b a b i l i t y a n d t h e e f f e c t s o f r i s k . E x p e c t e d v a l u e o r E V i s t h e e x p e c t e d m o d e r a t e v a l u e f o r a n a s s e t a t s o m e m o m e n t i n t h e f u t u r e . E V = \sum_{} P r o b a b i l i t y \times P a y o f f$

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