management science solution

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Starting Right: There are two events: a favorable market (event 1) and an unfavorable market (event 2). There are four alternatives, which include do nothing (alternative 1), invest in corporate bonds (alternative 2), invest in preferred stock (alternative 3), and invest in common stock (alter-native 4). The decision table with returns is presented below. Event 1 Event 2 Alternative 1 0 0 Alternative 2 25,273 -10,000 Alternative 3 90,000 -15,000 Alternative 4 210,000 -30 Maximin Alternative Expected Value 1 0 2 -10,000 3 -15,000 4 -30,000 Best: Alternative 1 Maximax Alternative Maximax Payoff 1 0 2 25,273 3 90,000 4 210,000 Best : Alternative 4

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decision theory solution

Transcript of management science solution

Page 1: management science solution

Starting Right:

There are two events: a favorable market (event 1) and an unfavorable market (event 2). There are four alternatives, which include do nothing (alternative 1), invest in corporate bonds (alternative 2), invest in preferred stock (alternative 3), and invest in common stock (alter-native 4). The decision table with returns is presented below.

Event 1 Event 2Alternative 1 0 0Alternative 2 25,273 -10,000Alternative 3 90,000 -15,000Alternative 4 210,000 -30

Maximin

Alternative Expected Value1 02 -10,0003 -15,0004 -30,000

Best: Alternative 1

Maximax

Alternative Maximax Payoff1 02 25,2733 90,0004 210,000

Best : Alternative 4

Hurwicz alpha coefficient: 0.110

Minimax

Alternative Maximum Regret1 210,000

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2 184,7273 120,0004 30,0

Best : Alternative 4

Ans 1: a. Sue Pansky is a risk avoider and should use the maximin decision approach. She should do nothing and not make an investment in Starting Right.

Ans 2: Ray Cahn should use a coefficient of realism of 0.11. The best decision is to do nothing.

Ans 3: Lila Battle should eliminate alternative 1 of doing nothing and apply the maximin criterion. The result is to invest in the corporate bonds.

Ans 4: George Yates should use the equally likely decision criterion. The best decision for George is to invest in common stock.

Ans 5: Pete Metarko is a risk seeker. He should invest in common stock.

Ans 6: Julia Day can eliminate the preferred stock alternative and still offer alternatives to risk seekers (common stock) and risk avoiders (doing nothing or investing in corporate bonds).

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Case Study 2

Abbreviations and values used in the following decision trees:

Normal - proceed with research and development at a normal pace

6 Month - Adopt the 6-month program: if a competitor’s product is available

at the end of 6 months, then copy; otherwise proceed with research and

development.

8 Month - Adopt the 6-month program: proceed for 8 months; if no

competition at 8 months, proceed; otherwise stop development

Success or failure of development effort:

Ok—Development effort ultimately a success

No—Development effort ultimately a failure

Column:

S—Sales revenue

R—research and development expenditures

E—Equipment costs

I—Introduction to market costs

Market size and Revenues:

Without WithCompetition Competition

S—Substantial (P = 0.1) $800,000 $400,000

M—Moderate (P = 0.6) $600,000 $300,000

L—Low (P = 0.3) $500,000 $250,000

Competition:

C6—Competition at end of 6 months (P = .5)

No C6—No competition at end of 6 months (P = .5)

C8—Competition at end of 8 months (P = .6)

No C8—No competition at end of 8 months (P = .4)

C12—Competition at end of 12 months (P = .8)

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No C12—No competition at end of 12 months (P = .2)

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The optimal program is to adopt 6-month program