Assignment 1: LASA – Final Project Report

Probability Analysis

Chatae M Falls

Argosy University

April 26, 2015

Problem Statement : A General Manger of Harley-Davidson has to decide on the size of a new facility. The GM has narrowed the choices to two: large facility or small facility. The company has collected information on the payoffs. It now has to decide which option is the best using probability analysis. The decision tree model is made and accurately labeled showing all possible scenarios and corresponding payoffs.

Methodology that is adopted : By the help of probability analysis, a person will be able to find the required value of monetary for both the choices that is of having a large facility or a small facility. After the analysis is over, that choice having higher monetary value will be chosen.

Probability Analysis:

Option 1 : Build Small Facility : If the GM decides on going for the large facilities, the chances of having low demand becomes 0.4 and the chances of having high demand becomes 0.6. Now if the demand is low then $40 will be required for doing payoff. But if the demand is high then $40 will fetch nothing, whereas $50 will be fetched by doing overtime and the option of expansion will fetch a payoff $55. So one will think of going for expansion is such a case where the demand is high. The anticipated value of monetary for building a facility that is small is equal to the sum of the products of the demand probabilities with their corresponding payoff.

So the anticipated monetary value of building a small facility is=

The Probability of having a High Demand*The Payoff of High Demand+ The Probability of having a Low Demand*The Payoff of Low Demand

=0.6*$55+0.4*$40=$33+$16=$49

Option 2 : Build Large Facility : Now if the GM thinks of building small facilities, The chances of having low demand becomes 0.4 and of having high demand becomes 0.6. So in cases when there is a very low demand then around $10 will be fetched by doing nothing but at the same time there will be a payoff of around $50 when there is reduction in the overall prices. Thus it is assumed that in a situation when the demand is low, a person will think of reducing the overall prices. In case when there is high demand, a payoff of $70 is seen. The anticipated value of monetary for building a facility that is large is equal to the total sum of the products of the probabilities of demand with their corresponding payoff.

So the anticipated monetary value of building a large facility is=

The Probability of having a High Demand*The Payoff of High Demand + The Probability having a Low Demand*The Payoff of Low Demand

=0.6*$70+0.4*$50=$42+$20=$62

Result/Conclusion : Thus we see that the expected monetary value for building a large facility is $62 and that for building a small facility is $49, so Harley Davidson’s GM should certainly go for building a facility that is large.

Reference

· Optimal Investment Decisions: Rules for Action and Criteria for Choice (Englewood Cliffs, New Jersey, Prentice-Hall, Inc., 1962)

· “Long-Range Planning,” Management Science, April 1959