Using Decision Tree to Solve Expansion Problem

What is Decision Tree?

    A decision tree is a graphical representation of all possible solutions to a decision based on certain conditions

From statement above we will try solve a case scenario bellow

Case:

    As operations manager of NBM Furniture, you must make a decision about adding a line of NBM furniture. In discussing the possibilities with your sales manager, Steve Gilbert, you decide that there will definitely be a market and that your firm should enter that market. However, because NBM furniture has a different finish than your standard offering, you decide you need another process line. 

There is no doubt in your mind about the decision, and you are sure that you should have a second process. But you do question how large to make it. 

A large process line is going to cost $400,000; 

a small process line will cost $300,000. 

The question, therefore, is the demand for NBM furniture. After extensive discussion with Mr. Gilbert and Tim Ireland of Ireland Market Research, Inc., you determine that the best estimate you can make is that there is a two-out-of-three chance of revenue from sales as large as $600,000 and a one-out-of-three chance as low as $300,000. 

With a large process line, you could handle the high figure of $600,000. 

However, with a small process line you could not and would be forced to expand (at a cost of $150,000), after which time your revenue from sales would be $500,000 rather than the $600,000 because of the lost time in expanding the process. If you do not expand the small process, your revenue from sales would be held to $400,000. 

If you build a small process and the demand is low, you can handle all of the demand.

Should you open a large or small process line?

Answer:

    To solve this case problem with decision tree, we will calculate the we will calculate the profit of each production line with each condition.

The description can be seen in the following table.

Alternative	Chance	Revenue	Cost	Rev – Cost x Chance	Value
Large strong	0.6666666667	600000	400000	133333.3333	100000
Large weak	0.33	300000	400000	-33333.33333
Small strong growth do nothing	0.6666666667	400000	300000	100000	66666.66667
Small strong growth expand		500000	450000	50000	33333.33333
Small Weak	0.33	300000	300000	0	0

    after getting the calculation above we will enter it in the Decision Tree and make a decision

    from the decision tree above it can be concluded that NBM Furniture should open Large Process Line with value of $100.000.

This is an explanation of the decision tree. hopefully useful for you all.

Reference:

Chase, R. and Jacobs, R. (2013) Operations and Supply Chain Management. 14th Edition, McGraw-Hill Higher Education, New York.