Problem:
Decision Tree Use for Production Capacity Determination at Toyota Motor Manufacturing of Canada (TMMC)
This exercise illustrates how determination of an "optimal" production capacity option can be made from among several possible options based on the probability of their occurrence and the provided payoffs of events that influence these options.
It is spring 2000, and TMMC has indeed just been chosen to produce the new Lexus RX 330 line, with the first units deliverable in 2003. Toyota must now determine the amount of annual production capacity it should build.
Toyota's goal is to maximize the profit from this line over the five years from 2003-2007. These vehicles will sell for an average of $37,000 and incur a unit production cost of $28,000.
10,000 units of annual production capacity can be built for $50M (M=million) with additional blocks of 5,000 units of annual capacity each costing $15M. Each block of 5,000 units of capacity will also cost $5M per year to maintain, even if the capacity is unused.
Marketing has provided three vehicle demand scenarios with associated probabilities:
| Demand |
2003 |
2004 |
2005 |
2006 |
2007 |
Probability |
| Low |
10000 |
10500 |
11000 |
11500 |
12000 |
0.25 |
| Moderate |
15000 |
16000 |
17000 |
18000 |
19000 |
0.5 |
| High |
20000 |
24000 |
26000 |
28000 |
30000 |
0.25 |
Assume that the number of units actually sold each year will be the lesser of the demand and the production capacity.
Should TMMC in 2000 decide to build a facility with a production capacity of 10,000, 15,000, 20,000, 25,000, or 30,000 cars? Justify your choice. What are the flaws or limitations in your analysis?
Please provide as many as details possible for me to understand this practice.