A manager must decide how many machines of a certain type to buy. The machines will be used to manufacture a new gear for which there is increased demand. The manager has narrowed the decision to two alternatives: buy one machine or buy two. If only one machine is purchased and demand is more than it can handle, a second machine can be purchased at a later time. However, the cost per machine would be lower if the two machines were purchased at the same time.
The net present value associated with the purchase of two machines initially is $75,000 if demand is low and $130,000 if demand is high. The net present value for one machine and low demand is $90,000. If demand is high, there are three options. One option is to do nothing, which would have a net present value of $90,000. A second option is to subcontract; that would have a net present value of $110,000. The third option is to purchase a second machine. This option would have a net present value of $100,000.
a. Identify the choice that would be made using each of the four approaches for decision making under uncertainty.
i. Maximin
ii. Maximax
iii. Laplace
iv. Minimax regret
The estimated probability of low demand is 0.40, and the estimated probability of high demand is 0.60.
b. Analyze this problem using a decision tree. What would be your suggestion? How many machines should the manager purchase initially?
c. Compute the EVPI and interpret it.
d. Perform sensitivity analysis on P(high).