An automobile manufacturer stocks an electric motor unit that is used in many of their production line robots. As this is the major item to fail in a robot, it is important that enough of them are kept in storage. Since these precision motors are very expensive (over $10,000 each) it is also very important not to keep too many on the shelf. Long costs are $200 and short costs are $325 per unit. Data on monthly breakdown experience is as follows:
a. Construct a table showing the cost associated with each decision alternative (number of motors stocked) and state of nature (number of motors needed) combination.
b. Compute the probability of each state of nature.
c. How many standby motors should be stocked in order to minimize their expected costs?

Question

An automobile manufacturer stocks an electric motor unit that is used in many of their production line robots. As this is the major item to fail in a robot, it is important that enough of them are kept in storage. Since these precision motors are very expensive (over $10,000 each) it is also very important not to keep too many on the shelf. Long costs are $200 and short costs are $325 per unit. Data on monthly breakdown experience is as follows:  
a. Construct a table showing the cost associated with each decision alternative (number of motors stocked) and state of nature (number of motors needed) combination.
b. Compute the probability of each state of nature.
c. How many standby motors should be stocked in order to minimize their expected costs?

Quizplus · Accepted Answer

The Answer of An automobile manufacturer stocks an electric motor unit that is used in many of their production line robots. As this is the major item to fail in a robot, it is important that enough of them are kept in storage. Since these precision motors are very expensive (over $10,000 each) it is also very important not to keep too many on the shelf. Long costs are $200 and short costs are $325 per unit. Data on monthly breakdown experience is as follows:  
a. Construct a table showing the cost associated with each decision alternative (number of motors stocked) and state of nature (number of motors needed) combination.
b. Compute the probability of each state of nature.
c. How many standby motors should be stocked in order to minimize their expected costs?

An Automobile Manufacturer Stocks an Electric Motor Unit That Is