A maintenance department replaces a malfunctioning machine with a standby machine if one is available; otherwise, they repair the broken machine as soon as possible. When a standby machine is available, production down time is greatly reduced. The department has reviewed its historical maintenance records on machine breakdowns and found this pattern for the past four weeks: If a standby machine is not available when a breakdown occurs, the estimated cost is $400 due to lost production time, overtime usage on the other machines, and emergency repair procedures. On the other hand, weekly cost for machines not in use is estimated to be $200 due to storage and special handling expenses. The department manager wants to use a payoff table to determine how many standby machines they should maintain.
a. Construct a table showing the cost associated with each decision alternative (number of computers stocked) and state of nature (number of computers needed) combination.
b. Compute the probability of each state of nature.
c. How many standby computers should be stocked in order to minimize their expected costs?

Question

A maintenance department replaces a malfunctioning machine with a standby machine if one is available; otherwise, they repair the broken machine as soon as possible. When a standby machine is available, production down time is greatly reduced. The department has reviewed its historical maintenance records on machine breakdowns and found this pattern for the past four weeks:  If a standby machine is not available when a breakdown occurs, the estimated cost is $400 due to lost production time, overtime usage on the other machines, and emergency repair procedures. On the other hand, weekly cost for machines not in use is estimated to be $200 due to storage and special handling expenses. The department manager wants to use a payoff table to determine how many standby machines they should maintain. 
a. Construct a table showing the cost associated with each decision alternative (number of computers stocked) and state of nature (number of computers needed) combination.
b. Compute the probability of each state of nature.
c. How many standby computers should be stocked in order to minimize their expected costs?

Quizplus · Accepted Answer

The Answer of A maintenance department replaces a malfunctioning machine with a standby machine if one is available; otherwise, they repair the broken machine as soon as possible. When a standby machine is available, production down time is greatly reduced. The department has reviewed its historical maintenance records on machine breakdowns and found this pattern for the past four weeks:  If a standby machine is not available when a breakdown occurs, the estimated cost is $400 due to lost production time, overtime usage on the other machines, and emergency repair procedures. On the other hand, weekly cost for machines not in use is estimated to be $200 due to storage and special handling expenses. The department manager wants to use a payoff table to determine how many standby machines they should maintain. 
a. Construct a table showing the cost associated with each decision alternative (number of computers stocked) and state of nature (number of computers needed) combination.
b. Compute the probability of each state of nature.
c. How many standby computers should be stocked in order to minimize their expected costs?

A Maintenance Department Replaces a Malfunctioning Machine with a Standby