Employees arrive randomly to use the fax machine at an average rate of 20 per ho
ID: 409100 • Letter: E
Question
Employees arrive randomly to use the fax machine at an average rate of 20 per hour. This arrival process is approximated by a Poisson distribution. Employees spend an average of two minutes using the fax machine, either transmitting or receiving items. The time spent using the machine is distributed according to a negative exponential distribution. Employees line up in single file to use the machine, and they obtain access to it on a first come, first-served basis. There is no defined limit to the number who can line up to use the machine. Management has determined that by assigning an operator to the fax machine rather than allowing the employees to operate the machine themselves, it can reduce the average service time from the current 2 minutes to 1.5 minutes. However, the fax operator's salary is $8 per hour, which must be paid 8 hours per day even if there are no employees wishing to use the fax machine part of the time. Management has estimated the cost of employee time spent waiting in line and at the fax machine during service to be 17¢ per minute (based on an average salary of $10.20 per hour per employee). Should the firm assign an operator to the fax machine?
Explanation / Answer
if the average value of employees per hour is- $10.20, and the amount is ready to pay the operator is $8 per hour
the employee time save is 1/4th only, that means the cost will be saved by 10.2/4= $2.55
and for that the firm is paying $8 per hour. so, it is not advisable to appoint the operator.
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