Question:There are four copying center/file rooms serving a relatively large and active legal research firm. One attendant staffs each service room. The average arrival rate and service rate are the same for each room and are as follows:

Arrival rate = 10.9 arrivals per hour

Service rate = 14.6 services per hour

The coefficients of variation of the inter-arrival times and the service times are both equal to 1.

Although the relationships between the average number of arrivals and the average service capacity of each room seem to indicate that a line should rarely exist, most of the time a line of some length has been observed. Sometimes there is no line, and the attendant has nothing to do of any consequence. Management is concerned about this situation because of the lost effectiveness involved in having lawyers idle while researchers are waiting in line for files or other services, and because room attendants are sometimes not performing any work.

Costs are given as follows:

Cost of waiting time = $15.45/hour

Cost of channel time = $6.30/hour

PART A:

While being mindful of cost, management wants to improve utilization and reduce the queues. One consideration is to add attendants to the present rooms. Is this a good idea, if so how many should be added to each room?

No, this is not a good idea, costs increase.

Yes, it is a good idea for management to add 1 attendant to each room.

Yes, it is a good idea for management to add 2 attendants to each room.

Yes, it is a good idea for management to add 3 attendants to each room.

PART B:

While being mindful of cost, management wants to improve utilization and reduce the queues. Another consideration is to combine therooms without adding attendants. What is the total cost savings of this option?

A $25.47 cost savings over separate rooms.

B $112 cost savings over separate rooms.

C $121 cost savings over separate rooms.

D No cost savings, this is more expensive.