A major operation in an outpatient medical office is answering the telephones. This is especially true in primary care, such as pediatrics. Patients mostly use the telephone to communicate with the physician's office. In pediatrics, such interactions include calling for appointments, refills, medical advice, referrals, and forms (for example: school forms, camp forms.) Because of the frequent use of the telephone in outpatient pediatrics, it is an important focus for assessing productivity and efficiency. A pediatric practice consists of nine physicians and two nurse practitioners. The practice has two offices.

The patient population is approximately ten thousand children, with nearly fifty thousand visits per year. The phone system consists of sixteen telephone lines, most of them at the main office. As the practice has grown, there have been increasing complaints from patients about wait time on the phone lines. All incoming calls are routed to the main office. When a patient dials the practice's office telephone number, a voicemail system directs the caller to press a number according to the purpose of the call (for example, " Press‘ one 'for appointments " ).

The system also distributes the phone calls according to whether the person calling is a patient, physician, laboratory, or hospital. During the winter months, when the volume of sick patients is highest, a patient ' s wait can sometimes be as long as ten to fifteen minutes on the appointment line before speaking to a person. Since most customer service guidelines recommend telephone hold times no longer than one minute, this is an area that greatly needs improvement. Telephone calls form a single waiting line and are served on a first - come, first - served basis. Arrival rates can be described by Poisson distribution, and service times can be described by negative exponential distribution. With these characteristics, a multiple - channel model for queuing analysis is most appropriate.

The queuing analysis of the practice's phone system can be divided into three parts of the workday, which lasts from 8:00 A.M.to 5:00 P.M. For the first hour of the day (8:00 A.M.to 9:00 A.M. ) there are usually three receptionists working to answer telephone calls only. For the last hour of the day (4:00 P.M.to 5:00 P.M. ), there are usually five receptionists answering phones as well as checking patients in and out. For the bulk of the day, there are usually six receptionists working.

The use of fewer servers during the first and last hours is primarily because fewer patients are being seen during those hours, so fewer servers are needed for checking patients in and out. To determine the customer arrival rate (or phone calls/hour), incoming monthly phone call data for the previous year were obtained from the telephone company (Table EX 14.5.1 ). From examining previous studies of the office's phone call volume distribution, it is estimated that 30 percent of the phone calls occur between 8 A.M. and 9 A.M. ; 40 percent between 9 A.M. and 4 P.M . , and the remaining 30 percent arriving from 4 P.M. to 5 P.M. (Table)

Month                      Phone Calls

January                    6,640

February                   6,756

March                       6,860

April                         6,226

May                         6,671

June                        7,168

July                         6,802

August                     6,971

September                7,205

October                    6,944

November                  6,623

December                  6,875

Total                         81,741

To estimate the service rate (or phone calls/hour/receptionist), several sample studies were performed by an office administrator. It is important to note that the receptionists perform functions other than answering phones, such as checking patients in and out. Therefore, the number of phone calls that a server can answer per hour depends on the other responsibilities that the person has that day. In order to arrive at a service rate, the assumption was made that

Customer Arrival Rates (λ)

8:00 A.M. to 9:00 A.M.               31 phone calls/hr

9:00 A.M. to 4:00 P.M.                  42 phone calls/hr

4:00 PSI. to 5:00 P.M.               31 phone calls/hr

8:00 A.M. to 9:00 A.M.               31 phone calls/hr

the average maximum of phone calls per hour for the sample days would represent the servers operating at the maximum phone - call - answering capacity when having other responsibilities. While this assumption may underestimate actual server rate, for purposes of this study, the conservative estimate is acceptable in the absence of further data. There is one exception to this assumption. During the first hour of the day, from 8:00 A.M.to 9:00 A.M. , patients are not yet being seen in the office. Therefore, during that hour the servers have a faster telephone service rate, since they have no other primary duties (Table EX 14.5.3 ). From samples studied, we have determined that the maximum service capability when only answering phones is approximately four minutes per phone call, or fifteen calls per hour per server.

This number was used for the service rate for the first hour (8:00 A.M. to 9:00 P.M. ). Cost studies were then performed based on the financial data from the previous year. Capacity costs were calculated based on salary and benefits per server and a percentage of the equipment maintenance, phone line costs, rent, and other capital expenditures (Table).

Service Rate (μ)

8:00 A.M. to 9:00 A.M.                                   15 phone calls/hr*

9:00 A.M. to 4:00 P.M.                                   8 phone calls/hr

4:00 P.M. to 5:00 P.M.                                   8 phone calls/hr

With a total of fifty employees and a total of thirty full - time equivalents (FTEs), the portion of capital expenditures was determined as 1/30 of costs. Phone line charges were determined by a per - line charge, since one server would utilize one line each day. Capacity cost or busy server cost would be equivalent to idle server cost. Regardless of whether or not the receptionist is answering the phone, she is paid the same salary and benefits and is using the same space and utilities. In addition, the practice must pay the phone line and equipment maintenance charges, regardless of usage. For calculation purposes, a value was assigned to the cost of the customer of waiting. A value of $ 50/hour was assigned to customer waiting costs. In reality, though, customer waiting costs

Total Hourly Cost for Busy Server Summary

are likely to vary with the length of time waited, with a steep exponential increase in cost to the patient for longer times waited. Using Excel queuing template, perform a queuing analysis for the pediatric practice's telephone system to determine the optimal server capacity for the volume of phone calls that they receive. Are there enough servers/receptionists and enough phone lines?