The name is absent

AN APPLICATION

The community leaders of Alfalfa County,
Oklahoma, were forced to provide ambulance
service when the private suppliers refused to
continue the service. The leaders were not only
confronted with the expensive problem of pro-
viding one complete ambulance, but also had
to decide whether a back-up ambulance was
needed for a multiple injury accident or over-
lapping requests for service. Alfalfa County
has a population of 7,224; the town of Cherokee
with 2,119 residents is in the center of the
county.¹ A small hospital is located in
Cherokee.

A calculation procedure developed by
Doeksen, Frye, and Green [1] indicated that
335 calls per year could be expected for the
county system. In addition, an analysis of the
previous year’s calls revealed an average round
trip service time of 77.9 minutes. An estimate
of the service rate, u, can be calculated as (60
min∕hr)∕(77.9 min∕call) = 0.7702 calls handled
per hour.

The same method can be used to derive the
annual number of calls consistent with a given
probability of the queue length exceeding the
number of service facilities. A similar method
determines the expected probability of
capacity being exceeded associated with a
given number of annual calls.

Suppose the community leaders are willing
to accept at most a probability of one occur-
rence per year that more than one patient will
require the ambulance at the same time, i.e.,
for the 335 calls expected a = 1/335. For a
single ambulance system, к = 2, and from equa-
tion 5, this probability has an associated traf-
fic intensity ratio, p*, of 0.0546. Solving for v
from the traffic intensity ratio formula, one ob-
tains V = p*u = (0.0546) (.7702) = 0.0421. The
mean arrival rate for service is 0.0421 calls per
hour, which translates into 1.01 calls per day
or 369 calls per year, slightly more than the
335 expected calls estimated previously.

By a reverse method, given that the
estimated number of calls is 335 per year, the
average arrival rate v= (335) (1/365) (1/24) =
0.03824 calls per hour. As before u is 0.7702.
Substituting into equation 4, one obtains

P(>2) = p — (ð ) = 0.00247.

This probability is approximately one occur-
rence in every 400 calls.

To weigh the trade-offs associated with over-
lapping demand, the decision makers must
know the costs of providing a back-up unit.

'1970 Census population estimates. Population has changed very little since 1970.

122

Table 1 shows budgets for the main ambulance,
a new ambulance as a back-up unit, and a used
ambulance as a back-up unit. This budget in-
formation is taken from [1] and is updated to
present prices. It is based on the assumption of
a hospital-based system with four Emergency
Medical Technicians (EMT) and a Licensed
Practical Nurse or a Registered Nurse
accompanying the ambulance on calls. It is as-
sumed that if a back-up is provided, one of the
EMTs will be on call during each eight hours of
the day and will be paid $5 for being on call.
Pocket pagers are provided to allow the EMT
freedom of movement within town.

Estimated yearly costs for providing a one-
ambulance system with the ambulance
replaced after 75,000 miles or every three years
would be $39,053 (Table 1). If the decision
makers provide a new back-up unit, mileage
could be alternated between the vehicles and
each would last six years. Thus, additional
yearly capital depreciation because of the back-
up would be much less than for the original
ambulance. In either case many of the
operating expenses can be allocated between
vehicles. The main additional charge for the
back-up unit is labor costs. Total yearly costs
under these conditions for a new back-up unit
are $8,760. If a used ambulance is purchased as
a back-up unit for $3,000 and is depreciated
over three years, then total yearly costs are
$7,930.

TABLEl. ANNUAL BUDGET FOR
FIRST-RUN AMBULANCE
AND FOR BACK-UP
AMBULANCE

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