A Proposed Scheduling Model

8/6/2019 A Proposed Scheduling Model

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62 Reinus, Enyan, Flanagan, Pim, Sallee, and Segrist

scan. Today, because of helical CT scanning technology, the actual amount of timerequired to scan a patient is only a few minutes, even for a sizable study such asa chest, abdomen, and pelvis. A large amount of the time a patient spends in thescan room is for pre-scan activities, including starting an IV, loading the contrast

injector and giving nal amounts of oral contrast.Because of improvements in CT technology, the traditional design of CT scan-ning facilities has become inefcient (Fig. 1). Care providers are unable to obtainhigh utilization of available resources, and consequently capture potential revenue.Patients, on the other hand, may face long waiting times. Waiting is frustrating,demoralizing, agonizing, aggravating, annoying, time consuming and incredibly ex-pensive. (1) In order to avoid these shortcomings organizations are attempting tobecome more service (customer) oriented. Nowadays, even in health care settings,

patients value their time and are less likely to accept unreasonable waits. (2)

Fig. 1. Traditional single scanner model.


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Improved CT Throughput 63

Little work has been done to evaluate the problem of patient scheduling toimprove scanner utilization. Some early studies have been done to examine clinicaldemand for body CT when it was introduced as a viable clinical modality. (35) Muchhas changed since that time. The question we ask is whether helical scanning

technology, scanning in order to use the scanner more effectively, demands modi-cation of the traditional patient service model of CT. After all, the scanner representsa large xed investment whose xed costs could be reduced on a per patient basisby increasing scanner throughput (Table I).

Queuing theory is a mathematical technique that is useful to study situationswhere individuals wait on line for service. We will use queuing theory to reviewthe traditional model for scanner utilization in a hospital setting and then modifythe system in order to obtain more protable use of the scanner. Seltzer et al. have

shown previously that academic radiology departments can be more productivedespite staff reductions. (6) This observation suggests that there is slack in the system.

METHODS AND MATERIALS

Model Development

The basic queuing system for CT scanning in a hospital is nonpreemptive. Thatis to say there are at least two different classes of scans performedemergent andnonemergent. Patients requiring an emergent CT scan are brought to the head of the queue, but they do not preempt the patient currently on the scanner.

In fact there may be several classes of patients coming to the CT scanner:outpatients, inpatients, and emergent cases. While we assume that outpatients arriveon a set schedule of o, the rate often varies as many are late and others arriveearly. The rate of emergencies cases added on, e, is unpredictable. Similarly, the

scheduling of inpatient add-ons, i, will vary from day to day. If we assume thatwe wish to perform as many scans as possible without incurring overtime charges,then we must also t these patients into the normal working day. These arrivalrates may be summed to give an overall average arrival rate:

o e i .

Considering the variability of all three components of patient arrival rates, wewill assume that patient arrival follows a Poisson distribution over the T timeperiods for which scans are scheduled each working day. In addition we mustconsider that there are two priority classes of patients in this non-preemptive system.One class is nonemergent (average arrival rate: e) and another emergent class(average arrival rate: e).

Because we assume that all patients who require scans during the day can beserviced in the necessary time period, we will have an average service rate, , thatfollows an exponential distribution such that . If the arrival rate were greaterthan the potential service rate, patients would overwhelm the facility. This wouldmean that the number of time periods would have to be extended at the end of the working day in order to accomplish the workload. This, in turn, would mean


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T a

b l e I . H e l i c a l S c a n n e r S c a n R o o m T i m e s b y

S t u d y T y p e ( M i n u t e s )

H e a d C T

H e a d C T

A b d o m e n

C h e s t

R e n a l

w i t h a n d

w i t h o u t

a n d

a b d o m e n

N e c k a n d

s t o n e

w i t h o u t

c o n t r a s t

C h e s t C T

p e l v i s C T

a n d p e l v i s

c h e s t C T

C T

A L L

S a m p l e S i z e

1 8

1 2 7

7 1

2 1 2

5 7

5

1 8

5 0 9

A v e r a g e

2 3 . 2

1 4 . 4

2 0 . 5

2 3 . 9

2 7 . 8

3 6 . 0

1 9 . 1

2 1 . 4

S T D

1 0 . 9

1 0 . 1

8 . 9

9 . 7

1 2 . 0

1 2 . 7

5 . 0

1 0 . 9

M i n i m u m

1 0

5

5

1 0

1 3

1 5

1 0

5

M a x i m u m

5 0

1 1 3

4 7

8 5

8 3

4 7

2 5

1 1 3


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paying overtime and so be undesirable. At this juncture, depending upon costs, thepossibility of adding an additional scanner might be considered.

Accordingly, we may calculate the steady-state waiting time for a member of priority class k, including service time, as:

W k1

AB k 1 B k1

where

A s! s s

s 1

j 0

s

j ! s , B 0 1, B k 1

k

i 1i

sfor k 1 or 2,

and s is the number of scanners in operation at the facility. (7) We assume that allof the scanners at a given institution are the same quality and have the same abilities.

If we assume that subscript 1 represents the emergent class of patients andsubscript 2 represents the nonemergent class of patients, then the explicit averagewaiting times for patients receiving emergent and nonemergent scans are respec-tively:

W e1

s! s s

s 1

j 0

j j !

s 1 e s

1 (1a)

and

W n1

s! s

s 1

j 0

j

j ! s 1 e

s1 e

( e) s

1

1

s!

s 1

j 0

j

j ! s 1 e

s1

s

1(1b)

To determine the average amount of time that a patient spends waiting for service,simply subtract the 1 term (the actual service time for a patient in the scanner)from W k. Furthermore, Littles formula still applies to the individual priority classes.Thus, at steady state the number of patients of priority class k in the system(including those being served) will be L e e W e and L n ( e) W n for emergentand nonemergent patients respectively.

TRADITIONAL SERVICE MODEL

The traditional model for CT scheduling (Fig. 1) allocates a certain numberof patient slots per hour for outpatient appointments. If the scanner is located ina hospital, it is expected that in addition to these designated appointments therewill be a certain number of patients who will require emergency scans throughout


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the day. These emergency patients will be prioritized and moved to the head of the line in a nonpreemptive manner. Similarly, in a hospital-based system therewill be a supply of in-patients who are scheduled for scans and are added onthroughout the day. Most facilities anticipate these last patients by leaving a few

slots in their appointment schedule open for expected in-patients requirements.These slots may be interspersed throughout the schedule or left to the end of the day. Either way, the demand for these slots may be more or less than theallocated number.

Besides scanning, a patient undergoing a scan may require several other servicesthat depend upon the part of the body scanned. In order for the best possible scanto be obtained, the radiologist will need to be intimately aware of the patientsmedical history and certain laboratory values. This means that the radiologist (or

her representative) must spend a few moments interviewing each outpatient, aprocess that on average requires fewer than 10 min. Otherwise, the radiologistmust review each emergency and inpatients chart in order to obtain the pertinentinformation. This review also requires fewer than 10 min on average. Fortunately,this process usually can be carried out while the prior patient is in the scanner andtherefore only impacts the scan schedule for the rst scan of the day. Thus we canignore the time required for the interview when developing the model.

In addition to the pre-scan interview, patients may require that an intravenous

(IV) line be started to allow administration of intravascular contrast material forthe scan. If intravascular contrast is administered, the appropriate dose must bedrawn up into a special syringe that ts an automated injector. Generally theseactivities occur once the patient has entered the scan room. Those patients scheduledto undergo an abdominal scan may also require oral contrast to make the boweleasier to differentiate from other non-viscal structures. Although most of the con-sumption of the oral contrast occurs prior to the patient entering the scan room,a nal cup is often administered immediately prior to scanning. This cup is usually

given while the patient is in the scan room.After completion of the CT scan images, the patient often remains in the

scanner until the scan is reviewed, the images printed and the patient released.With the exception of the scout images and review of the scan, all other

activities may actually be accomplished either before or after the patient has beenin the scanner. We will examine the effect of removing these activities from thepatients scan room time and provide parameters for determining the effects onpatient throughput.

DISTRIBUTED SERVICE MODEL

A system that minimizes the traditional scanner room functions would reducethe amount of time that a patient would have to spend in the scan room. Hence,service time for the portion of the examination where the patient is in the scannerwould be shorter. This would imply the possibility of scheduling patients at a higherrate for scans, i.e., at shorter intervals. Of course, the overall service time for ascan will include the time spent with the other functions necessary to accomplish


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the examination. This overall time could be less, the same or greater than with thetraditional model. Regardless, the time each patient spends in scan room would bereduced drastically using a distributed system.

The distributed model would have the features shown in Fig. 2. Here, the

patients service time in the scanner is minimized and includes only placing thepatient on the scan table, connecting the intravenous contrast to the patients IV,obtaining scout images and obtaining the scan. Administration of oral contrast,starting the intravenous line and preparation of the intravenous contrast boluswould be done prior to the scan. Image processing and reconstruction would be done

Fig. 2. Distributed single scanner model.


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on a slave unita specialized and limited unit devoted to postprocessingafter thescan or using automated lming, a feature available on most late model CT scanners,during the scan.

It is important to note that at steady state, the in-scan-room activities and the

pre- and postscan activities may be pursued contemporaneously in different patients.This means that if our primary interest is improved utilization of the scanner, ratherthan shortening patient service times, we need to focus on the actual amount of time different types of CT scans require.

RESULTS

We will use a simple example with a single scanner to explore the differencesimplied by fragmenting the system into pre-scan, scan and postscan activities. In thisevent the waiting times, including service, for the two classes of patients collapse to:

W e1

1 e

12

e

1 (2a)

W n 1

1 e 1

1 ( )( e) 1 (2b)

In order to evaluate the validity of the model on the current non-distributedsystem we have collected data to verify our assumptions. Using Kolmogorov-Smir-nov test it was veried that patient arrival rates and scan times follow respectivelythe Poisson and exponential distributions that our model assumes. (8) Table I and

Table II show measured scan room times and scan times respectively for severalcommon types of CT studies.

TRADITIONAL SCHEDULING TIME CALCULATIONS

In the traditional system, patients are scheduled at rate of two patients/hour/scanner. Accounting for inpatient cases does not change this rate signicantly be-cause at our facility four service slots are saved for these patients at the end of each day/s schedule. Therefore n 2 patients/hour. Emergency patients mayaccount for between two and six patients per day in this facility. If we assume fourpatients on average, then the arrival interval for emergency patients during workinghours is e 0.5 patients/hour. From the data in Table I, the average time a patientspends in the scanner is approximately 20 min giving a service rate of 3patients/hour.

Thus, for the traditional system, equations 2a and 2b give: W e 20 min 20min and W n 120 min 20 min where the rst time in each equation representsaverage waiting time and the second time represents actual average service time.


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T a

b l e I I .

C T S c a n T i m e s f o r H e l i c a l S c a n n e r ( M i n u t e s )

M e a s u r e d a s t i m e f r o m s c o u t i m a g e t o l a s t i m a g e

C h e s t ,

H e a d w i t h

H e a d

A b d o m e n

A b d o m e n

a b d o m e n

a n d w i t h o u t

w i t h o u t

b e f o r e a n d

a n d

a n d

c o n t r a s t

c o n t r a s t

S i n u s

R e n a l s t o n e

a f t e r c o n t r a s t

p e l v i s

p e l v i s

C h e s t

H i R e s

c h e s t

A L L

S a m p l e s i z e

3

1 3

3

4

2

2 9

1 1

1 6

3

8 4

A v e r a g e

4 . 0

4 . 1

7 . 7

3 . 8

1 3 . 0

7 . 3

1 0 . 9

6 . 4

1 1 . 3

7 . 1

S T D

2 . 6

2 . 3

1 . 2

0 . 5

0 . 0

2 . 6

5 . 0

2 . 8

0 . 6

3 . 7

M i n i m u m

2

1

7

3

1 3

4

7

3

1 1

1

M a x i m u m

7

9

9

4

1 3

1 5

2 5

1 4

1 2

2 5


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This means that despite the fact that e n, at steady state routine patientswill wait 2 hr on average for service. Emergent patients will wait a period of oneaverage service time, i.e, 20 min.

Distributed System Time Calculations

The data in Table II show that different types of studies require differentaverage helical scan times. Besides the measured time for the scan, we assume thatwe must allow 3 additional min for patient entry and exit from the scanner alongwith any necessary housekeeping chores. This means that on average the actualtime a patient spends in the scanner room will be 7 min for a head CT withoutcontrast, 7 min for a head CT with contrast, 8 min for a chest CT and 10 min for

an abdomen and pelvis CT using the distributed model (Fig. 2). For simplicityssake, we assume that the average of all the times measured in Table II (plus 3 minentry and exit time) represents a reasonable estimation of the service intervals forpatients entering the scan room. This means the service rate for nonemergentpatients would be 6 patients/hr. The emergent patient arrival rate, e, will beunchanged compared with the traditional model.

Assuming that the total service time for all scan-related activities would bethe same as in the traditional model, the pre-scan and postscan activities would

together take 10 min. The post scan activities should be minimal and we will assign1 min to this activity ( 60). We will assign the remaining 9 min of service time( 6.67) to the pre-scan activities, including starting an IV when necessary,drawing up the IV contrast into a syringe and administering the nal cup of oral con-trast.

The distributed system can be analyzed by evaluating each part individually. (7)Hence, the expressions presented earlier for the traditional system can be appliedto each part of the distributed system (with the only change being to use the

appropriate service rate). Consequently, using these parameters, we may calculatethe total wait time including service time, W T, that a patient will experience in thedistributed model. This time will be the sum of the total wait times for the pre-scan, scan and postscan activities: W T W pre W scan W post Tr, where Tr represents an additional amount of time required to walk patients from one locationto the next.

Given that scheduling is unchanged from the traditional model, the arrivalrates will also be unchanged. This means that we can calculate the activity times foremergent and nonemergent patients from equations 2a and b under the distributedsystem as shown in Table III.

Table III. Total Wait Times for Distributed Model (Single Scanner)

e W non (minutes) W emerg (minutes)

W pre 0.5 2.5 6.67 5.8 9 3.6 9W scan 0.5 2.5 6 7.8 10 4.5 10W post 0.5 2.5 60 0.04 1 .04 1W T Tr 13.64 20 8.14 20


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As this table shows, redistributing the services normally provided in the scanshould substantially reduce the time a patient, either nonemergent or emergentwill spend waiting for service. Compared with the traditional model the timesavingsare 106.36 (89 % ) and 11.86 (59 % ) min for these patients respectively. Even assuming

a total transfer time, Tr , of 2 min, the distributed system still should provide muchimproved service over the traditional system. Of course, as Table III shows, theactual service times will be identical in total.

We should also point out that these wait times only apply to a system in steadystate. Since most scanners shut down for some period of the day, steady state willonly represent a small part of the schedule. Prior to achieving steady state, the waittimes will be building to this time and hence be shorter. Regardless, the distributedsystem shows superior service performance compared with the traditional system.

Determining the Desired Arrival Rate

For the purposes of comparing the two models, we assumed that the patientarrival rates were the same in each. Given that the distributed system providessuperior service, we may choose an average arrival rate that will create optimalwait times. If we determine that we want a nonemergent patient to wait no morethan z times the time they will spend in the scanner, then W n (z 1)/ . Based

upon these criteria we can calculate the desired nonemergent patient arrival interval.Substituting we have:

z 12

e e

1

z 2 z e(z 1) z e

Since n e,

nz 2 z e

(z 1) z ee

z 2 (2z 1) e z 2e(z 1) z e

(3)

This means that if 6 patients/hour and as before e 0.5 patients/hour, thenwe can calculate the steady-state average number of nonemergent patients thesystem can handle in an hour for different waiting times expressed as a multipleof .

As can be seen from Table IV and Fig. 3, increases in permissible wait timesbefore service do not necessarily cause substantial increases in patient throughput.This is a function of the fact that patients come in whole, not fractional, units. Amore important implication of this table is that given the laws of inertia, patientwait times will likely be at their maximum for any given scheduling interval. Thus,for scheduling intervals of 15 and 14 min, the patient wait times are likely to be 35and 50 min, respectively.

Wait times are not necessarily undesirable. They represent time that can beused to accomplish other pre-scan activities. Thus for CTs requiring IV contrast,the time could be used to start the patients IV (or check an existing one), and


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Table IV. Wait Time, Arrival Rate and Appointment Interval asa Function of Multiples ( z) of Service Rate 6 pts/hr

Desirednonemergent Appointment

Total wait arrival rate intervalz (minutes) (patients/hour) (minutes)0.5 5.0 1.4 431 10.0 2.4 251.5 15.0 3.0 202 20.0 3.4 182.5 25.0 3.7 163 30.0 3.9 153.5 35.0 4.1 154 40.0 4.2 144.5 45.0 4.3 145 50.0 4.4 145.5 55.0 4.5 136 60.0 4.6 136.5 65.0 4.6 137 70.0 4.7 137.5 75.0 4.7 138 80.0 4.8 138.5 85.0 4.8 129 90.0 4.9 129.5 95.0 4.9 12

10 100.0 4.9 1210.5 105.0 4.9 1211 110.0 5.0 1211.5 115.0 5.0 1212 120.0 5.0 12

prepare the contrast syringe. If we assume that these two activities together take20 min, we could set the scheduling interval to provide waiting times that are at

least 20 min long. Similarly, if it takes on average an hour to contrast the bowelfor abdominal CT, then the scheduling interval for abdominal CT could be set sothat the expected waiting time would accommodate this need.

DISCUSSION

Hospitals with multiple scanners may consider dedicating machines or portionsof machine days to certain types of scans. The disparity in time required to performdifferent types of scans (range: 3.515 min) suggests that dedicating machines toparticular types of scans may be efcacious because it would allow optimization of scheduling intervals for the scanner. For example, head CTs take only 3 or 4 min.This suggests that scheduling a machine only for head CTs could result in a veryefcient use of the dedicated machine. If we take the service interval to be 7 minfor the average head scan, then we should be able to schedule nine patients/hourand their wait for service would be less than 6 or 7 min.

An even more sophisticated scheduling technique might be to schedule exami-nations so that the build time to steady state is accelerated. This would mean


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F i g

. 3

.

W a i t t i m e s a n d a p p o i n t m e n t i n t e r v a l a s a f u n c t i o n o f a r r i v a l r a t e ( s e r v i c e r a t e

6 ) .


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scheduling shorter examinations earlier in the day and setting arrival times forexaminations with long pre-scan activity requirements to coincide with the initialshort examinations. For example, an outpatient schedule could be arranged to startwith several head CTs while other patients were reporting for bowel contrasting

for their abdominal CTs.The other side of the coin, in terms of schedule optimization, is the few casesthat require extensive equipment and personnel to accompany an extremely sickpatient to the scanner. Such cases, e.g., intubated patients, will inevitably causesevere perturbations in a steady state schedule. This would mean that these patientsshould be done as late as possible during the scheduling day. Unfortunately, thesepatients often require emergency scanning and even if they arent emergent arebest brought to the department when there is a full complement of personnel

available to care for the patient. Hence, late scheduling for these patients becomesimpractical. An alternative solution for these schedule buster patients in an institu-tion with multiple scanners would be to have a machine dedicated to difcultcases so as to minimize workow perturbations.

Another problem is patients who require further scans after the initial setof images, e.g., high resolution images, unexpected administration of intravenouscontrast or rectal contrast. Under most current scheduling systems, patients maylanguish on the scan table until a radiologist makes a determination that no further

imaging is necessary and releases the patient. The radiologist, because of availability,may not immediately review the patients scan and so delay the schedule. Twopotential solutions exist to this problem.

One solution to this problem is to keep a physician or other responsible personpresent in the scan room to make the release/rescan determination as the patientsscan is completed. Except in teaching institutions, this policy may prove to be aninefcient use of this individuals time. In a teaching institution, a student, e.g.,resident, actually may prot from such a triage type of role. (This individual also

might be the same individual responsible for interviewing patients pre-scan andsetting the scan protocol.)

The other solution is to remove all patients from the scan room immediatelyupon completion of the scan. The patient would be kept in the imaging waitingarea until the individual responsible for releasing the patient reviews the scan. If additional images need to be obtained then the patient would be taken back intoa scan room. For outpatients, this process should function smoothly. For inpatients,this system may pose a problem if the patient is severely debilitated. These are thepatients, however, who more than likely should have contemporaneous monitoringof their scan.

Regardless, a system of removing patients from the scanner immediately afterscanning may cause the patient to spend a greater overall time obtaining a scansince this process may increase their post scan activities. It is essential to understandthat the potential for increased overall scan time with this system does not arisefrom the patient waiting for scan review and determination of scan completion.This is merely time that the patient would have spent in the scanner in the traditionalsystem. What may increase the overall wait is the time required to put the patientsback into a scanner for further imaging. Most likely, the overall additional time


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fostered by this system will be small in contrast to a policy of leaving patientson a scanner pending image review, especially if few patients actually requirefurther imaging.

Another important issue to consider is the total time a patient spends at the

CT imaging facility. Using the traditional model, the steady state time that a patientspends in a single scanner system will, on average, be over 2 hr. This waiting timemay or may not be used productively.

In the distributed model there is a possibility to use the waiting time produc-tively and thereby telescope the waiting time for each portion of the scanningprocess. To accomplish this efciency will require adequate personnel and equip-ment to handle the pre-scan and post-scan activities associated with a patients scan.The waiting time would occur in three segments, where only the rst one (with

average of 5.8 min for nonemergent patients) takes place prior to any process. Theother two segments (7.8 and 0.04 min) would arise after patients have been alreadyreceived some treatment. In situations like this where waiting is broken into smallerperiods, studies have shown that the waiting times do not feel as long. (9)

The distributed system may require additional personnel to handle the pre-scan activities such as starting IV lines, giving oral contrast, lling the IV contrastsyringe and getting the patients clothes changed. These added personnel costscould only be justied if the distributed model provides adequate savings over the

traditional service model. Rhea et al suggested that taking a systems approach toCT scanning could reduce costs and increase patient throughput as much as 25 %by adding a single extra technologist. (10)

According to our calculations, serving only one more patient per scanner perhour using the distributed queuing model would represent an increase in expectedservice by 40% ( ). Such an increase in patient throughput may allow the imagingfacility either to perform a higher volume of scans during the working day or tomaintain their volume with fewer scanners. In the case of the former, each scanner

would be performing at least eight additional scans per day. If the usual 18 to 20scans/day allow an imaging facility to man and pay overhead on a scanner, thenclearly the addition of eight scans would permit hiring more FTEs to man thescanner.

On the other hand, if the center had a minimum of three scanners, it couldeliminate at least one of them using the distributed model. The elimination of ascanner (cost in the vicinity of $1,000,000/scanner), its debt service and maintenancecosts, the resulting decreased physical plant requirement and the decreased FTEsrequired to man the scanner would result in substantial savings. Hence properimplementation of the distributed service model should provide more than adequaterevenue either in the way of increased scan volume or capital savings in the caseof fewer scanners. Both the revenue and the savings should be enough to permitthe addition of FTEs responsible for the activities necessary to perform both beforeand after patient scanning. Indeed, assuming that the scanning facility meets over-head costs, both variable and xed, this increase in efciency should improve thecontribution margin to the imaging facility from the scanner.

In summary, proper implementation of a distributed model of CT scan queuingshould increase the efciency of scan throughput and decrease steady-state waiting


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times. The key is to minimize the amount of time a patient spends in the scan roomand to set the waiting time so that other functions telescope appropriately into thewaiting period. This increased efciency can in turn be used either to increaserevenue through increased patient volume per unit time or decrease costs through

elimination of expensive xed overhead. Finally, by dividing the scanning processinto multiple smaller tasks, the patient may feel better attended than with thetraditional model, particularly since there will be more personnel manning the site.

ACKNOWLEDGMENT

We would like to thank Stuart Sagel, MD FACR for his review and comments

on this manuscript.

REFERENCES

1. Federal Express, Fortune, July 28, 1980, p. 10.2. Kleineld, N.R., Conquering Those Killer Queues, The New York Times, September 25, 1988.3. Winter, J., Efciency of utilization of a computed tomography scanner. AJR 131:8993, 1978.4. Evens, R.G., and Jost, R.G., Economic analysis of body computed tomography units including data

on utilization. Radiology 127:151157, 1978.5. Evens, R.G., and Jost, R.G., Economic analysis of computed tomography units. AJR 127:191198, 1976.

6. Seltzer, S.E., Saini, S., Bramson, R.T., Kelly, P., and Levine, L., Can academic radiology departmentsbecome more efcient and cost less? Radiology 209:405410, 1998.

7. Hillier, F.S., and Lieberman, G.J., Introduction to Operations Research, McGraw Hill, 6th Edi-tion, 1995.

8. Conover, W.J., Practical Nonparametric Statistics. Wiley, 3rd Edition, 1999, p. 430.9. Maister, D.H., The Psychology of Waiting Lines, The Ser v ice Encounter, (J.A. Czepiel, M.R. Solo-

mon, and C.F. Surprenant, eds.), Lexington Books, 1985.10. Rhea, J.T., Thrall, J.H., Saini, S., and Sumner, J., Improving the efciency and service of computed

tomographic scanning. Acad. Radiol. 1:164170, 1994.

A Proposed Scheduling Model

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