from emergency department to hospitalization: using ... · pdf file1 introduction and...

From Emergency Department to Hospitalization:Using Simulation, Empirical and Theoretical Models forthe Operational Analysis of ED, IW, and their Interface

or

Emergency Department, Hospitalization (or IW), andeverything in between: Using Simulation, Empirical and

Theoretical Models for the Operational Analysis ofHospitals

January 8, 2009

Avishai Mandelbaum • Yariv Marmor • Yulia Tseytlin • Galit Yom-Tov

Faculty of Industrial Engineering and Management,Technion – Israel Institute of Technology, Haifa, 32000, ISRAEL

[email protected] • [email protected] • [email protected] •[email protected]

Abstract

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Contents

1 Introduction and Literature Review 3

1.1 Background: Hospital, ED and IW . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Process Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 ED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.2 ED to IW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 IW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1

2 Analysis of the collected data and validation of the empirical and simula-

tion models 16

2.1 Empirical Analysis of Emergency Department . . . . . . . . . . . . . . . . . 16

2.1.1 Arrival, Departure, and Occupied Beds rate in the ED . . . . . . . . 16

2.1.2 Length Of Stay (LOS) in the ED . . . . . . . . . . . . . . . . . . . . 18

2.1.3 The impact of Bed Occupancy on LOS . . . . . . . . . . . . . . . . . 18

2.2 Empirical Analysis of Internal Wards . . . . . . . . . . . . . . . . . . . . . . 23

2.2.1 Length Of Stay (LOS) in the IW . . . . . . . . . . . . . . . . . . . . 23

2.2.2 Arrivals and Departures in the IW . . . . . . . . . . . . . . . . . . . 23

2.2.3 Determining Length Of Stay in IW as a function of the work load (see

Appendix A - 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Empirical Analysis of Transfers in the system . . . . . . . . . . . . . . . . . 31

2.3.1 Waiting times from ED to IW . . . . . . . . . . . . . . . . . . . . . . 31

2.3.2 Waiting times from ED to ICU . . . . . . . . . . . . . . . . . . . . . 31

3 Analysis of the system (using combined simulation and/or analytical mod-

els). 32

3.1 Two interesting questions for ED . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Two interesting questions for IW . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3 Two interesting questions for the transfer process from ED to IW . . . . . . 32

3.4 Two interesting questions for the whole process . . . . . . . . . . . . . . . . 33

4 Special events 33

A Meetings summary 35

2

1 Introduction and Literature Review

Health care systems in general, and hospitals in particular, represent a very important part

of the service sector. Over the years, hospitals have been successful in using medical and

technical innovations to deliver more effective clinical treatments while reducing patients’

time spent in the hospital. However, hospitals are typically rife with inefficiencies and delays,

thus present a propitious ground for many research projects in numerous science fields, and

in the Operations Research field in particular.

A hospital is an institution for health care, which is able to provide long-term patient

stays. Hospitals include numerous medical units specializing each in a different area of

medicine, such as internal, surgery, intensive care, obstetrics, and so forth. In most of the

large hospitals there are several similar medical units operating in parallel. In our research

we focus on an Emergency Department (ED), five Internal Wards (IW) and an interface

between them in Rambam/ Anonymous? Hospital.

This report is structured as follows: first we provide a background on the hospital, the

medical units in question, the problems involved, and survey the relevant literature. Then

...

1.1 Background: Hospital, ED and IW

Anonymous Hospital is a large Israeli hospital with about 1000 beds, 45 medical units,

and about 75,000 patients hospitalized yearly. Among the variety of its medical sections,

the hospital has a large Department of Emergency Medicine with a capacity of 40 beds; and

five Internal Wards, denoted from A to E.

The ED receives and treats more than 200 patients daily, and is divided into two major

subunits: Internal and Trauma (surgical and orthopedic patients), each of those is divided

into “walking” and “lying” subunits, according to the state of patients treated there. An

internal patient, whom the ED decides to hospitalize, is directed to one of the five Internal

Wards according to a certain routing policy - and this process is precisely our focus of

interest.

Internal Medicine Departments are responsible for the treatment of a wide range of

internal disorders, providing inpatient medical care to thousands of patients each year. Wards

A-D are more or less the same in their medical capabilities - each can treat multiple types

3

of patients. Ward E, on the other hand, treats only “walking” patients, and the routing

process from the ED to it differs from the one to the other wards.

1.2 Process Charts

Below we describe the simulation models (ED, ED to IW, and IW) by using flow charts,

such as Resources Flow charts, Information Flow charts, Activities Flow Charts, and Activ-

ities - Resources Flow Chart.

1.2.1 ED

When patients arrive to the ED, either walking or assisted by a stretcher or wheelchair, the

first step is assessment, which is typically followed by directing the patients to an appropriate

bay where they wait for their next stage of treatment. This stage of the medical-process is

called Triage if performed by the medical staff (nurse or physician). There are possibly pro-

cedures prior to the Triage, which include an initial assessment, by medical and non-medical

personnel, such as clerks and ambulance officers (Brentnall 1997), and/or the initiation of

diagnostic tests, by a (registered) nurse (Cheung et al., 2002). Such pre-Triage steps aim at

accelerating patients flow.

In the following figures, we depict the overall patient’s process within the ED, from

some varying point of views: a precedence diagram of activities, patients’ flow among the

resources, a combined activity-resource diagram, and information flow.

1.2.2 ED to IW

One can fully appreciate the complexity of the process in the Integrated (Activities - Re-

sources) Flow Chart (see Figure 5) and other flow charts (see Figures 6, 7 and 8).

1.2.3 IW

4

) 08/01/2009(

4

Figure 1 - Activity (Flow) Chart

Labs

Treatment

Awaiting

evacuation

Administrative reception

Vital signs & Anamnesis

First

Examination

Imagine:

X-Ray, CT,

Ultrasound

Follow-up

Instruction prior

discharge

Waiting

hospitalized

Administrative discharge

Consultation

Decision

A A A B

B

B

C

C C C

C

Alternative Operation -

Ending point of alternative operation -

C

Figure 1: Activities Flow Chart in the ED

5

) 08/01/2009(

5

Administrative secretary

Nurse

Labs

Physician

Consultant

CT

X-Ray

Ultrasound


Recourse Queue - Synchronization Queue –


C

Figure 2 - Resource (Flow) Chart

A

A

A

A

A A B

B

B

B

B

C

C D

D

Figure 2: Resources Flow Chart in the ED

6

) 08/01/2009(

6


Figure 3 - Information (Flow) Chart

Backgrounds

Receptions

Family doctor/ Internet/

Community

Clinical Information

Nursing Information

Nurse

Physician

Test tube and results

Labs

Shot result or prognosis

Imagine


Consult

Collecting ResultNurse


Coordination with outsources

Nurse / ED Receptions

Figure 3: Information Flow Chart in the ED

7

) 08/01/2009(

7

Figure 4 - Activities-Resources (Flow) Chart

Physician NurseImagineLabOther

Follow-up

Instruction prior discharge

Awaiting evacuation

Administrative release

First

Examination

Decision

Labs Treatment

Administrative reception

Vital signs & Anamnesis

Imagine:

X-Ray, CT, Ultrasound

Treatment

Consultation

First Examination


Recourse Queue - Synchronization Queue –


C

A A A A B

B

B

C

C

C

Figure 4: Activities - Resources Flow Chart in the ED

8

Figure 5: Integrated (Activities - Resources) Flow Chart

ED physician

IW nurse, Help force

Stretcher Bearer

IW nurse in charge

General NurseReceptionistED nurse in

chargeIW

physician

Hospitaliza-tion

decision

Patient allocation request

Transferal time

decision

Patient’s status

updating

Coordination with the IW

Running the Justice Table

Request skipping?

Approve skipping?

Initial measurements

collection

Patient’s transferal

Availability check

Bed preparation

Initial medical check

Yes

No

YesNo

Resource Queue - Synchronization Queue -

Availability check

Ventilated patient

- Ending point of simultaneous processes

Transferal time

decision

“Walking patient” Ward E

Ward E

Ward E

9

Figure 6: Activities Flow Chart

Hospitalization decision

Assigning Ward (A-D) with the Justice Table

Ward requests skipping

Transferal time decision

Patient’s status updating

Management approves skipping

Bed preparation

Yes

No

Yes

No

Initial measurements collection

Transferal to the Ward

Initial physician check

Coordination with medical staff

Ventilated patient?

No

YesCoordination with medical staff in

the ED

“Walking” patient? Yes

No

Assigned to Ward E

* Processes in broken line occur in the IW


Ward E

Wards A-D

Bed preparationWard E

10

Figure 7: Resources Flow Chart

Resource Queue - Synchronization Queue -

ED physician

ED nurse in chargeReceptionist IW nurse in

charge

General Nurse

IW physicianStretcher Bearer

Help forceIW nurse

Allocation

Skippingrequest

Ventilated patient


Transferal

Measurements

Medical check

Coordination

11

Figure 8: Information Flow Chart

ED medical file

ED physician

Type (regular, special care, ventilated)

ED nurse in charge

Allocation: Ward A-D

Receptionist

Transfer time

IW nurse in charge

Skipping granted/ not granted

General nurse

Skipping request + reasons

IW nurse in charge

Patient’s status updating

ED nurse in charge

Type + medical information

ED nurse in charge

Preparation for patient’s admission

IW nurse in charge

Medical check results

IW physician

Initial measurements results

IW nurse in charge

Availability check

Bed readiness check

Help force

Clinical information

ED physician

Ventilatedpatient

Transfer time updating

ED nurse in charge

Availability check


Availability check

ED physician or nurse

Ventilatedpatient

Ventilatedpatient

IW nurse

IW physician

12

1.3 Literature Review

OR in health care - general (Green): [4], [5]

Yariv’s simulation: [7]

The Impact of Work Load on LOS: [3]

Some more on hospitals...: [1], [6], [2]

Add: Galit’s thesis, paper about measures, Yulia’s and Asaf’s project, more?

1.4 Measurements

As it was shown in above, the ED presents a very complicated service system. As we

know, every patient that enters the hospital implies a certain amount of workload on the

system. The uniqueness of the ED emerges from several facts (but these facts are true for

all the wards?):

1. Each patient undergoes few processes in the ED, and some of them are recurrent. For

example, a typical walking patient’s routing might be: nurse, doctor, blood test, nurse,

doctor.

2. There are several types of patients (internal, surgical, walking, lying etc.), and each

type requires different resources of the ED.

3. The arrival process to the ED is time-dependent.

These facts might arouse difficulties in using the typical OR measurement - some measure-

ments require adjustments. From the literature we learn about several measurements that

were designed exclusively for measuring ED workload, such as EDWIN, NEDOCS, READI

and Work Score (add reference).

1.5 Data Description

This documentation describes patient-level data at Emergency Department of “Anony-

mous” Hospital in Israel. The data was recorded over the following periods: 1/1/2004 -

1/12/2008. There are four compatible tables, that describe the hospital operations. The

first table (ED) contains the following individual patient’s arrivals data records: The details

of the patients and time stamp of his arrival and his departure. The second table (Jus-

tice Table) contains the details of the patients transferred from ED to IW. The third table

13

(Hospital Transfers) contains individual patient’s arrivals and departures records from hos-

pital’s wards. The fourth table (OR) contains individual patient’s arrivals and departures

records from hospital’s operation rooms.

We now present the field descriptions for each of the tables.

1. ED Table

• key - a unique number identifies each patient. The hospitals replaced the patients

ID numbers with a unique generate number.

• AdmissionNo - Patients in ”Anonymous ED” are identified by a serial num-

ber starting with the year and continued by sequential 6 digits number (e.g.

1999000001)

• AdmissionDate - The patient’s arrival time and date. It is recorded when the

admission secretary type the patient into the system. The format is ”dd/mm/yyyy

hh:mm:ss”.

• Discharge - The patient’s departure time and date. It is recorded when the ad-

mission secretary type the patient into the system. The format is ”dd/mm/yyyy

hh:mm:ss”.

• SubUnitID - The code type of ward where the patients are admitted in the ED

(as typed by the admission secretary). The explanations of the codes are given in

the next column. (5 digits)

• UnitName- The name of the ward where the patients are admitted in the ED.

• BirthDate - The patient’s day of birth.

• Gender - The gender of the patient (”M” for male and ”F” for female).

• AdmissionCode - The code describing the patients general cause of admitting (as

typed by the admission secretary). The description of the code is listed in the

next column.

• AdmissionDesc - The description of the patients general cause of admitting.

• SendByCode - The code describing the authority that sends the patients to the

ED (as typed by the admission secretary). The description of the code is listed

in the next column.

14

• SendByDesc - The description of the authority that sends the patients to the ED.

• SendLetter - The presence / absence of an application letter from the authority

that send the patients to the ED. (”Y” for presence and ”N” for absence).

• ComplainRsnCode - The code describing the patient’s complains in his arrivals

to the ED (as typed by the admission secretary). The description of the code is

listed in the next column.

• ComplainRsnDesc - The description of the patient’s complains in his arrivals to

the ED.

• BodyPartCode - The code describing the patient body part on which he com-

plained for admitting (as typed by the admission secretary). The description of

the code is listed in the next column.

• BodyPartDesc - The description of the patient body part on which he complained

for admitting.

• ArrivalStateCode - The status code of the patient arrivals (as typed by the ad-

mission secretary). The description of the code is listed in the next column.

• ArrivalStatusDesc - The description of the patient’s status arrivals to the ED -

wheelchair / stretcher.

• ProcedureCode - The code describing the procedures the patient went through

while in the ED (the procedures that the staff typed into the patient’s log). The

details are listed just for the patients that released from the ED. The description

of the code is listed in the next column.

• ProcedureDesc - The description of the procedures the patient went through while

in the ED.

• ReleaseStatCode - The status code of the patient departure from the ED (as

typed by the admission secretary). The description of the code is listed in the

next column.

• ReleaseStatDesc - The description of the patient departure from the ED.

• Ward - The ward where the patient is hospitalized to .

15

2 Analysis of the collected data and validation of the

empirical and simulation models

2.1 Empirical Analysis of Emergency Department

As we started investigating the database that we have on the ED, we have found four different

patients types: Internal (Int), Surgical (S), Orthopedic (O), and Trauma (Trauma) patients.

We also know from the hospitalization data, which of the patients were sent to ICU, and

which of the patients were sent to semi-intensive care units. We have marked those patients

by their future severity classes as ’ICU’ and ’V’ respectively. Those not belong to ICU nor

to V classes were marked as regular patients (R). In Figure ?? we can see the number of

patients in each category.

Table 1: Number of Patients in each category

ED Type R ICU V Total

Int ED 257,708 (97%) 5,915 (2%) 2,782 (1%) 266,405 (59%)Ort ED 109,941 (100%) 212 (0%) 49 (0%) 110,202 (25%)Surg ED 67,045 (98%) 1,194 (2%) 65 (0%) 68,304 (15%)Tra ED 2,237 (56%) 1,687 (42%) 52 (1%) 3,976 (1%)Total 436,931 (97%) 9,008 (2%) 2,948 (1%)

In the following subsections we shall show the arrivals, departures, and occupied beds

rate. We shall analyze the Average Length of Stay (ALOS) of the different types of patients.

Finally, we shall try to show how the crowdedness in the ED can influence the patients’

ALOS.

2.1.1 Arrival, Departure, and Occupied Beds rate in the ED

We shall start by analyzing the arrivals rate from a database of about four years. In Figure

9 we can see the minor fluctuation of the arrivals over time, except in a distinguished period

of two months around June 2006. It seems that a war fought in the north of Israel had

an influence on the arrivals rate. From Figure 10 we can see more clearly that in the two

months of war the regular patients rate (Int, Ort, and Sur) dropped rapidly, while the rate

of patients that need more intense care, such as Trauma patients, dramatically increased.

The next step is to look on the time variation during a day. As the day of week is

influencing the patient’s arrivals patterns, we have analyzed those separately. Figure 11

16

0

20

40

60

80

100

120

140

160

180

2004

_01

2004

_04

2004

_07

2004

_10

2005

_01

2005

_04

2005

_07

2005

_10

2006

_01

2006

_04

2006

_07

2006

_10

2007

_01

2007

_04

2007

_07

2007

_10

2008

_01

2008

_04

2008

_07

2008

_10

Time [Year_Month]

Dai

ly A

vera

ge A

rriv

als

Int_ED Ort_ED Surg_ED Tra_ED

Figure 9: ED Arrival rate by Time

0%

50%

100%

150%

200%

250%

300%

350%

400%

2004

_01

2004

_04

2004

_07

2004

_10

2005

_01

2005

_04

2005

_07

2005

_10

2006

_01

2006

_04

2006

_07

2006

_10

2007

_01

2007

_04

2007

_07

2007

_10

2008

_01

2008

_04

2008

_07

2008

_10

Time [Year_Month]

Dai

ly A

vera

ge A

rriv

als

[%]

Int_ED

Ort_ED

Surg_ED

Tra_ED

Figure 10: Percentage of ED Arrival rate by Time

17

shows us the arrival, departure and occupied beds pattern of Orthopedic (O) patients during

Sunday. We can see that all measurements have low rate during the night. The arrival rate

is getting to its first peak at 11 AM, while the number of beds and departure rates are

keep climbing until late afternoon. The same pattern we can see with Internal (Int) patients

during Sundays on Figure 12.

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

Am

ount

of P

atie

nts

/ Bed

s

Arrived Departured Occupied Beds

Figure 11: Arrivals, Departures, and Occupied Beds for Orthopedic patients on Sundays

2.1.2 Length Of Stay (LOS) in the ED

Figure 13 shows the LOS distribution of the four ED patients. It can be seen that, excluding

some very short stays, the gamma and log-normal distributions fit the data well.

We have further investigate the influence of the severity of the patients on the LOS

distribution. In Figure 14, and Figure 15, we can see that the higher the severity the shorter

the patient stays in the ED.

2.1.3 The impact of Bed Occupancy on LOS

Figure 16 shows the ALOS of the four ED patients type by their Regular Severity Beds

Occupancies. We see that ALOS is starting to increase when the Occupancy rate is rising,

until a certain point when it stopped influencing the LOS, and when the occupancy is in its

peak, the LOS start to decrease. We can provide the following psychological explanation:

When the ED is empty, each patients adds to the staff load, and the patients waiting times

18

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

Am

ount

of P

atie

nts

/ Bed

s [%

]Arrived Departured Occupied Beds

Figure 12: Arrivals, Departures, and Occupied Beds rate for Internal patients on Sundays

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Oth

er

LOS [Hour]

Freq

uenc

ey

Int_ED

Ort_ED

Surg_ED

Tra_ED

Figure 13: LOS (hours) in the ED by Patient Type

19

0%

20%

40%

60%

80%

100%

120%

0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600

LOS

Acc

umul

ated

Fre

quen

cyInt_ED, R Int_ED, ICU Int_ED, V

Figure 14: LOS (Minutes) of Internal Patient by Severity

0%

20%

40%

60%

80%

100%

120%

0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600

LOS

Freq

uenc

y

Tra_ED, R Tra_ED, ICU Tra_ED, V

Figure 15: LOS (Minutes) of Trauma Patient by Severity

20

start to increase. When the ED start to be overcrowded, the staff gives high priority to the

patients that are waiting to leave the ED and promote them in the queues.ED_Clean_Q_new2 By (AvgQ)- Overlay Plot Page 1 of 1

0

1

2

3

4

5A

LOS

[Hou

r]

-5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Average Occupancy of Regular Beds

Overlay Y's

Y ED_Int ED_O ED_S ED_Trauma

Overlay Plot

Figure 16: ALOS (hours) in the ED by Regular Beds Occupancy for each Patient Type

Figure 17 shows the ALOS of the four ED patients type by the average amount of

ICU cases the patients saw while in the ED. It seems that Internal and Surgical patients

LOS decrease while the amount of ICU cases the ED exposed to while in the system. The

explanation could be that the staff knows in advance when ICU patients are expected to

arrive. It could force them to give high priority for preparing patients for departure. Figure

18 shows the ALOS of the Internal patients by the average amount of V cases the patients

saw while in the ED. It seems that Internal ICU patients are not influence by the amount

of V cases, while both V and Regular Internal patients mostly go faster out of the ED when

the number of semi-intensive cases are in the ED. Since these last two figures are not easily

explained, we can provide kind of mathematical explanation: The ICU and V patients are

relatively sparse, and seeing on average couple of cases during patients stay is more rare.

The shorter the stay the higher the chance of catching more rare events on average, and

not vice versa. Therefor, more investigation is needed before making any assumption on the

influence of ICU and V beds occupancy on the ALOS.

21

Journal: Untitled 3 Page 1 of 1

0

1

2

3

4

5A

LOS

-1 0 1 2 3 4Average Occupancy of ICU Beds

Overlay Y's

Y ED_Int ED_O ED_S ED_Trauma

Overlay Plot

Figure 17: ALOS (hours) in the ED by ICU Beds Occupancy for each Patient Type


0

1

2

3

4

5

ALO

S

-1 0 1 2 3 4 5Average Occupancy of V Beds

Overlay Y's

Y ED_Int R ED_Int ICU ED_Int V

Overlay Plot

Figure 18: ALOS (hours) in the ED by V Beds Occupancy for each Patient Type

22

2.2 Empirical Analysis of Internal Wards

2.2.1 Length Of Stay (LOS) in the IW

As a first stage we would like to investigate the distribution of LOS in the various departments

of the hospital. We can find various patterns in the LOS distribution. Figures 19 and 20 show

the LOS distribution in one of the Internal Wards. It can be seen that, when considering

daily resolution, the gamma and log-normal distributions fit the data well. The second graph

is on hourly resolution and illustrates the impact of the discharge policy: the decision on

discharging patients is done once a day, hence the stay distribution has peaks in jumps of

24 hours.Journal: Untitled 2 Page 1 of 1

0.03

0.05

0.08

0.10

0.13

Pro

babi

lity

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

MeanStd DevStd Err Meanupper 95% Meanlower 95% MeanN

6.45246747.38443520.07987496.60904166.2958933

8547

MomentsLOS_days

0.01

0.01

0.01

0.02

0.03

0.03

0.04

Pro

babi

lity

0 6 12 21 30 39 48 57 66 75 84 93 102 114 126 138 150 162 174 186 198 210 222 234 246 258 270 282 294


154.85922177.226451.9169981

158.617151.10144

8547

MomentsLOS_hous

LOS (days)

LOS (hours)

Figure 19: LOS (days) in internal ward A


0.03

0.05

0.08

0.10

0.13

Pro

babi

lity

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50


6.45246747.38443520.07987496.60904166.2958933

8547

MomentsLOS_days

0.01

0.01

0.01

0.02

0.03

0.03

0.04

Pro

babi

lity

0 6 12 21 30 39 48 57 66 75 84 93 102 114 126 138 150 162 174 186 198 210 222 234 246 258 270 282 294


154.85922177.226451.9169981

158.617151.10144

8547

MomentsLOS_hous

LOS (days)

LOS (hours)

Figure 20: LOS (hours) in internal ward A

2.2.2 Arrivals and Departures in the IW

Patients arrive to the hospital on random times according to Poisson process with time

dependent arrival rate (prove!!). Most patients arrive to the ED during the day (see Figure

??). The process of admissions to the wards (transferals from the ED) has the following

pattern: most of the patients arrive between 15:00 - 24:00, and depart between 13:00-17:00.

Thus, the number of patients in the ward during the afternoon hours (when the rate of

23

arrivals and departures is high) is significantly lower then the average number of patients

during the whole day or during the patients’ stay. For example Figure 21 illustrates such

pattern in Ward A - it shows average of all week days. Figure 22 illustrates such pattern

in Ward A by week days for days 1,2, and 7, and Figure 23 illustrates the same pattern in

Ward A during the entire week.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

Fluc

tuat

ions

aro

und

the

aver

age

Number of patientsArrivalDeparture

Figure 21: Arrival, Departures, and Number of Patients Patterns in Ward A

2.2.3 Determining Length Of Stay in IW as a function of the work load (seeAppendix A - 1).

We want to determine the impact of workload on the LOS in Internal Wards. The similar

attempt was done at [3]. There are few ways to define workload. The simplest way is to look

at the patient-load, for example, the number of patients in the ward or the percentage of

occupied beds. A more sophisticated view is to look at the workload on the service providers

(i.e. nurses and doctors). These two workloads are connected; we shall examine both.

Length of stay as a function of patients load in the ward

When considering the LOS versus the patient load in the system, we find that during

one patient’s stay the load can be changed dramatically.

Figure 24 illustrates the number of patients a random patient sees in the ward during

his/her stay, and the workload on nurses s/he sees. The work load on nurses is calculated

using Formula 1 assuming Ts = 0.25, TINI = 0.5 hours and fs = 0.4 requests per patient

24

-3

-2

-1

0

1

2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Hour

Fluc

tuat

ions

aro

und

the

aver

age

1 - Number of Patients1 - Arrival1 - Departure2 - Number of Patients2 - Arrival2 - Departure7 - Number of Patients7 - Arrival7 - Departure

Figure 22: Arrival, Departures, and Number of Patients Patterns in Ward A for Days 1,2,and 7 in the Week

-5

-4

-3

-2

-1

0

1

2

3

4

1_00

1_06

1_12

1_18

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3_18

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4_06

4_12

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5_06

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6_00

6_06

6_12

6_18

7_00

7_06

7_12

7_18

Day Of Week and Hour

Fluc

tuat

ions

aro

und

the

aver

age

Number of Patients Arrival Departure

Figure 23: Arrival, Departures, and Number of Patients Patterns in Ward A During theWeekdays

25

per hour. (WE MUST ESTIMATE IT AGAIN) One can observe the same patterns of the

number of patients in the ward. It is important to notice that, while the number of patients

drops between 13:00 and 23:00, the workload does not decrease but increases. (remark: can

we add the waiting probability or averages he observes?)Chart1

Page 1

30

35

40

45

50

55

3_24

4_06

4_12

4_18

4_24

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5_12

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7_06

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1_24

2_06

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Time (DOW_Hour)

Num

ber o

f Pat

ient

s

3

4

5

6

7

8

9

10

Offe

red

Load

Number of Patients

Offered Load

Figure 24: Number of patients and workload during the LOS of a random patient

Summarizing the above, we conclude that although one usually measures the load that

patient sees at his/her entering time to the system, in our case this will underestimate the

real load that the patient observes. In order to overcome this problem, we calculate the

average number of patients in the ward during each patient’s stay. Figure 25 shows the

ALOS [in days] of patients as a function of the average beds occupancy rate. Occupancy

rate is calculated relatively to the maximal number of beds in the ward.

We also need to calculate it by average number of people at 7:00.

Length Of Stay as a function of nurses work load in the ward

In order to define the workload that each patient brings to the ward, we use a model

that is close to the one described in Galit’s thesis (reference). Each patient during his

stay alternates between “needy” and “content” states. When a patient is needy he requires

service from a nurse. A patient starts and ends his stay in a needy states. The average time

26


-2

0

2

4

6

8

LOS

(day

s)

0 .5 1 1.5

Beds Occupancy

Overlay Y's

Y Mean of LOS_D, IW_A Mean of LOS_D, IW_B Mean of LOS_D, IW_C Mean of LOS_D, IW_D Mean of LOS_D, IW_E

Overlay Plot

ByMaximal Number of Beds

Journal: Untitled Page 1 of 1

-2

0

2

4

6

8

10

LOS

(day

s)

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Beds Ocuupancy

Overlay Y's

Y Mean of LOS_D, IW_A Mean of LOS_D, IW_B Mean of LOS_D, IW_C Mean of LOS_D, IW_D Mean of LOS_D, IW_E

Overlay Plot

ByStandard (“TEKEN”) Number of Beds

Figure 25: ALOS as a function of bed occupancy in wards A-E

27

of the first and last services (when her is admitted or discharged from the ward) could be

different from the average service time of regular service (we don’t have data on that, but it

is reasonable to assume that, and that is what the IW B nurse has told us). Thus, in order

to define the workload that a specific patient sees during his stay, we shall count the number

of patients that arrive and depart during his stay and the number of patients hospitalized

in his ward in every hour, and multiply them in the service time they require.

Define At - The total number of customers that entered the system till time t, Dt - The

total number of customers departed from the system till time t. A−1(i) - The arrival time of

customer i, D−1(i) - The departure time of customer i. Qt - The number of customers in the

system at time t, therefore Qt = At−Dt. Define Ei[Q] - The average number of customers in

the system when customer i is in the system, and LOS(i) - The Length of Stay of customer

i, LOS(i) = D−1(i)− A−1(i), therefore:

Ei[Q] =

D−1(i)∫A−1(i)

Qtdt

LOS(i).

Define INIi as the average number of admissions and discharges during the stay of customer

i, and Loadi as the average load customer i sees during his stay. Therefore:

INIi =A(D−1(i))− A(A−1(i)) + D(D−1(i))−D(A−1(i))

LOS(i),

and

Loadi = INIi ∗ TINI + Ei[Q] ∗ Ts ∗ fs, (1)

where TINI is the average time that admission or discharge takes, Ts is the average service

time , and fs is the frequency of service requirements of customer per hour (?). We assumed

Ts = 0.25, TINI = 0.5 hour and fs = 0.4.

Figure 26 shows ALOS of patients as a function of their INIi for each ward.

Figure 27 shows ALOS of a patient as a function of the total service work load s/he

observes during his stay - Loadi.

In order to account for the influence of ward size the Figure 28 shows ALOS as a function

ofEj [Loadi]

Nj, where Nj is the maximum number of beds in ward j and Ej[Loadi] is the average

load of customers in ward j.

28


-1

01

2

34

56

7

89

10

LOS

(day

s)

0 5 10 15 20 25 30 35 40

INI (days)

Overlay Y's

Y IW_A IW_B IW_C IW_D IW_E

Overlay Plot


-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

LOS

(day

s)

0 5 10 15 20 25 30 35 40

INI (days)

Overlay Y's


Figure 26: LOS as a function of INI by ward

29


-1

0

1

2

3

4

5

6

7

8

LOS

(day

s)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

Load

Overlay Y's


Overlay Plot

Figure 27: ALOS as a function of working load of a nurseJournal: Untitled 15 Page 1 of 1

0

1

2

3

4

5

6

7

8

9

LOS

(day

s)

1 1.5 2 2.5 3 3.5 4 4.5 5

Load per bed

Overlay Y's


Overlay Plot

Figure 28: LOS as a function of working load of a nurse

30

2.3 Empirical Analysis of Transfers in the system

2.3.1 Waiting times from ED to IW

Empirical analysis of waiting time for transferring from ED to the IW (see Appendix A - 3)

by customer type (patients that are given artificial respiration or not).

2.3.2 Waiting times from ED to ICU

is there blocking? maybe we should transfer this to the next chapter?

31

3 Analysis of the system (using combined simulation

and/or analytical models).

Answering what-if questions. Two for each part; the first will consider an operational issue

(such as pooling or priority), and the second will try to explain an interesting empirical

findings.

3.1 Two interesting questions for ED

For example capacity analysis of ED:

a. Resources (staff, beds, and supported activities) utilization

b. How many patients’ arrival per day can the system handle?

c. The impact of time-varying arrivals and the impact of mass casualty events (e.g. car

accident or terrorist attack).

d. What is the bottleneck of the process?

e. Staffing policy - the use of analytical models (see Appendix A - 6a).

f. input control - ambulance diversions.

h. Using simple analytical model for the ED.

i. Replacing simulation sub-models with analytical models (see Appendix A - 4)

j. Using priorities (see Appendix A - 9).

k. Designing of teams (pooling decisions as in Appendix A - 6c).

3.2 Two interesting questions for IW

Investigating the connection between Lambda, Mu, Q and time in IW

3.3 Two interesting questions for the transfer process from ED toIW

For example:

justice

heterogenic wards?

a. How do different routing schemes affect system’s performance (fair allocation)?

b. Where the queue should be: IW or ED (see Appendix A - 5).

c. Using incentive (auction) mechanism (game theory -Pulling method)?

32

3.4 Two interesting questions for the whole process

For example:

The impact of IW/OR/ICU work load on the capacity analysis of the ED (see Appendix A

- 1).

4 Special events

a. The war. b. Moving to the temporary location. c. Special days (with many Multi

Trauma). d. Months with flu patients.

33

References

[1] R. Bekker and A.M. de Bruin, Time-dependent analysis for refused admissions in clinical

wards, Submitted to AOR-ORAHS’s special volume (2008).

[2] A.B. Cooper, E. Litvak, M.C. Long, and M.L. McManus, Emergency department diver-

sion: causes and solutions, Academic Emergency Medicine 8 (2001), 1108–1110.

[3] K.C. Diwas and C. Terwiesch, The impact of work load on productivity and quality: an

econometric analysis of hospital operations, Manuscript under review (2008).

[4] L. Green, Capacity planning and management in hospitals, Operations Research and

Health Care (Brandwau et al editors) (2004), 14–41.

[5] , Using operations research to reduce delays for healthcare, Tutorials in Operations

Research, Informs (2008).

[6] O.B. Jennings and F.d. Vericourt, Nurse-to-patient ratios in hospital staffing: a queuing

perspective, Working Paper, Duke University.

[7] Y. Marmor and D. Sinreich, Emergency departments operations: the basis for developing

a simulation tool, IIE Transactions 37 (2005), no. 3, 233–245.

34

A Meetings summary

1. The impact of load (workload per server per time unit) on the length of service (in

Internal Wards - LOS, in ED - treatment time (nurse, physician), in Call Center -

duration).

Remark: one need to consider the influence of ward size and the number of nurses and

doctors.

(a) Empirical model (statistical approach): from the Hospital Database and observa-

tions.

(b) Compare with other fields (call centers). Explanation based on psychological

/ economical model. We would look on papers from Health care (Yulia) or in

OR/MS.

(c) Influences on Analytical model (call centers staffing; health care staffing, bed al-

location and routing policy).

1. Compare simulation with changing service time (M/Mρ/N/(K)) to M/M/N,

M/M/N/K models check the accuracy of probability of blocking and beds’ uti-

lization.

2. Can we estimate LOS function in such a way that one can develop a closed

form solution to (M/Mρ/N/(K))?

Challenges: how to define Load.

2. Support mathematical basis for the QED model: check empirically that the probability

of waiting, in the meaning of the probability for an empty bed, is between 0 and 1.

Check it for different seasons.

3. Modeling waiting time for moving from ED to IW (accounting for constrains in the

IW). The possible approaches are :

(a) As currently in the simulation - the delay is exponentially distributed with em-

pirically found average (does not account for congestion in Internal Wards).

(b) Empirical model possibly based on the database from Rambam.

(c) Green and Yancovitch model which accounts for blocking that are caused by lack

of nurses, physician, or beds.

35

(d) Combined with Galit’s model (use the probability of blocking and waiting to

predict nurses’ availability).

(e) Procedural constrains in the IW, such as shift changing periods, meals times,

cleaning patients time and so on.

4. Comparison of Simulation Model of the ED+IW to Erlang-C, Erlang-B, or M/M/? or

Galit’s model:

(a) What is the meaning of ”the number of servers” in such models, and how to

estimate the right one as the combination of Nurses, X-Ray, Beds, or Physicians?

M/M/S + M (2)

S = WP ∗ P + WN ∗N (3)

where P is the Number of Physicians and N is the Number of Nurses

(b) Different measures: LOS pdf, waiting times, occupancy, patients’ departures from

the ED etc.

(c) Influences of the model on operational decisions (e.g. staffing, bed allocation, and

routing).

5. Moving patients from the ED to the IW: Compare between policy in which patients are

waiting in the ED for their placement (Rambam) vs. in which patients are waiting in

the IW for their admission (Nahariya or Pnimit Hei in Rambam). (Could be relevant

to ED vs. ER). Green also mentioned this conflict in the US.

6. Using the Simulation for interesting questions:

(a) Determine staffing policy for Beds, Nurses, and Physicians (developing staffing

algorithm and use of Analytical Model vs. Simulation).

(b) The influence of IW congestion on the ED.

(c) Treatment times are influenced by learning and forgetting. Forgetting is influ-

enced by congestion (time between treatments of the same patient) and by amount

of patients per staff member (information overload problems). Can one estimate

these influences and their impact on staffing decisions?

36

(d) Using shared X-Ray or dedicated X-Ray to the ED. If shared, then how the

priorities are determined.

(e) The operational strategies impact on the LWBS/abandonment-rate and the Re-

turns rate.

(f) DEA (Data Envelop Approach).

7. Combination of incentives mechanism (in IW) and routing policy (ED to IW) in a way

that encourages operational improvement (e.g. reduce LOS, increase staffing and bed

efficiency) without interfering with the clinical aspects (as quality of care). Remark:

patient allocation can be in Push-mode or by Pull-mode (e.g. auction-like).

8. Clinical aspects: building a connection between quality of treatment (urgency of treat-

ment needed) and waiting time using known clinical procedures for different cases and

their frequency in population. The outcome would be the quality of service function

that can be used for staffing decisions instead of the regular waiting time function,

or in order to define appropriate waiting time standards for staffing in EDs (opti-

mal ”cost/profit as opposed to constraint satisfaction). Return rate as a quality of

treatment measure.

9. The impact of using priority on operational decisions and measures:

(a) Triage and priority schemes.

(b) Imaging priority (can be used to reduce the load in the ED).

Our hypotheses for 1 and 5c:

Updated on 31/08/08

3

9. The impact of using priority on operational decisions and measures:

a. Triage and priority schemes.

b. Imaging priority (can be used to reduce the load in the ED).

Our hypotheses for 1 and 5c:

Treatment time

Work Load

Pressure increases

productivity Learning and Forgetting or

cognitive pressure reduces productivity

37

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