Transcript Productivity

Chapter 9.
Productivity
Chapter 9: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
1
Outline



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Trends in Healthcare Productivity: Consequences of PPS
Productivity Definitions and Measurements
– Productivity Benchmarking
– Multifactor Productivity
Commonly Used Productivity Ratios
– Hours per Patient Day or Visit
Adjustment for Inputs
– Skill-Mix Adjustment to Worked Hours
– Cost of Labor
Adjustments for Output Measures
– Service/Case-Mix Adjustments
Productivity Measures Using Direct Care Hours
Productivity – Quality Relationship
Productivity Dilemmas
Multiple Dimensions of Productivity: New Methods
– Data Envelopment Analysis (DEA)

Productivity Improvement
Chapter 9: Quantitatve
Methods in Health Care
Management
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Trends in Productivity: Consequences of PPS
•
The recent decades’ changes in reimbursement
strategies aimed to end waste and promote
innovative and cost-efficient delivery systems.
•
productivity gains from PPS have not materialized
to the extent predicted.
•
Hospitals now employ more people to treat fewer
patients, and the increase is not accounted for by
the greater severity of patient illness in the late
1980s and in1990s.
•
Although employers, insurers and public are
spending less on inpatient care, the rising use of
outpatient procedures has simply increased costs
in that area which counters the savings (Altman,
Goldberger, and Crane, 1990).
Chapter 9: Quantitatve
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Trends in Productivity: Consequences of PPS
•
The constraints that force healthcare institutions
into the role of cost centers, coupled with shifting
patterns of inpatient acuity, tight healthcare labor
markets, and society's expectations of high quality
of care are leading healthcare organizations to a
"productivity wall." When the wall is reached, it
is quality of care that inevitably is sacrificed for
the sake of productivity and profit (Kirk, 1990).
•
It must be recognized that there are limits to
ratcheting up productivity.
•
It is not always possible to do more with less.
Chapter 9: Quantitatve
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Productivity Definitions and Measurements
• Productivity is one measure of the effective
use of resources within an organization,
industry, or nation.
• The classical productivity definition
measures outputs relative to the inputs
needed to produce them. That is,
productivity is defined as the number of
output units per unit of input
Output
Pr oductivity
Input
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Productivity Definitions and Measurements
• Sometimes, an inverse calculation is used
that measures inputs per unit of output. Care
must be taken to interpret this inverse
calculation appropriately; the greater the
number of units of input per unit of output,
the lower the productivity.
• For example, traditionally productivity in
hospital nursing units has been measured by
hours per patient day (HPPD). That requires
an inversion of the typical calculations:
meaning total hours are divided by total
patient days.
Total Hours
HPPD 
Patient Days
Chapter 9: Quantitatve
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Example 9.1
Nurses in Unit A worked collectively a total of 25 hours to
treat a patient who stayed 5 days, and nurses in Unit B
worked a total of 16 hours to treat a patient who stayed 4
days. Calculate which of the two similar hospital nursing
units is more productive.
Solution:
First, define the inputs and the outputs for the analysis. Is
the proper measure of inputs the number of nurses or of
hours worked? In this case the definition of the input would
be total nursing hours. When the total number of nursing
hours worked per nurse is used as the input measure, then
the productivity measures for the two units are:
Total Hours
25
HPPD A 

5
Patient Days
5
Total Hours 16
HPPDB 

4
Patient Days 4
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Productivity Definitions and Measurements
• Productivity Benchmarking. Productivity must be considered
as a relative measure; the calculated ratio should be either
compared to a similar unit, or compared to the productivity
ratio of the same unit in previous years. Such comparisons
characterize benchmarking. Many organizations use
benchmarking to help set the direction for change.
• Historical Benchmarking is monitoring an operational units’
own productivity or performance over the last few years.
Another way of benchmarking is to identify the best practices
(best productivity ratios of similar units) across health
organizations and incorporate them in one’s own.
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Productivity Definitions and Measurements
Multifactor Productivity. Example 9.1 demonstrated a
measure of labor productivity. Because it looks at only
one input, nursing hours, it is example of a partial
productivity measure. Looking only at labor
productivity may not yield an accurate picture.
Newer productivity measures tend to include not only
labor inputs, but the other operating costs for the product
or service as well.
Service Item * Pr ice
Multifactor Pr oductivity 
Labor  Material  Overhead
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Example 9.2
A specialty laboratory performs lab tests for the area
hospitals. During its first two years of operation the
following measurements were gathered:
.
Measurement
Year 1
Price per test ($)
50
Annual tests
10,000
Total labor costs($) 150,000
Material costs ($)
8,000
Overhead ($)
12,000
Year 2
50
10,700
158,000
8,400
12,200
Determine and compare the multifactor productivity for
historical benchmarking.
Solution:
10,000 * 50
Multifactor Pr oductivityYear 1 
 2.9
150 ,000  8,000  12,000
Multifactor Pr oductivityYear  2 
Chapter 9: Quantitatve
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10,700 * 50
 3.0
158,000  8,400  12,200
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Commonly Used Productivity Ratios
• Hours Per Patient Day (or Visit)
Hours Worked
Hours per Patient Day 
Patients Days
inpatient
HoursWorked
Hours per Patient Visit 
Patient Visits
outpatient
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Commonly Used Productivity Ratios
Example 9.3:
Annual statistical data for two nursing units in Memorial Hospital are
as follows:
Measurements
Unit A
Unit B
Annual Patient Days
14,000
10,000
Annual Hours Worked
210,000
180,000
Calculate and compare hours per patient day for two units of this
hospital.
Solution:
Hours per Patient DayUnit A 
210,000
 15 hours
14,000
Hours per Patient DayUnit B 
180,000
 18 hours
10,000
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Commonly Used Productivity Ratios
Example 9.4:
Performsbetter Associates – a two-site group practice,
requires productivity monitoring. The following initial data
are provided for both sites of the practice:
Measurements
Annual Visits
Annual Paid Hours
Suburban
135,000
115,000
Downtown
97,000
112,000
Calculate and compare the hours per patient visit for the
suburban and the downtown locations of this practice.
Solution:
Hours per Patient Visit Suburb 
115,000
 .85
135,000
Hours per Patient Visit Downtown 
112,000
 1.15 hours or 69 minutes.
97,000
Chapter 9: Quantitatve
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hours or 51 minutes.
13
Adjustments for Inputs
Skill-Mix Adjustment weigh the hours of personnel of different
.
skill levels by their economic valuation.
One approach is to calculate weights based on the average
wage or salary of each skill class. To do that, a given skill
class wage/salary would be divided into the top class skill
salary.
If RNs, LPNs and Aides are earning $35.00, $28.00, and
$17.50 an hour, respectively;
Then, one hour of a nurse aide’s time is economically
equivalent to 0.5 hours of a RN's time; and one hour of a LPN's
time is equal to 0.8 hours of a RN's time.
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Adjustments for Inputs
Adjusted Hours 
w * X
i
i
Adjusted Hours = 1.0*(RN hours) + 0.8*(LPN hours) + 0.5*(Aide hours)
Adjusted Hours
Adjusted Hours per patient day 
Patients Days
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Adjustments for Inputs
Adjusted Hours 
w * X
i
i
Adjusted Hours = 1.0*(RN hours) + 0.8*(LPN hours) + 0.5*(Aide hours)
Adjusted Hours
Adjusted Hours per patient day 
Patients Days
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Adjustments for Inputs
Similarly, in outpatient settings, if one hour of a nurse
.
practitioner's
(NP) time is economically equivalent to 0.6 hours
of a specialist's (SP) time, and if one hour of a general
practitioner’s (GP) time is equal to 0.85 hours of a specialist’s
time, adjusted hours would be calculated as:
Adjusted Hours = 1.0 (SP hours) + 0.85 (GP hours) + 0.6 (NP hours)
Adjusted Hours
Adjusted Hours per Visit 
Patient Visits
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Adjustments for Inputs
Example 9.5: Using data from Example 9.3, and economic
equivalencies of 0.5 Aide = RN, 0.8 LPN = RN, calculate the
adjusted hours per patient day for Unit A and Unit B.
Unit A at Memorial Hospital employs 100% RNs.
The current skill mix distribution of Unit B is 45% RNs, 30%
LPNs, and 25% nursing aides (NAs).
Compare unadjusted and adjusted productivity scores.
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Adjustments for Inputs
Solution:
The first step is to calculate adjusted hours for each unit.
For Unit A, since it employs 100% RNs, there is no need for adjustment. For Unit B:
Adjusted Hours (Unit B) = 1.0 (180,000*.45) + 0.80 (180,000*.30) + 0.50 (180,000*.25).
Adjusted Hours (Unit B) = 1.0 (81,000) + 0.80 (54,000) + 0.50 (45,000).
Adjusted Hours (Unit B) = 146,700.
In this way, using the economic
equivalencies
of the
Standardized
Cost
of skill-mix,
Labor. the number of hours is
standardized as 146,700 instead of 180,000.
210,000
 15.0 hours.
14,000
146,700

 14.7 hours.
10,000
Adjusted Hours per Patient DayUnit A 
Adjusted Hours per Patient DayUnit B
Using adjusted hours, Unit A, which appeared productive according
to the first measure (see example 9.3), no longer appears as productive.
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Adjustments for Inputs
Standardized Cost of Labor. Total labor cost comprises the
.
payments
to various professionals at varying skills. To
account for differences in salary structure across hospitals or
group practices, cost calculations can be standardized using a
standard salary per hour for each of the skill levels
Labor Cost   ci * X i
Labor Cost = RN wages (RN hours) +
LPN wages (LPN hours) +
NA wages (Aide hours).
Labor Cost of Care
Labor Cost Patient Day 
Patient Days
Labor Cost of Care
Labor Cost per Visit 
Patient Visits
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Adjustments for Inputs
Example 9.6:
Performsbetter Associates in Example 9.4 pays $110, $85, and
$45 per hour, respectively, to its SPs, GPs and NPs in both
locations.
Currently, the suburban location staff comprises of 50% SPs,
30% GPs, and 20% NPs.
The downtown location, on the other hand, comprises 30%
SPs, 50% GPs, and 20% NPs.
Calculate and compare the labor cost of care, and labor cost
per visit for both locations.
Chapter 9: Quantitatve
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Adjustments for Inputs
Solution:
First, calculate “Labor Cost of Care” for each location.
Labor Cost = SP wages (SP hours) + GP wages (GP hours) + NP wages (NP hours),
Labor CostSuburban = $110 (115,000*0.50) + $85 (115,000*0.30) + $45 (115,000*0.20).
Labor CostSuburban = $110 (57,500) + $85 (34,500) + $45 (23,000).
Labor CostSuburban = $10,292,500.
Labor CostDowntown = $110 (112,000*.30) + $85 (112,000*0.50) + $45 (112,000*0.20).
Labor CostDowntown = $110 (33,600) + $85 (56,000) + $45 (22,400).
Labor CostDowntown = $9,464,000.
10,292 ,500
Labor Cost per Visit Suburban 
 $76.24
135,000
9,464,000
Labor Cost per Visit Downtown 
 $97.57
97,000
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Adjustments for Outputs
Service-Mix
Adjustments. Service-mix adjustment is useful
.
tool for comparison of, for instance, two community hospitals
that provide different services or have significantly different
distributions of patients among their services. The servicemix adjusted volume is weighted by a normalized serviceintensity factor.
Hi
Wi 
 Hi n
Adjusted Volume  Wi * X i
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Adjustments for Outputs
Service-Mix Adjustments
.
Example
9.7:
Two hospitals, each with unadjusted volume of 10,000 patient
days per month, provide only two services, S1 and S2,
requiring respectively 3 and 7 hours of nursing time per
patient day.
Hospital A has a service-mix distribution of 2000 patient days
for S1 and 8000 patient days for S2.
Hospital B has 8000 days for S1 and 2000 days for S2.
Calculate adjusted patient days for both hospitals.
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Adjustments for Outputs
Service-Mix Adjustments
Solution:
In this case, total unadjusted volume is simply the sum of the volume for each service
in each hospital, or Unadjusted Volume = X1 + X2.
.
W1 

Hospital-A
Hospital-B
Service S1 (3 hours/patient day)
X1=2000
X1=8000
Service S2 (7 hours/patient day)
X2=8000
X2=2000
Total Unadjusted Volume
10,000
10,000
W2 
H1
3
3
3


  0.6
H i n (3  7) 2 10 2 5
H2
7
7
7


  1.4
 H i n (3  7) 2 10 2 5
Adjusted Volume = W1X1 + W2X2.
Adjusted volume for Hospital-A = 0.6*2,000+1.4*8,000 = 12,400.
Adjusted volume for Hospital-B = 0.6*8,000+1.4*2,000 = 7,600.
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Adjustments for Outputs
Case-Mix Adjustments. The methodology for case-mix
adjustment is similar to that for service-mix adjustment.
Although most hospitals rely on advanced acuity systems,
each system is based on the weight factors for the different
acuity categories.
Patients in each category require similar amounts of nursing
care over a given 24 hour time period; however, across
categories the care requirements differ significantly.
For acuity, the focus is on patients’ direct care requirements.
The ratio of the hours of direct care provided to the total hours
worked is another measure of productivity.
Case  Mix Indexj 
Chapter 9: Quantitatve
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W * P
i
ij
26
Adjustments for Outputs
Case-Mix Adjustments
Example 9.8:
Unit A and Unit B (from Example 9.3), a medical care unit in
Memorial Hospital, classify patients into four acuity categories
(Type I through Type IV), with direct care requirements per
patient day being respectively, 0.5, 1.5, 4.5, and 6.0 hours.
Annual distributions of patients in these four acuity categories in
Unit A were 0.15, 0.25, 0.35, and 0.25.
Annual distributions of patients in Unit B were 0.15, 0.30, 0.40,
and 0.15.
Calculate the case mix for these two units, and determine which
unit has been serving more severe patients.
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Adjustments for Outputs
Case-Mix Adjustments
Solution:
.
W1 
H1
0.5
0.5 0.5



 0.17
H
n
(
0
.
5

1
.
5

4
.
0

6
.
0
)
4
12
4
3
 i
W2 
H2
1.5
1.5 1.5



 0.5
 H i n (0.5  1.5  4.0  6.0) 4 12 4 3
W3 
H3
4.0
4.0 4.0



 1.33
 H i n (0.5  1.5  4.0  6.0) 4 12 4 3
W4 
H4
6.0
6.0 6.0



 2.00
H
n
(
0
.
5

1
.
5

4
.
0

6
.
0
)
4
12
4
3
 i
.
.
Case  mix IndexA 
W * P
 (0.17 * 0.15)  (0.5 * 0.25)  (1.33 * 0.35)  (2.00 * 0.25)  1.12.
Case  mix IndexB 
W * P
 (0.17 * 0.15)  (0.5 * 0.30)  (1.33 * 0.40)  (2.00 * 0.15)  1.01.
i
Chapter 9: Quantitatve
Methods in Health Care
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i
iA
iB
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Adjustments for Outputs
Case-Mix Adjustments
Once the case-mix is determined, the output side of the productivity
ratios can be adjusted by simply multiplying volume (patient days,
discharges, visits) by case-mix index as:
Adjusted Patient Days = Patient Days * Case-mix index.
Adjusted Discharges = Discharges * Case-mix index.
Adjusted Visits = Visits * Case-mix index.
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Productivity Measures Using Direct Care Hours
Hours of Direct Care. “Hours of direct care” is an
important component of productivity ratios. It serves as
a building block for other ratios.
To illustrate its development, let us assume that
patients are categorized into acuity groupings requiring
H1, H2, H3, …., Hm hours of direct nursing care per
patient day.
Further, assume that there are N1, N2, N3, .…, Nm
annual patient days in units 1 through m.
The total amount of direct nursing care in nursing unit j
would be calculated as:
Hours of Direct Care j 
n
H
i
* Pij * N j
i 1
Chapter 9: Quantitatve
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Management
Yasar A. Ozcan
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Productivity Measures Using Direct Care Hours
Percentage of Hours in Direct Care. This is an
additional measure can be derived from the “Hours of
Direct Care” calculation, as the ratio of direct care
hours to total care hours.
Hours in Direct Care
Percent of Hours in Direct Care 
Hours Worked
Percentage of Adjusted Hours in Direct Care. We also
can determine the percentage of adjusted nursing hours
as adjusted for skill-mix in direct patient care.
Hours in Direct Care
Percentageof Adjusted Hours in Direct Care 
Adjusted Hours
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Productivity Measures Using Direct Care Hours
Example 9.9:
Using information from Examples 9.3 and 9.8
calculate:
a) hours of direct care
b) percentage of hours in direct care, and
c) percentage of adjusted hours in direct care
for Units A and B of Memorial Hospital.
Compare these results in terms of percentage of
adjusted hours in direct care.
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Productivity Measures Using Direct Care Hours
Solution:
Memorial Hospital uses an acuity classification system with 4 categories
of direct hours of care per patient day: 0.5, 1.5, 4.0, and 6.0 hours.
The annual distributions of patients in these four acuity categories in Unit
A were 0.15, 0.25, 0.35, and 0.25.
The annual distributions of patients in Unit B were 0.15, 0.30, 0.40, and
0.15.
Annual patient days for Unit A were 14,000, and for unit B 10,000.
Annual hours worked were 115,000 and 112,000, respectively.
Chapter 9: Quantitatve
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Productivity Measures Using Direct Care Hours
Solution:
Hours of Direct CareA 
4
 (H
i
* PiA * N A ).
i 1
Hours of Direct Care A  (0.5 * .15 *14,000 )  (1.5 * .25 *14,000 )  (4.0 * .35 *14,000 )  (6.0 * .25 *14,000 )
Hours of Direct Care A  46,900
.
Hours of Direct CareB 
4
 (H
i
* PiB * N B ).
i 1
Hours of Direct Care B  (0.5 * .15 *10,000 )  (1.5 * .30 *10,000 )  (4.0 * .40 *10,000 )  (6.0 * .15 *10,000 )
Hours of Direct Care B  30,250
Chapter 9: Quantitatve
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Productivity Measures Using Direct Care Hours
Solution:
Percentage of Hours in Direct Care A 
Hours in Direct Care 46,900

 0.223 or 22.3%
Hours Worked
210,000
Percentage of Hours in Direct CareB 
Hours in Direct Care 30,250

 0.168 or 16.8%
Hours Worked
180,000
.
Percentage of Adjusted Hours in Direct CareA 
Hours in Direct Care 46900

 0.223 or 22.3%.
Adjusted Hours
210,000
Percentageof Adjusted Hours in Direct CareB 
Hours in Direct Care 30250

 0.206 or 20.6%.
Adjusted Hours
146,700
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Figure 9.1 Productivity and Quality Tradeoff
Quality of Output
QA
QA”
QB
Hospital A
A
Q
A’’
A’
Hospital B
B
I
I2
Quantity of Inputs
(Staffing Level)
IA” I1
Source: Shukla, R.K. Theories and Strategies of Healthcare: Technology-Strategy-Performance,
Chapter 4, Unpublished Manuscript, 1991. Printed with permission.
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Productivity Wall?


Chapter 9: Quantitatve
Methods in Health Care
Management
Quality is difficult to measure,
and its definition is
ambiguous
The relationships between
quantity of care provided and
quality are often uncertain
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Many people confuse. . .
The concepts of
productivity, efficiency,
and effectiveness.
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It’s quite simple really!
 Efficiency--
using the minimum
number of inputs for a given
number of outputs
 Effectiveness-- refers to outputs;
are the proper inputs being used
to produce the appropriate
outcomes?
 Productivity-- a broader concept
than efficiency; refers to effective
use of a given set of resources
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But efficiency has varying dimensions..
 Technical
Efficiency-- relationship
between various inputs and related
outputs; use minimum combination
of resources for a given level of
quantity or level of care.
 Allocative (Economic) efficiency- adds cost to the measure of
technical efficiency.
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Graphically,
Iso-cost
MDs
Isoquant
4
C
3
A
2
B
1
0
1
2
3
4
5
Nurse
Practitioners
(NPs)
Assume NPs and MDs can
be substituted. The hospital
can either use 3 MDs and
2 NPs (pt. A), or 1 MD and
5 NPs (pt. B). Both result
in the same level of quality
and can produce the same
quantity of output.
Are points A and B both technically efficient?
Is point C technically efficient, why or why not?
Remember what an isoquant is? Are all points on an
isoquant technically efficient? economically efficient?
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Let’s expand our discussion. . .
 Data
envelopment analysis is a
recently developed technique that
can be used to measure the
multiple dimensions of
productivity.
 It allows multiple inputs and
outputs to be used in a linear
programming model that develops
a score of technical efficiency.
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Data Envelopment Analysis (DEA)
DEA can be used to measure
productivity of hospitals, physicians,
group practices, or any other unit of
analysis, referred to as the decision
making unit (DMU)
 The technical efficiency score of
optimally producing DMUs equals 1
(and lies on the isoquant). All other
DMUs are measured against these
technically efficient DMUs, and have a
score of between 0 and 1.

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DEA-- A Simple Example
Inputs
P1
Visits
2
Medications 1
Physicians
P2
P3
1
3
4
1
P4
2
3
Physicians P1, P2, and P3 are
Supplies
technically efficient, ceteris
4
paribus, and would receive an
efficiency score of 1. Physician 4,
3
however is inefficient and must
reduce either visits and or use of
2
medications to become as efficient as
his/her peers. The amount of the
reduction necessary is called inefficiency.1
0
Chapter 9: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
Inefficiency
P2
P4
P1
1
2
P3
3
LOS
44
DEA-- An Application
Ozcan and Luke (1993), A National Study of the Efficiency
of Hospitals in Urban Markets



The study examines the contribution of various hospital
characteristics to hospital technical efficiency
Outputs included:
– Treated cases
– Outpatient visits
– Teaching FTEs
Inputs included:
– Capital
– Plant complexity
– Labor
– Supplies
Chapter 9: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
45
DEA Applications, cont.
Slack values allow the manager to
determine just how much the
input/output mix must be changed for
inefficient DMUs to reach efficiency
 DEA is also useful for benchmarking or
development of report cards, making it
particularly useful in a managed care
environment

Chapter 9: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
46
Improving Healthcare Productivity
1. Develop productivity measures for all
operations in their organization,
2. Look at the system as a whole (do not suboptimize) in deciding on which
operations/procedures to focus productivity
improvements.
3. Develop methods for achieving productivity
improvements, and especially benchmarking
by studying peer healthcare providers that
have increased productivity; and reengineer
care delivery and business processes.
4. Establish reasonable and attainable standards
and improvement goals.
5. Consider incentives to reward workers for
contributions and to demonstrate
management’s support of productivity
improvements.
6. Measure and publicize improvements.
Chapter 9: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
47
The End
Chapter 9: Quantitatve
Methods in Health Care
Management
Yasar A. Ozcan
48