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Management Science for Healthcare
INTRODUCTION INTO STAFFING MODELING
WITH RANDOM DEMAND:
EXAMPLES AND PRINCIPLES
Alexander Kolker, PhD
Hartford, WI
Alexander Kolker. All rights reserved
Outline
• Main Concept and Some Definitions.
• The “newsvendor” framework approach.
Staffing a nursing unit with variable census (demand)
• Linear optimization framework approach.
Minimizing staffing cost subject to variable constraints
• Discrete event simulation framework approach.
Staffing a unit with cross-trained staff
• Key Points and Conclusions
Alexander Kolker. All rights reserved
• Using Data Analytics to Work Smarter
• Workforce management involves data-driven decision-making. From
productivity measurements to patient safety outcomes to staff
satisfaction metrics, healthcare executives must be focused on
tracking and managing complex variables.
• Hospitals that use business analytics to make data-driven staffing
decisions can optimize their most valuable resource, labor.
• Organizations that invest in a robust talent optimization solution, and
then encourage system usage and compliance will be able to utilize
real-time data to make better decisions regarding their valuable
workforce.
• With real-time labor and staffing information available, healthcare
providers can focus on managing productivity. That requires
understanding the relationship between three key variables: (1)
patient needs and acuity, (2) actual staffing, and (3) budgeted staffingAlexander Kolker
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• “Section 5.1 of the Baldrige Criteria for Performance Excellence asks
"How do you assess your workforce capacity… including staffing
levels?"
• The best answers to that question have all described approaches that
were static and based on average arrivals, average demand for
service and average length of stays.
• However, given the dynamic nature of healthcare systems, failure to
understand patterns, anticipate variation and prepare for the
uncertainty creates two types of problems:
• one, excess staffing, which hurts margins;
• and two, being understaffed, which requires overtime and/or
premium pay that also hurts margins and causes less than
optimum quality of care.
• The latter problem adversely affects patients and staff satisfaction.”
From an ASQ Baldrige Application Examiner, 2012.
Alexander
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Some definitions
• Staffing- determining the appropriate number of FTEs to be hired
and retained in each skill set (RN, LPN, aides, MHA, MBA, etc..) in
the most cost efficient way to provide high level of clinical
outcomes (quality)
• Scheduling- allocation of care providers assigned on and off duty
by weeks, days and shifts; operational procedures
• Reallocation-fine tunes of the previous decisions; daily and/or
shift by shift
Alexander
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20
21
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23
24
25
26
27
28
29
30
31
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35
36
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40
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43
44
45
MidnightCensus
Typical NICU Daily Census
for the period 7/31/2010 - 9/30/2011 (Children’s
Hospital of Wisconsin)
Staff at this level ?
or Staff at these levels ?
The main root cause of staffing issues is VARIABILITY
Alexander
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.
Staff at this level ?
Typical PACU daily average census (on an annual basis)
or Staff on these levels ?
Alexander
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Key Points:
• Nursing managers typically adjust nursing staffing needs
manually based on the past historical average number of
patients (census)
Because of high variability of the patient census, the
resulting staffing usually
• (i) either is not enough to deliver proper quality of care
and it is not cost-effective due to excessive overtime, or
call from the extra staff pool at a premium rate
• (ii) or excessive and results in idle time and/or pay under
contractual obligation.
Alexander
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Optimized annual budgeted staffing level:
“Newsvendor” framework (example 1)
Input Information:
(i) census data (collected several times a day, usually at midnight, at
noon, or in the afternoon)
(ii) patient: nurse ratio (PNR) broken down by patient acuity:
Example:
acuity 1: 28% of patients. Required PNR=1:1
acuity 2: 67% of patients. Required PNR=2:1
acuity 3: 5% of patients. Required PNR=3:1
The average PNR= 1.77
Problem Statement:
Given the variable patient census, determine for the given long-time
period the optimal (budgeted) staffing level that minimizes the cost of
daily/shift fluctuations of too many nurses (calls-off) and not enough
nurses (calls-on)
Alexander
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Solution:
This type of problem – choosing an optimal minimal cost
staffing level that faces random demand- is best addressed
using a “newsvendor” type framework:
If the random demand follows the cumulative probability
distribution function in a single time period, F(s), then the
optimal staffing level, s*, that balances the cost of “too
many” (overage cost, Co) and the cost of “too little”
(underage cost, Cu) is calculated as:
F(s*)= Cu/(Cu+Co) (for derivation see Appendix 1)
Note:
A similar equation that is used in retail, supply chain management,
finance, etc. is: F(s*)= (p-w)/(p-v),
where p is the retail price, w- is the wholesale price, and v is the salvage
price (if available).
Alexander
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Calculation of the understaffing cost , Cu, (in excess to the
regular nursing pay rate, R, $/hr)
If too few nurses are scheduled, then an additional nurse can be called
from:
(i) the internal float pool at no extra cost (if a trained nurse is
available-30% of time in this example), or
(ii) an off-duty nurse pool / staffing agency at a premium 60% above
normal pay (in this example).
Thus, understaffing cost per shift per nurse, Cu=(1-0.3)*0.6*R =
0.7 *0.6*R.
Note: This cost can be somewhat underestimated because float nurses
are usually less efficient than the crew staff nurses.
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Calculation of the overstaffing cost , Co, (in excess to the
regular nursing pay rate, R, $/hr)
If too many nurses are scheduled, then the extra nurses can be:
(i) Floated out to another unit if the need arise (about 40% of time in
this example), or
(ii) Offered to take paid/unpaid vacation day, or
(iii) Put on-call for the contractual pay of 25% of the base rate, R
Thus, overstaffing cost per shift per nurse, Co=(1-0.4)*0.25*R .
Note: Being sent home after showing up for work is not popular and
impacts nurse satisfaction; therefore the true cost of overstaffing can be
somewhat underestimated.
Thus, the right-hand side of the optimal staffing equation is:
Cu/(Cu+Co)=0.7*0.6*R/(0.7*0.6*R + 0.6*0.25*R)=0.74 Alexander
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Frequency Cumulative %
1 0.22%
0 0.22%
3 0.88%
4 1.75%
7 3.28%
11 5.69%
13 8.53%
19 12.69%
23 17.72%
20 22.10%
36 29.98%
29 36.32%
35 43.98%
36 51.86%
40 60.61%
40 69.37%
48 79.87%
41 88.84%
31 95.62%
12 98.25%
2 98.69%
6 100.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
50.00%
55.00%
60.00%
65.00%
70.00%
75.00%
80.00%
85.00%
90.00%
95.00%
100.00%
0
10
20
30
40
50
60
Frequency
staffing, FTE
Staffing Distribution
Calculation staffing cumulative distribution function
Optimal core staffing:
24 FTE (Cu>Co)
Average staffing:
22 FTE (Cu=Co)
Optimal core staffing:
19 FTE (Cu<Co)
Alexander
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NOTE:
If, for example,
• the internal float nurse is available 80% of time (instead of
30%), and
• the regular rate must be paid for nurses that were
scheduled and showed up for work (instead of 25% of the
regular pay for those sent home), then the ratio
Cu/(Cu+Co)= 0.2*0.6/(0.2*0.6+0.6*1)=0.166, and
the optimal core staffing level will be 19 FTE vs. the
average level of 22 FTE
Alexander Kolker
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Alexander Kolker
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St. John Hospital, MBU unit: Optimized budgeted staffing on
a monthly basis (Example 2)
Alexander Kolker
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16
Annual budgeted staffing level
Key Points
• Choosing the optimal long-term core staffing level that
face random demand is best addressed using a
“newsvendor” type framework.
• Depending on the ratio of the overage and underage costs,
the optimal core staffing level can be higher or lower than
the average.
• Only if the overage and underage costs are same, then the
optimal staffing will be close to the average.
• The optimal staffing provides a trade-off between “ too
few nurses” and “too many nurses” (this improves the
quality of care and staff utilization, thus reducing the
overall cost of doing business).
Alexander
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Linear Optimization framework
Optimization and Scheduling of a Clinical Unit Staff for 24/7
Three-Shift Operations: Is Staffing Cost Minimized?
•A typical full time unit nurse (such as an ICU nurse) usually works five
days a week with two consecutive rotating days off and rotating shifts.
•Usually three 8-hours shifts per day should be covered.
• A typical clinical unit has some minimal staffing requirement based on
the average shift patient census and the assumed nurse : patient ratio.
This ratio is based on assessed patient acuity level or external
regulations.
•Suppose that the pay rate is $50/hour (base wages and overhead) with
50% pay rate increase for Saturday and Sunday shifts Alexander
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Problem statement:
Develop a staffing schedule to meet the minimum coverage
for each day and shift with five work days and two
consecutive days off for each staff member in such a way that
the total weekly staffing cost is minimized .
Alexander
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Solution.
Step 1. Identify decision variables
For a seven-days week and three shifts per day there are total 21
different schedules possible
These schedules are presented in Table along with the average shift
census and the minimal staff demands for each shift assuming nurse
to patient ratio 1:2 for all shifts (only Monday to Thursday are shown
in this Table. Friday, Saturday and Sunday are structured similarly but
not shown here to save space).
Decision variables for this problem are the number of nurses, Xs
(s=1,.., 21) assigned to each of s=21 schedules
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Binary index variable for s=21 schedules and days and shifts: 1- on shift, 0-off shift. Nurse to
patient ratio is assumed to be 1:2 for all shifts
Schedule
s
Days Off
Mon_
shift_1
Mon_
shift_2
Mon_
shift_3
Tue_
shift_1
Tue_
shift_2
Tue_
shift_3
Wed_
shift_1
Wed_
shift_2
Wed_
shift_3
Thu_
shift_1
Thu_
shift_2
Thu_
shift_3
1 Sat, Sun 1 0 0 1 0 0 1 0 0 1 0 0
2 Sat, Sun 0 1 0 0 1 0 0 1 0 0 1 0
3 Sat, Sun 0 0 1 0 0 1 0 0 1 0 0 1
4 Sun, Mon 0 0 0 1 0 0 1 0 0 1 0 0
5 Sun, Mon 0 0 0 0 1 0 0 1 0 0 1 0
6 Sun, Mon 0 0 0 0 0 1 0 0 1 0 0 1
7 Mon, Tue 0 0 0 0 0 0 1 0 0 1 0 0
8 Mon, Tue 0 0 0 0 0 0 0 1 0 0 1 0
9 Mon, Tue 0 0 0 0 0 0 0 0 1 0 0 1
10 Tue, Wed 1 0 0 0 0 0 0 0 0 1 0 0
11 Tue, Wed 0 1 0 0 0 0 0 0 0 0 1 0
12 Tue, Wed 0 0 1 0 0 0 0 0 0 0 0 1
13 Wed, Thu 1 0 0 1 0 0 0 0 0 0 0 0
14 Wed, Thu 0 1 0 0 1 0 0 0 0 0 0 0
15 Wed, Thu 0 0 1 0 0 1 0 0 0 0 0 0
16 Thu, Fri 1 0 0 1 0 0 1 0 0 0 0 0
17 Thu, Fri 0 1 0 0 1 0 0 1 0 0 0 0
18 Thu, Fri 0 0 1 0 0 1 0 0 1 0 0 0
19 Fri, Sat 1 0 0 1 0 0 1 0 0 1 0 0
20 Fri, Sat 0 1 0 0 1 0 0 1 0 0 1 0
21 Fri, Sat 0 0 1 0 0 1 0 0 1 0 0 1
Average Census
per Shift
10 24 20 21 18 15 8 15 24 18 20 21
Minimal Staff
Demand per Day
and Shift,
N ds, MinDemand
5 12 10 10 9 7 4 7 12 9 10 10
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Step 2. Identify the Objective function
Objective function is the total weekly staffing cost for all
shifts that should be minimized by placing the right staff
in the right shift:
Cost= Mon_staffing * pay rate ($/hour) * shift length (hour) +
Tue_staffing * pay rate ($/hour) * shift length (hour) + etc.
(for each day of the week) -> MIN
Alexander
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Step 3. Identify Constraints
•Constraints for decision variables Xs (s=1,.., 21) are
the minimal total staff demand for each day and shift,
Nds, Min Demand
•These values are calculated using the average census
per shift (indicated in Table) and the nurse to patient
ratio (1:2 in this case).
•Nds, Min Demand values are indicated in the last row of
Table
•Thus, the optimal solution Xs (s=1,.., 21) must satisfy
these conditions Alexander
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Step 4. Identify parameters
Model parameters are:
•The nurse to patient ratio (1:2)
•The average census per shift
• Pay rates ($50/hr weekdays, $75/hr weekend)
• Shift length (8 hrs)
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SolutionSchedul
e ID Days off
1 Sat, Sun
2 Sat, Sun
3 Sat, Sun
4 Sun, Mon
5 Sun, Mon
6 Sun, Mon
7 Mon, Tue
8 Mon, Tue
9 Mon, Tue
10 Tue, Wed
11 Tue, Wed
12 Tue, Wed
13 Wed, Thu
14 Wed, Thu
15 Wed, Thu
16 Thu, Fri
17 Thu, Fri
18 Thu, Fri
19 Fri, Sat
20 Fri, Sat
21 Fri, Sat
Mon_
shift_1
Mon_
shift_2
Mon_
shift_3
Tue_
shift_1
Tue_
shift_2
Tue_
shift_3
Wed_
shift_1
Wed_
shift_2
Wed_
shift_3
2 2 2
7 7 7
8 8 8
5 5
1 1
1 1
1
1
4
1 1
1 1 1
2 2 2
2 2 2
5 12 10 10 9 11 10 9 12 <-Sub-total
Objective
function:
Goal to
minimize total
cost per week $ 77,800
Alexander Kolker
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26
Key Points
Linear Optimization framework for staffing is preferred if:
• the primary goal is the minimal staffing pool needed for
continuous time (shift) coverage, such as the number of
nurses, residents (or attending physicians) that should
always be available for the specific time length or shift
due to safety or legal regulations regardless of their
actual workload.
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Discrete Event Simulation framework
Staffing of the Unit with Cross-Trained Staff
Problem description:
• A hospital case management department performs three types of
transactions: reservation, urgent admissions and pre-registration.
• About 14% of all transactions are reservation, 32% is urgent
admissions and 52% is pre-registration.
• Case management specialists for urgent admissions and pre-
registration are cross-trained and could substitute each other if
needed. Reservation specialists work independently and they are not
involved in performing other type of transactions.
• The department works Monday to Friday from 8 am to 4:30 pm, with
a 30 min lunch time and two 15 min breaks during a typical day.Alexander
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Actual
2009
Projected
2010
Projected
2011
Projected
2012
Transaction
volume
49,559 50,763 52,286 53,855
Transaction volumes
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Analysis and Estimation FTEs
• Transaction time data have been collected for:
• Reservation IP
• Urgent_Admission IP
• Pre_Registration IP
• Urgent_Adm and Pre_Reg are mutually interchangeable
• Case related activity time, as well as non-case related
activity time have been collected.
•Percentage of case related activity time has been estimated
as the availability metrics
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Transaction type Time, min
Mean Median
Reservation 4.9 3.0
Urgent Admission 8.7 6.0
Pre-Registration 4.5 3.0
Transaction time data were collected over some representative
period and summarized in Table
Summary of Mean and Median Time per Transaction
Problem Statement:
Develop minimal staffing (FTE) requirement for each
transaction type that allows performing the annual
transaction volume without overtime. Alexander
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Traditional FTE estimation based on the average
transaction time
• Reservation:
FTE(2009)=49559*0.14*4.9 min/(255*8*60)/0.87 = 0.32
• Urg_Adm:
FTE(2009)=49559*0.32*8.7 min/(255*8*60)/0.85= 1.33
• Pre_Reg:
FTE(2009)=49559*0.54*4.5 min/(255*8*60)/0.78= 1.26
Total average-based calculated(2009): 2.9
Actual (2009): 3.5
NOTE:
Cross-trained staff cannot be taken into account by the
simple formulas based on average transaction time 32
Actual Time study: Reservation time distribution
Mean=4.9 min
Median=3 min
33
Actual Time study: Urgent_Adm time distribution
Mean=8.7 min
Median=6 min
34
Actual Time study: Pre_Reg_IP
Mean=4.5 min
Median=3 min
35
Simulation Process Model layout
Interchangeable
(cross-trained) staff
36
FTEs Required to Meet Annual IP_Verification Patient Volume Target
2009- Baseline: Model Validation
Conclusion
0.6 FTE
Reservation
(Time study
availability
87%)
1 FTE
Urg_Adm
(Time study
availability
85%)
2 FTE
Pre_Reg
(Time study
availability
68%)
Total 3.6
FTEs
Annual
Transaction
volume range
(Target 49,559)
99% CI:
6892-6974
99% CI:
15763-15902
99% CI:
26716-26856
99% CI:
49543-
49559
2010
Conclusion
0.5 FTE
Reservation
1 FTE
Urg_Adm
2.5 FTE
Pre_Reg
Total 4
FTEs
Annual
Transaction
volume range
(Target 50,763)
99% CI:
7100-7200
99% CI:
16138-16255
99% CI:
27332-27497
99% CI:
50760-
50763
2011
Conclusion
0.5 FTE
Reservation
1.5 FTE
Urg_Adm
2.5 FTE
Pre_Reg
Total 4.5
FTEs
Annual
Transaction
volume range
(Target 52,286)
99% CI:
7266-7361
99% CI:
16623-16768
99% CI:
28211-28341
99% CI:
52284-
52286
2012
Conclusion
0.6 FTE
Reservation
1.5 FTE
Urg_Adm
2.6 FTE
Pre_Reg
Total 4.7
FTEs
Annual
Transaction
volume range
(Target 53,855)
99% CI:
7516-7636
99% CI:
17121-17301
99% CI:
28995-29139
99% CI:
53854-
53856
4 FTEs
required;
4.5 FTEs
required;
4.7 FTEs
required;
3.6 FTEs
required;
current level
3.5 FTEs.
The Model is
Valid
37
Key Points
• The benefits of cross-training exhibits the law of
diminishing return: just a little bit of cross-training (staff
flexibility) goes a long way.
• However, there are non-technical (staff comfort zone)
issues with cross-training.
3.5
3.7
3.9
4.1
4.3
4.5
4.7
4.9
49000 50000 51000 52000 53000 54000
FTE
Annual transaction volume
FTE with cross-training
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Overall Key Points of the Staffing Modeling and Simulation
• Proper staffing and scheduling can mean the difference between
profitability and business failure
• There are three main methodology frameworks for
modeling staffing with variable demand:
 ‘newsvendor’ framework- best for determining the
optimal staffing level in the specified time period
 linear optimization (including integer, mix-integer and
stochastic)-best for determining the optimal staffing if the
objective function and constraints can be presented as linear
functions of the decision variables
 discrete event simulation- best for highly stochastic systems with
multiple staff types, shared and cross-trained staff Alexander
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APPENDIX 1
Alexander Kolker.
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41
The Newsvendor equation derivation
If the distribution density function of demand, D, is f(D), then the
average loss due to overage, i.e. when staffing S > D (loss from the
overstaffing) is:
𝐶0 𝑆 − 𝐷 𝑓 𝐷 𝑑𝐷
𝑆
0 ,
where Co is the unit cost of overage;
The average loss due to underage, i.e. when staffing S < D (loss from
understaffing-unmet demand) is:
𝐶 𝑢 𝐷 − 𝑆 𝑓 𝐷 𝑑𝐷
𝐷 𝑚𝑎𝑥
𝑆
, where Cu is the unit cost of underage;
Total loss function is:
L(S)=𝐶0 𝑆 − 𝐷 𝑓 𝐷 𝑑𝐷
𝑆
0
+𝐶 𝑢 𝐷 − 𝑆 𝑓 𝐷 𝑑𝐷
𝐷 𝑚𝑎𝑥
𝑆
and it should be minimized with respect to staffing, S, by taking the
derivative and making it equal to 0.
42
𝑑𝐿
𝑑𝑆
= 𝐶0 𝑓 𝐷 𝑑𝐷 − 𝐶 𝑢 𝑓 𝐷 𝑑𝐷
𝐷 𝑚𝑎𝑥
𝑆
𝑆
0
=0;
Here, the derivative of L(S) with respect to S is taken using the general
rule:
If 𝑓 𝑝 = 𝑓 𝑥, 𝑝 𝑑𝑥, 𝑡ℎ𝑒𝑛
𝑏(𝑝)
𝑎(𝑝)
𝑑𝑓
𝑑𝑝
=
𝜕𝑓(𝑥,𝑝)
𝜕𝑝
𝑏
𝑎
dx+𝑓(𝑏, 𝑝)
𝑑𝑏
𝑑𝑝
- f(a,p)
𝑑𝑎
𝑑𝑝
The 2-nd derivative is
𝑑2 𝐿
𝑑𝑆2 = 𝐶0f(S)+𝐶𝑢 f(S)>0, hence this is minimum.
Thus,
𝐶0F(S)-𝐶 𝑢(1-F(S))=0; and F(S opt)=Cu/(Cu+Co)
APPENDIX 2
Alexander Kolker.
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Key Points
Management Engineering/Science is indispensable in addressing the
following typical hospital issues:
- Capacity: How many beds are required for a department or unit? How
many procedure rooms, operating rooms or pieces of equipment are
needed for different services?
- Staffing: How many nurses, physicians and other providers are needed
for a particular shift in a unit (department) in order to best achieve
operational and service performance objectives?
- Scheduling: What are the optimized staff schedules that help not only
delivering a safe and efficient care for patients but also take into account
staff preferences and convenience?
- Patient flow: What patient wait time at the service stations is
acceptable (if any at all) in order to achieve the system throughput
goals? Alexander
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Key Points (cont.)
- Resource allocation: Is it more efficient to use specialized resources or
pooled (interchangeable) resources (operating/procedure rooms,
beds, equipment, and staff)?
- Forecasting: How to forecast the future patient volumes (demand) or
transaction volumes for the short- and long-term budget and other
planning purposes?
And the ultimate goal (and the holy grail of Management Engineering):
Given the variable patient volume and patient mix,
design and manage hospital operations efficiently,
i.e. increase profitability (reduce operating expenses, increase
revenue) while keeping high quality, safety and outcomes standards
for patients.
Alexander
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One of the Most Powerful Methodologies of Operations
Management is Simulation Modeling
A Simulation Model is the computer model that mimics the behavior of a
real complex system as it evolves over the time in order to visualize and
quantitatively analyze its performance in terms of:
• Cycle times
• Wait times
• Value added time
• Throughput capacity
• Resources utilization
• Activities utilization
• Any other custom collected process information
•The Simulation Model is a tool to perform ‘what-if’ analysis and play
different scenarios of the model behavior as conditions and process
parameters change
•This allows one to build various experiments with the computer model
and test the effectiveness of various solutions (changes) before
implementing the change Alexander
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Main Steps for Application of ME methodology
• Describe your process
• Depict the logical flow and the boundaries of the process in
the graphical form by developing a flow map
• Define Performance Objectives
• Examples: target utilization; target wait time; the number of
served patients or transactions; target net revenue; etc.
• Develop a simulation model layout and action logic
using model building software package
Alexander
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Cont.
• Collect the data required to feed the model:
•Examples of required data:
•Entities, their quantities and arrival times: periodic, random, scheduled,
daily pattern, etc
•Time the entities spend in the activities: This is usually not a fixed time
but a statistical distribution. The wider the time distribution the higher
the variability of the system behavior
• Capacity of each activity: The max number of entities that can be
processed concurrently in the activity
•The size of input and output queues for the activities (if needed)
•The routing type or the logical conditions for a specific routing
•Resource Assignments: the number of resources, their availability,
and/or resources shift schedule
• Validate the model
• Compare the model’s outcome/prediction with the actual baseline
process performance
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Healthcare Institutions that widely use ME methodology:
• Mayo Clinic has defined the Science of Healthcare Delivery as one of its four
strategic directions. The Center for the Science of Healthcare Delivery was created,
that will focus on developing new approaches to how healthcare is delivered
www.mayoclinic.org/news2011-rst/6151.html
• Texas Children’s Hospital. Clinic Flow Optimization & Patient Scheduling using
Process Simulation. www.Createasoft.com
• Texas Medical Center, Houston, TX. A new center of Systems Engineering in
Healthcare has recently opened. The program called ‘Systems and Workflow
Improvements Flexible Team’ will be working on Medical Centers throughout
the region. An integral part of this program will be Industrial (Systems)
Engineers
• Cincinnati Children’s Medical Center. CEO and CFO provided the Webcast:
http://www.ihi.org/knowledge/Pages/AudioandVideo/WIHIAllHospitalsinFavorofS
avingMoneySayPatientFlow.aspx
• Southern California Region. Cooperatively work on the use of ME for Operations
Improvement in 20+ Regional Hospitals (Led by University SC)
• York Hospital, PA. ED & Health Services Design
•University of Iowa, Carver College of Medicine, Department of Anesthesia-
Operations Research for Surgical Services. Alexander
Kolker
All rights
reserved

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Optimized Staffing with variable demand

  • 1. Management Science for Healthcare INTRODUCTION INTO STAFFING MODELING WITH RANDOM DEMAND: EXAMPLES AND PRINCIPLES Alexander Kolker, PhD Hartford, WI Alexander Kolker. All rights reserved
  • 2. Outline • Main Concept and Some Definitions. • The “newsvendor” framework approach. Staffing a nursing unit with variable census (demand) • Linear optimization framework approach. Minimizing staffing cost subject to variable constraints • Discrete event simulation framework approach. Staffing a unit with cross-trained staff • Key Points and Conclusions Alexander Kolker. All rights reserved
  • 3. • Using Data Analytics to Work Smarter • Workforce management involves data-driven decision-making. From productivity measurements to patient safety outcomes to staff satisfaction metrics, healthcare executives must be focused on tracking and managing complex variables. • Hospitals that use business analytics to make data-driven staffing decisions can optimize their most valuable resource, labor. • Organizations that invest in a robust talent optimization solution, and then encourage system usage and compliance will be able to utilize real-time data to make better decisions regarding their valuable workforce. • With real-time labor and staffing information available, healthcare providers can focus on managing productivity. That requires understanding the relationship between three key variables: (1) patient needs and acuity, (2) actual staffing, and (3) budgeted staffingAlexander Kolker All rights reserved
  • 4. • “Section 5.1 of the Baldrige Criteria for Performance Excellence asks "How do you assess your workforce capacity… including staffing levels?" • The best answers to that question have all described approaches that were static and based on average arrivals, average demand for service and average length of stays. • However, given the dynamic nature of healthcare systems, failure to understand patterns, anticipate variation and prepare for the uncertainty creates two types of problems: • one, excess staffing, which hurts margins; • and two, being understaffed, which requires overtime and/or premium pay that also hurts margins and causes less than optimum quality of care. • The latter problem adversely affects patients and staff satisfaction.” From an ASQ Baldrige Application Examiner, 2012. Alexander Kolker All rights reserved
  • 5. Some definitions • Staffing- determining the appropriate number of FTEs to be hired and retained in each skill set (RN, LPN, aides, MHA, MBA, etc..) in the most cost efficient way to provide high level of clinical outcomes (quality) • Scheduling- allocation of care providers assigned on and off duty by weeks, days and shifts; operational procedures • Reallocation-fine tunes of the previous decisions; daily and/or shift by shift Alexander Kolker All rights reserved
  • 6. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 MidnightCensus Typical NICU Daily Census for the period 7/31/2010 - 9/30/2011 (Children’s Hospital of Wisconsin) Staff at this level ? or Staff at these levels ? The main root cause of staffing issues is VARIABILITY Alexander Kolker All rights reserved
  • 7. . Staff at this level ? Typical PACU daily average census (on an annual basis) or Staff on these levels ? Alexander Kolker All rights reserved
  • 8. Key Points: • Nursing managers typically adjust nursing staffing needs manually based on the past historical average number of patients (census) Because of high variability of the patient census, the resulting staffing usually • (i) either is not enough to deliver proper quality of care and it is not cost-effective due to excessive overtime, or call from the extra staff pool at a premium rate • (ii) or excessive and results in idle time and/or pay under contractual obligation. Alexander Kolker All rights reserved
  • 9. Optimized annual budgeted staffing level: “Newsvendor” framework (example 1) Input Information: (i) census data (collected several times a day, usually at midnight, at noon, or in the afternoon) (ii) patient: nurse ratio (PNR) broken down by patient acuity: Example: acuity 1: 28% of patients. Required PNR=1:1 acuity 2: 67% of patients. Required PNR=2:1 acuity 3: 5% of patients. Required PNR=3:1 The average PNR= 1.77 Problem Statement: Given the variable patient census, determine for the given long-time period the optimal (budgeted) staffing level that minimizes the cost of daily/shift fluctuations of too many nurses (calls-off) and not enough nurses (calls-on) Alexander Kolker All rights reserved
  • 10. Solution: This type of problem – choosing an optimal minimal cost staffing level that faces random demand- is best addressed using a “newsvendor” type framework: If the random demand follows the cumulative probability distribution function in a single time period, F(s), then the optimal staffing level, s*, that balances the cost of “too many” (overage cost, Co) and the cost of “too little” (underage cost, Cu) is calculated as: F(s*)= Cu/(Cu+Co) (for derivation see Appendix 1) Note: A similar equation that is used in retail, supply chain management, finance, etc. is: F(s*)= (p-w)/(p-v), where p is the retail price, w- is the wholesale price, and v is the salvage price (if available). Alexander Kolker All rights reserved
  • 11. Calculation of the understaffing cost , Cu, (in excess to the regular nursing pay rate, R, $/hr) If too few nurses are scheduled, then an additional nurse can be called from: (i) the internal float pool at no extra cost (if a trained nurse is available-30% of time in this example), or (ii) an off-duty nurse pool / staffing agency at a premium 60% above normal pay (in this example). Thus, understaffing cost per shift per nurse, Cu=(1-0.3)*0.6*R = 0.7 *0.6*R. Note: This cost can be somewhat underestimated because float nurses are usually less efficient than the crew staff nurses. Alexander Kolker All rights reserved
  • 12. Calculation of the overstaffing cost , Co, (in excess to the regular nursing pay rate, R, $/hr) If too many nurses are scheduled, then the extra nurses can be: (i) Floated out to another unit if the need arise (about 40% of time in this example), or (ii) Offered to take paid/unpaid vacation day, or (iii) Put on-call for the contractual pay of 25% of the base rate, R Thus, overstaffing cost per shift per nurse, Co=(1-0.4)*0.25*R . Note: Being sent home after showing up for work is not popular and impacts nurse satisfaction; therefore the true cost of overstaffing can be somewhat underestimated. Thus, the right-hand side of the optimal staffing equation is: Cu/(Cu+Co)=0.7*0.6*R/(0.7*0.6*R + 0.6*0.25*R)=0.74 Alexander Kolker All rights reserved
  • 13. Frequency Cumulative % 1 0.22% 0 0.22% 3 0.88% 4 1.75% 7 3.28% 11 5.69% 13 8.53% 19 12.69% 23 17.72% 20 22.10% 36 29.98% 29 36.32% 35 43.98% 36 51.86% 40 60.61% 40 69.37% 48 79.87% 41 88.84% 31 95.62% 12 98.25% 2 98.69% 6 100.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% 45.00% 50.00% 55.00% 60.00% 65.00% 70.00% 75.00% 80.00% 85.00% 90.00% 95.00% 100.00% 0 10 20 30 40 50 60 Frequency staffing, FTE Staffing Distribution Calculation staffing cumulative distribution function Optimal core staffing: 24 FTE (Cu>Co) Average staffing: 22 FTE (Cu=Co) Optimal core staffing: 19 FTE (Cu<Co) Alexander Kolker All rights reserved
  • 14. NOTE: If, for example, • the internal float nurse is available 80% of time (instead of 30%), and • the regular rate must be paid for nurses that were scheduled and showed up for work (instead of 25% of the regular pay for those sent home), then the ratio Cu/(Cu+Co)= 0.2*0.6/(0.2*0.6+0.6*1)=0.166, and the optimal core staffing level will be 19 FTE vs. the average level of 22 FTE Alexander Kolker All rights reserved
  • 15. Alexander Kolker All rights reserved 15 St. John Hospital, MBU unit: Optimized budgeted staffing on a monthly basis (Example 2)
  • 16. Alexander Kolker All rights reserved 16 Annual budgeted staffing level
  • 17. Key Points • Choosing the optimal long-term core staffing level that face random demand is best addressed using a “newsvendor” type framework. • Depending on the ratio of the overage and underage costs, the optimal core staffing level can be higher or lower than the average. • Only if the overage and underage costs are same, then the optimal staffing will be close to the average. • The optimal staffing provides a trade-off between “ too few nurses” and “too many nurses” (this improves the quality of care and staff utilization, thus reducing the overall cost of doing business). Alexander Kolker All rights reserved
  • 18. Linear Optimization framework Optimization and Scheduling of a Clinical Unit Staff for 24/7 Three-Shift Operations: Is Staffing Cost Minimized? •A typical full time unit nurse (such as an ICU nurse) usually works five days a week with two consecutive rotating days off and rotating shifts. •Usually three 8-hours shifts per day should be covered. • A typical clinical unit has some minimal staffing requirement based on the average shift patient census and the assumed nurse : patient ratio. This ratio is based on assessed patient acuity level or external regulations. •Suppose that the pay rate is $50/hour (base wages and overhead) with 50% pay rate increase for Saturday and Sunday shifts Alexander Kolker All rights reserved
  • 19. Problem statement: Develop a staffing schedule to meet the minimum coverage for each day and shift with five work days and two consecutive days off for each staff member in such a way that the total weekly staffing cost is minimized . Alexander Kolker All rights reserved
  • 20. Solution. Step 1. Identify decision variables For a seven-days week and three shifts per day there are total 21 different schedules possible These schedules are presented in Table along with the average shift census and the minimal staff demands for each shift assuming nurse to patient ratio 1:2 for all shifts (only Monday to Thursday are shown in this Table. Friday, Saturday and Sunday are structured similarly but not shown here to save space). Decision variables for this problem are the number of nurses, Xs (s=1,.., 21) assigned to each of s=21 schedules Alexander Kolker All rights reserved
  • 21. Binary index variable for s=21 schedules and days and shifts: 1- on shift, 0-off shift. Nurse to patient ratio is assumed to be 1:2 for all shifts Schedule s Days Off Mon_ shift_1 Mon_ shift_2 Mon_ shift_3 Tue_ shift_1 Tue_ shift_2 Tue_ shift_3 Wed_ shift_1 Wed_ shift_2 Wed_ shift_3 Thu_ shift_1 Thu_ shift_2 Thu_ shift_3 1 Sat, Sun 1 0 0 1 0 0 1 0 0 1 0 0 2 Sat, Sun 0 1 0 0 1 0 0 1 0 0 1 0 3 Sat, Sun 0 0 1 0 0 1 0 0 1 0 0 1 4 Sun, Mon 0 0 0 1 0 0 1 0 0 1 0 0 5 Sun, Mon 0 0 0 0 1 0 0 1 0 0 1 0 6 Sun, Mon 0 0 0 0 0 1 0 0 1 0 0 1 7 Mon, Tue 0 0 0 0 0 0 1 0 0 1 0 0 8 Mon, Tue 0 0 0 0 0 0 0 1 0 0 1 0 9 Mon, Tue 0 0 0 0 0 0 0 0 1 0 0 1 10 Tue, Wed 1 0 0 0 0 0 0 0 0 1 0 0 11 Tue, Wed 0 1 0 0 0 0 0 0 0 0 1 0 12 Tue, Wed 0 0 1 0 0 0 0 0 0 0 0 1 13 Wed, Thu 1 0 0 1 0 0 0 0 0 0 0 0 14 Wed, Thu 0 1 0 0 1 0 0 0 0 0 0 0 15 Wed, Thu 0 0 1 0 0 1 0 0 0 0 0 0 16 Thu, Fri 1 0 0 1 0 0 1 0 0 0 0 0 17 Thu, Fri 0 1 0 0 1 0 0 1 0 0 0 0 18 Thu, Fri 0 0 1 0 0 1 0 0 1 0 0 0 19 Fri, Sat 1 0 0 1 0 0 1 0 0 1 0 0 20 Fri, Sat 0 1 0 0 1 0 0 1 0 0 1 0 21 Fri, Sat 0 0 1 0 0 1 0 0 1 0 0 1 Average Census per Shift 10 24 20 21 18 15 8 15 24 18 20 21 Minimal Staff Demand per Day and Shift, N ds, MinDemand 5 12 10 10 9 7 4 7 12 9 10 10 Alexander Kolker All rights reserved
  • 22. Step 2. Identify the Objective function Objective function is the total weekly staffing cost for all shifts that should be minimized by placing the right staff in the right shift: Cost= Mon_staffing * pay rate ($/hour) * shift length (hour) + Tue_staffing * pay rate ($/hour) * shift length (hour) + etc. (for each day of the week) -> MIN Alexander Kolker All rights reserved
  • 23. Step 3. Identify Constraints •Constraints for decision variables Xs (s=1,.., 21) are the minimal total staff demand for each day and shift, Nds, Min Demand •These values are calculated using the average census per shift (indicated in Table) and the nurse to patient ratio (1:2 in this case). •Nds, Min Demand values are indicated in the last row of Table •Thus, the optimal solution Xs (s=1,.., 21) must satisfy these conditions Alexander Kolker All rights reserved
  • 24. Step 4. Identify parameters Model parameters are: •The nurse to patient ratio (1:2) •The average census per shift • Pay rates ($50/hr weekdays, $75/hr weekend) • Shift length (8 hrs) Alexander Kolker All rights reserved
  • 26. SolutionSchedul e ID Days off 1 Sat, Sun 2 Sat, Sun 3 Sat, Sun 4 Sun, Mon 5 Sun, Mon 6 Sun, Mon 7 Mon, Tue 8 Mon, Tue 9 Mon, Tue 10 Tue, Wed 11 Tue, Wed 12 Tue, Wed 13 Wed, Thu 14 Wed, Thu 15 Wed, Thu 16 Thu, Fri 17 Thu, Fri 18 Thu, Fri 19 Fri, Sat 20 Fri, Sat 21 Fri, Sat Mon_ shift_1 Mon_ shift_2 Mon_ shift_3 Tue_ shift_1 Tue_ shift_2 Tue_ shift_3 Wed_ shift_1 Wed_ shift_2 Wed_ shift_3 2 2 2 7 7 7 8 8 8 5 5 1 1 1 1 1 1 4 1 1 1 1 1 2 2 2 2 2 2 5 12 10 10 9 11 10 9 12 <-Sub-total Objective function: Goal to minimize total cost per week $ 77,800 Alexander Kolker All rights reserved 26
  • 27. Key Points Linear Optimization framework for staffing is preferred if: • the primary goal is the minimal staffing pool needed for continuous time (shift) coverage, such as the number of nurses, residents (or attending physicians) that should always be available for the specific time length or shift due to safety or legal regulations regardless of their actual workload. Alexander Kolker All rights reserved
  • 28. Discrete Event Simulation framework Staffing of the Unit with Cross-Trained Staff Problem description: • A hospital case management department performs three types of transactions: reservation, urgent admissions and pre-registration. • About 14% of all transactions are reservation, 32% is urgent admissions and 52% is pre-registration. • Case management specialists for urgent admissions and pre- registration are cross-trained and could substitute each other if needed. Reservation specialists work independently and they are not involved in performing other type of transactions. • The department works Monday to Friday from 8 am to 4:30 pm, with a 30 min lunch time and two 15 min breaks during a typical day.Alexander Kolker All rights reserved
  • 29. Actual 2009 Projected 2010 Projected 2011 Projected 2012 Transaction volume 49,559 50,763 52,286 53,855 Transaction volumes Alexander Kolker All rights reserved
  • 30. Analysis and Estimation FTEs • Transaction time data have been collected for: • Reservation IP • Urgent_Admission IP • Pre_Registration IP • Urgent_Adm and Pre_Reg are mutually interchangeable • Case related activity time, as well as non-case related activity time have been collected. •Percentage of case related activity time has been estimated as the availability metrics Alexander Kolker All rights reserved
  • 31. Transaction type Time, min Mean Median Reservation 4.9 3.0 Urgent Admission 8.7 6.0 Pre-Registration 4.5 3.0 Transaction time data were collected over some representative period and summarized in Table Summary of Mean and Median Time per Transaction Problem Statement: Develop minimal staffing (FTE) requirement for each transaction type that allows performing the annual transaction volume without overtime. Alexander Kolker All rights reserved
  • 32. Traditional FTE estimation based on the average transaction time • Reservation: FTE(2009)=49559*0.14*4.9 min/(255*8*60)/0.87 = 0.32 • Urg_Adm: FTE(2009)=49559*0.32*8.7 min/(255*8*60)/0.85= 1.33 • Pre_Reg: FTE(2009)=49559*0.54*4.5 min/(255*8*60)/0.78= 1.26 Total average-based calculated(2009): 2.9 Actual (2009): 3.5 NOTE: Cross-trained staff cannot be taken into account by the simple formulas based on average transaction time 32
  • 33. Actual Time study: Reservation time distribution Mean=4.9 min Median=3 min 33
  • 34. Actual Time study: Urgent_Adm time distribution Mean=8.7 min Median=6 min 34
  • 35. Actual Time study: Pre_Reg_IP Mean=4.5 min Median=3 min 35
  • 36. Simulation Process Model layout Interchangeable (cross-trained) staff 36
  • 37. FTEs Required to Meet Annual IP_Verification Patient Volume Target 2009- Baseline: Model Validation Conclusion 0.6 FTE Reservation (Time study availability 87%) 1 FTE Urg_Adm (Time study availability 85%) 2 FTE Pre_Reg (Time study availability 68%) Total 3.6 FTEs Annual Transaction volume range (Target 49,559) 99% CI: 6892-6974 99% CI: 15763-15902 99% CI: 26716-26856 99% CI: 49543- 49559 2010 Conclusion 0.5 FTE Reservation 1 FTE Urg_Adm 2.5 FTE Pre_Reg Total 4 FTEs Annual Transaction volume range (Target 50,763) 99% CI: 7100-7200 99% CI: 16138-16255 99% CI: 27332-27497 99% CI: 50760- 50763 2011 Conclusion 0.5 FTE Reservation 1.5 FTE Urg_Adm 2.5 FTE Pre_Reg Total 4.5 FTEs Annual Transaction volume range (Target 52,286) 99% CI: 7266-7361 99% CI: 16623-16768 99% CI: 28211-28341 99% CI: 52284- 52286 2012 Conclusion 0.6 FTE Reservation 1.5 FTE Urg_Adm 2.6 FTE Pre_Reg Total 4.7 FTEs Annual Transaction volume range (Target 53,855) 99% CI: 7516-7636 99% CI: 17121-17301 99% CI: 28995-29139 99% CI: 53854- 53856 4 FTEs required; 4.5 FTEs required; 4.7 FTEs required; 3.6 FTEs required; current level 3.5 FTEs. The Model is Valid 37
  • 38. Key Points • The benefits of cross-training exhibits the law of diminishing return: just a little bit of cross-training (staff flexibility) goes a long way. • However, there are non-technical (staff comfort zone) issues with cross-training. 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 49000 50000 51000 52000 53000 54000 FTE Annual transaction volume FTE with cross-training Alexander Kolker All rights reserved
  • 39. Overall Key Points of the Staffing Modeling and Simulation • Proper staffing and scheduling can mean the difference between profitability and business failure • There are three main methodology frameworks for modeling staffing with variable demand:  ‘newsvendor’ framework- best for determining the optimal staffing level in the specified time period  linear optimization (including integer, mix-integer and stochastic)-best for determining the optimal staffing if the objective function and constraints can be presented as linear functions of the decision variables  discrete event simulation- best for highly stochastic systems with multiple staff types, shared and cross-trained staff Alexander Kolker All rights reserved
  • 41. 41 The Newsvendor equation derivation If the distribution density function of demand, D, is f(D), then the average loss due to overage, i.e. when staffing S > D (loss from the overstaffing) is: 𝐶0 𝑆 − 𝐷 𝑓 𝐷 𝑑𝐷 𝑆 0 , where Co is the unit cost of overage; The average loss due to underage, i.e. when staffing S < D (loss from understaffing-unmet demand) is: 𝐶 𝑢 𝐷 − 𝑆 𝑓 𝐷 𝑑𝐷 𝐷 𝑚𝑎𝑥 𝑆 , where Cu is the unit cost of underage; Total loss function is: L(S)=𝐶0 𝑆 − 𝐷 𝑓 𝐷 𝑑𝐷 𝑆 0 +𝐶 𝑢 𝐷 − 𝑆 𝑓 𝐷 𝑑𝐷 𝐷 𝑚𝑎𝑥 𝑆 and it should be minimized with respect to staffing, S, by taking the derivative and making it equal to 0.
  • 42. 42 𝑑𝐿 𝑑𝑆 = 𝐶0 𝑓 𝐷 𝑑𝐷 − 𝐶 𝑢 𝑓 𝐷 𝑑𝐷 𝐷 𝑚𝑎𝑥 𝑆 𝑆 0 =0; Here, the derivative of L(S) with respect to S is taken using the general rule: If 𝑓 𝑝 = 𝑓 𝑥, 𝑝 𝑑𝑥, 𝑡ℎ𝑒𝑛 𝑏(𝑝) 𝑎(𝑝) 𝑑𝑓 𝑑𝑝 = 𝜕𝑓(𝑥,𝑝) 𝜕𝑝 𝑏 𝑎 dx+𝑓(𝑏, 𝑝) 𝑑𝑏 𝑑𝑝 - f(a,p) 𝑑𝑎 𝑑𝑝 The 2-nd derivative is 𝑑2 𝐿 𝑑𝑆2 = 𝐶0f(S)+𝐶𝑢 f(S)>0, hence this is minimum. Thus, 𝐶0F(S)-𝐶 𝑢(1-F(S))=0; and F(S opt)=Cu/(Cu+Co)
  • 44. Key Points Management Engineering/Science is indispensable in addressing the following typical hospital issues: - Capacity: How many beds are required for a department or unit? How many procedure rooms, operating rooms or pieces of equipment are needed for different services? - Staffing: How many nurses, physicians and other providers are needed for a particular shift in a unit (department) in order to best achieve operational and service performance objectives? - Scheduling: What are the optimized staff schedules that help not only delivering a safe and efficient care for patients but also take into account staff preferences and convenience? - Patient flow: What patient wait time at the service stations is acceptable (if any at all) in order to achieve the system throughput goals? Alexander Kolker All rights reserved
  • 45. Key Points (cont.) - Resource allocation: Is it more efficient to use specialized resources or pooled (interchangeable) resources (operating/procedure rooms, beds, equipment, and staff)? - Forecasting: How to forecast the future patient volumes (demand) or transaction volumes for the short- and long-term budget and other planning purposes? And the ultimate goal (and the holy grail of Management Engineering): Given the variable patient volume and patient mix, design and manage hospital operations efficiently, i.e. increase profitability (reduce operating expenses, increase revenue) while keeping high quality, safety and outcomes standards for patients. Alexander Kolker All rights reserved
  • 46. One of the Most Powerful Methodologies of Operations Management is Simulation Modeling A Simulation Model is the computer model that mimics the behavior of a real complex system as it evolves over the time in order to visualize and quantitatively analyze its performance in terms of: • Cycle times • Wait times • Value added time • Throughput capacity • Resources utilization • Activities utilization • Any other custom collected process information •The Simulation Model is a tool to perform ‘what-if’ analysis and play different scenarios of the model behavior as conditions and process parameters change •This allows one to build various experiments with the computer model and test the effectiveness of various solutions (changes) before implementing the change Alexander Kolker All rights reserved
  • 47. Main Steps for Application of ME methodology • Describe your process • Depict the logical flow and the boundaries of the process in the graphical form by developing a flow map • Define Performance Objectives • Examples: target utilization; target wait time; the number of served patients or transactions; target net revenue; etc. • Develop a simulation model layout and action logic using model building software package Alexander Kolker All rights reserved
  • 48. Cont. • Collect the data required to feed the model: •Examples of required data: •Entities, their quantities and arrival times: periodic, random, scheduled, daily pattern, etc •Time the entities spend in the activities: This is usually not a fixed time but a statistical distribution. The wider the time distribution the higher the variability of the system behavior • Capacity of each activity: The max number of entities that can be processed concurrently in the activity •The size of input and output queues for the activities (if needed) •The routing type or the logical conditions for a specific routing •Resource Assignments: the number of resources, their availability, and/or resources shift schedule • Validate the model • Compare the model’s outcome/prediction with the actual baseline process performance Alexander Kolker All rights reserved
  • 49. Healthcare Institutions that widely use ME methodology: • Mayo Clinic has defined the Science of Healthcare Delivery as one of its four strategic directions. The Center for the Science of Healthcare Delivery was created, that will focus on developing new approaches to how healthcare is delivered www.mayoclinic.org/news2011-rst/6151.html • Texas Children’s Hospital. Clinic Flow Optimization & Patient Scheduling using Process Simulation. www.Createasoft.com • Texas Medical Center, Houston, TX. A new center of Systems Engineering in Healthcare has recently opened. The program called ‘Systems and Workflow Improvements Flexible Team’ will be working on Medical Centers throughout the region. An integral part of this program will be Industrial (Systems) Engineers • Cincinnati Children’s Medical Center. CEO and CFO provided the Webcast: http://www.ihi.org/knowledge/Pages/AudioandVideo/WIHIAllHospitalsinFavorofS avingMoneySayPatientFlow.aspx • Southern California Region. Cooperatively work on the use of ME for Operations Improvement in 20+ Regional Hospitals (Led by University SC) • York Hospital, PA. ED & Health Services Design •University of Iowa, Carver College of Medicine, Department of Anesthesia- Operations Research for Surgical Services. Alexander Kolker All rights reserved