2010 Healthcare Process Improvement Network (HPIN)Annual General Meeting

Staffing Decision-Making Using Simulation Modeling: Examples and Principles

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Annual General Meeting

September 29, 2010

Alexander Kolker, PhD

• The use of Management Engineering methodology for staffing decision-making.

• Part 1 - Quality and Cost: Outpatient Flu Clinic.

Outline

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• Part 2 - Quality and Cost : Optimal PACU Nursing Staffing.

• Overall Take-Away.

• Summary of Fundamental Management Engineering Principles.

Traditional (Intuitive) Management is based on• Past experience.• Intuition or educated guess. • Static pictures or simple linear projections.

What is Management?

Management is controlling and leveraging available resources (material, financial and human) aimed at achieving the performance objectives.

Some Definitions

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• Static pictures or simple linear projections.

Resource inputSystem output

Linear projection assumes that the output is directly proportional to the input, i.e. the more resources (material and human) thrown in, the more output produced (and vice versa.)

• Management Engineering (ME) is the discipline of building and using validated mathematical models of real systems to study their behavior aimed at making justified business decisions.

What is Management Engineering?

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• This field is also known as operations research.

Thus, Management Engineering is the application of mathematical methods to system analysis and decision-making.

Part 1

Quality and Cost:

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Quality and Cost:

Outpatient Flu Clinic

• An outpatient flu clinic is supposed to open during a flu season to provide flu vaccine shots on a walk-in basis •The clinic stays open from 8:00 a.m. to 6:00 p.m.

It is expected that on an average day patient arrival rate will be:• from 8:00 a.m. to 10:00 a.m. - about 9 patients per hour• from 10:00 a.m. to 2:00 p.m. - about 15 patients per hour• from 2:00 p.m. to 4:00 p.m. - about 9 patients per hour• from 4:00 p.m. to 6:00 p.m. - about 12 patients per hour

Problem Description

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Key point: the average patient arrival rate is highly variable during a typical day

• Giving a shot will take on average about 8 minutes but could be in the range from 6 minutes to 10 minutes

• Flu shot costs a patient $20; the clinic’s cost of one vaccine dose and supplies is $1. Staffing pay rate is $14/hour

Clinic’s management should decide:

• How many medical providers are needed to staff the clinic on a typical day?

The Goal

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a typical day?

• What will the projected net revenue be (on a weekly basis)?

• The projected total average number of patients for a typical day is 120 (=9*2+15*4+9*2+12*2)

• One provider is going to serve on average 60 minutes/8 minutes = 7.5 patients/hour

• Hence 120/7.5 =16 hours of staffing time will be needed to serve all patients

Traditional Management Approach

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patients

• Thus, two medical providers should be scheduled to staff the clinic

•One is scheduled to work from 8:00 a.m. to 5:00 p.m.

•Another one is scheduled to work from 9:00 a.m. to 6:00 p.m.

Both have unpaid 30 min lunch time and additional paid 30 min off for a few short breaks

• Practically no (or very short) patient waiting time is expected.

• The weekly average revenue is going to be 5 days*120*$20 = $12,000

• The weekly labor cost for two providers is: ($14/hr*8.5 hrs*5days)*2 = $1,190

• The total weekly vaccine and supplies average costs is $120*5 days=$600

Traditional Management Approach

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• Hence, the average clinic’s weekly net revenue is expected to be

$12,000 - $1,190- $600 = $10,210

• Because of inevitable variability of the daily number of patients coming for the shot and the time it takes to give a shot, the actual staffing needs and the actual estimated net revenue will differ significantly from the average values

• On top of that, it is observed that some patients will leave without a shot if their waiting time is longer than 20 min

Management Engineering Approach

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• In order to develop a realistic evaluation of clinic performance, the process variability and patients leaving without a shot should be taken into account

• It is possible only using simulation analysis of clinic’s operations

Management Engineering Approach

Layout of a simulation model

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Layout of a simulation model

Predicted Clinic’s Performance Results§ 99% percent Confidence Interval (CI) for the weekly number of served patients: 509 to 513

(much lower than anticipated 600 patients !!!)§ Because of waiting longer than 20 minutes, 105 to 109 patients (16% to 17%) will leave

without a shot

Management Engineering Approach

Scenario 1 - Baseline

One provider works from 8:00 a.m. to 5:00 p.m. (1 FTE)Another provider works from 9:00 a.m. to 6:00 p.m. (1 FTE)

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§ Total weekly clinic net revenue is going to be $8,483 to $8,560(much lower than expected $10,210 based on averages)

Next stepDoes it make sense to hire an additional part-time provider to increase net revenue and reduce the number of leaving patients?

NoteFrom a traditional management standpoint this is not needed because 16 hours of working time on average is enough to meet the average patient demand for service time. Therefore an additional provider would result in staff under-utilization.

Predicted Clinic’s Performance Results§ 99% CI of the weekly number of served patients: 556 to 559§ Because of waiting longer than 20 min, 58 to 61 patients will leave without a shot.§ Total weekly clinic net revenue is going to be from $9,026 to $9,088

(much better than the original amount $8,483 - $ 8,560 but still lower than the expected

Management Engineering Approach

Scenario 2

An additional part-time provider (on top of 2 FTEs) works 5 hours in the morning 8 am to 1 pm, ( 0.6 FTE) with 30 min paid time-off for short breaks

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(much better than the original amount $8,483 - $ 8,560 but still lower than the expected amount based on the averages)

Take-away§ An additional part-time provider (0.6 FTE) results in an additional operational and

staffing costs; however, these costs are well offset by the clinic’s higher revenue because more paying patients are served.

Management QuestionIs it possible to improve the clinic’s performance further if the same 0.6 FTE is placed in the second shift, from 1 pm to 6 pm?

• Predicted Clinic’s Performance Results§ 99% CI of the weekly number of served patients: 561 to 565§ Because of waiting longer than 20 minutes, 52 to 56 patients will leave without a shot.§ Total weekly clinic’s net revenue is going to be $9,158 to $ 9,238 which is better than

that in Scenario 2.

Management Engineering Approach

Scenario 3

An additional provider works in the afternoon from 1p.m. to 6 p.m. (0.6 FTE.)

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that in Scenario 2.

• Take-away§ Placing a part-time third provider (0.6 FTE) in the right shift (afternoon in this case) does help to serve more patients and increase the net revenue and clinic’s performance, despite the higher costs of keeping an additional provider

Summary of a few analyzed scenarios

# Operations Scenario

DescriptionWeekly

Number of served patients

Left without shot

Weekly net

revenue

NOTE

1 Baseline 2 providers: 8 a.m. – 5 p.m. and 9 a.m. to 6 p.m.

600 0 $10,210 Projected data are based on the average service time and the averagenumber of patients

509 –513 105 –109

$8483-$8560

Data are based on the variable service time and the variable number of patients

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patients

2 Additional 0.6 FTE in the morning

2 providers: 8 a.m. to 5 p.m. and 9 a.m. to 6 p.m.; additional 0.6 FTE from 8 a.m. to 1p.m.

556 – 559 58 –61 $9,026-$9,088

Additional staffing costs are offset by the revenue from serving more patients

3 Additional 0.6 FTE in the afternoon

2 providers: 8 a.m. to 5 p.m. and 9 a.m. to 6 p.m.; additional 0.6 FTE from 1 p.m. to 6 p.m.

561-565 52-56 $9,158-$9,238

Additional staffing cost is offset by revenue from serving more patients;It is better to place 0.6 FTE in the afternoon

Management Engineering ApproachNet revenue vs. the number of served patients and corresponding FTE

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CONCLUSIONS

• There is an important trade-off between the number of served patients and the net revenue

• The revenue generated by serving more patients offsets the operational and staffing costs of additional resources

• However, at some point the cost of resources exceeds the revenue generated by serving only a few more patients; hence the net revenue goes down

• Management engineering simulation methodology allows predicting process performance outcomes; thus, making truly efficient

Management Engineering Approach

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process performance outcomes; thus, making truly efficient managerial decisions

Savage, S., 2009. The Flaw of Averages. John Wiley & Sons, Inc, Hoboken, New Jersey, pp. 392.

Kolker, A., 2009. Queuing Theory and Discrete Events Simulation for Health Care: from basic processes to complex systems with interdependencies. Chapter 20. In: Handbook of Research on Discrete Event Simulation. Technologies and Applications. IGI-press Global, pp.443-483.

NoteMany other illustrations of fundamental deficiency of managerial decisions based on average input data without taking into account the inevitable process and data variability are provided, for example, in:

Part 2

Quality and Cost:

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Optimal PACU Nursing Staffing

• PACU nursing daily workload is highly variable because patient census often changes fast from 0 to the peak value within an hour or two.

• The required adequate number of nurses to care for the volume of patients entering the PACU from the OR is not known.

• The anesthesiologist and the OR nurse are required to take care of the patient until a PACU nurse becomes available. This in turn results in:

Problem Description

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§ Delays in OR because anesthesiologist and OR nurse are not available.§ Frustration among OR staff and surgeons due to delay of cases.§ A sense of urgency among PACU staff to ‘hurry’ with the current patient, so

they could take another waiting patient. § This pressure increases the risk of medical errors because the nurses are

rushed.

• Managers should manually reset the staffing (up or down) within a few hours of staffing periods trying to keep the required nurse-to-patient ratio (in acute care it is 1:1).

• The percent of patients cared for with the required nurse-to-patient ratio 1:1 (improving quality of care).

The Goal

Develop a methodology for calculating an optimal PACU nursing staffing plan that provides simultaneous maximizing of:

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and

• Staff utilization (decreasing the cost of overtime and the cost of extended shift coverage).

• PACU managers typically adjusted nursing staffing needs manually based on the past historical averagenumber of patients.

• Because of high variability of the actual number of patients around the average, the resulting staffing

Traditional Management

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patients around the average, the resulting staffing usually either is not enough to deliver proper quality of care or it is not cost-effective.

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Patients

Staff on this level ?

or Staff on these levels ?

Typical plot of the PACU daily average number of patients (on annual basis)

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0

2

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Time

MEAN 0 0.4 1.6 2.9 4.2 5.3 5.7 6 6.2 6.2 6 5.8 5.7 5.5 5.4 5.4 5.3 5.2 6.2 4.4 3.9 3.4 3 2.3 2 1.3 0.9 0.8 0.6 0.5 0.5 0.4 0.2

MIN 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

MAX 1 3 7 9 10 11 11 15 13 12 12 12 11 13 12 11 13 12 13 11 11 9 11 9 6 5 3 4 4 3 3 3 2

MEDIAN 0 0 1 3 4 5 6 6 6 6 6 6 6 5 5 5 5 5 6 4 4 3 3 2 2 1 1 1 0 0 0 0 0

MODE 0 0 1 3 5 6 6 6 6 7 5 5 6 6 6 5 4 4 7 4 3 3 3 2 2 1 1 0 0 0 0 0 0

0700

0730

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or Staff on these levels ?

Management Engineering Approach

Step 1

Layout of the simulation model for calculating PACU census at every moment in which it is changed based on the balance of admissions and discharges.

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Census (i) (current period) = census (i-1) (previous period) + [# admissions (i) – # discharges (i) ]; i = 1, 2, 3, …….

census PACU

0123456789

10111213

cns

Calculated census for 40 weeks

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3-rd floor PACU census, week 11

0

2

4

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1856 1858 1860 1862 1864 1866 1868 1870 1872 1874 1876 1878 1880 1882 1884 1886 1888 1890 1892 1894 1896 1898 1900 1902 1904 1906 1908 1910 1912 1914 1916 1918 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968

time, hrs

cns

00 168 336 504 672 840 1008 1176 1344 1512 1680 1848 2016 2184 2352 2520 2688 2856 3024 3192 3360 3528 3696 3864 4032 4200 4368 4536 4704 4872 5040 5208 5376 5544 5712 5880 6048 6216 6384 6552 6720

time, hrs

Example of week 11 census (from 7:30 am to 11:30 pm)

Mon Tue Wed Thu Fri

Time of day

Step 2

For each staffing time slot (for every hour from 7:30 a.m. to 11:30 p.m.) and for each possible number of nurses from the nursing pool (from 1 to 14) calculate:

• Percent of covered patients (with the patient-to-nurse ratio 1:1).

and

• Percent of time these nurses are utilized.

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Note:

National standard (American Society of Perianesthesia Nursing) requires that minimum two nurses be present at all times when a patient (even only one) is in the PACU. Therefore if the mathematically optimal number of nurses dropped down to one it should be kept equal to two to comply with the national standard.

• Percent of time these nurses are utilized.

• The optimal number of nurses corresponds to the combined maximum.

Example of Hourly PACU Census Variability

Day of week

Time of day

(decimal units) 7:30-8:30 8:30-9:30 9:30-10:30 10:30-11:30 11:30-12:30 12:30-13:30 13:30-14:30 14:30-15:30

1 9.06667 11 9.31667 21 9.41667 31 9.85 21 10.0333 11 10.0667 21 10.6 31 10.6667 41 10.8333 31 10.8667 21 11.2833 3

Staffing time slot (every hour)

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1 11.2833 31 11.6667 21 11.85 11 11.9167 01 12.0333 11 12.3667 21 12.4 31 12.6167 21 13.2 31 13.25 21 13.8667 11 13.8667 21 14 11 14 21 14.5833 11 14.5833 21 14.75 31 14.85 41 15 31 15.1167 41 15.4 3

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5

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3mber of nurses

The optimal daily number of nurses for each 1-hour staffing time slot daily time slot

optimal # of nurses

% of covered patients

7:30-8:30 2 96

8:30-9:30 4 100

9:30-10:30 5 98

10:30-11:30 5 96

11:30-12:30 7 99

12:30-13:30 6 93

13:30-14:30 6 99

Example of Calculated Optimal Staffing (1 hour slot)

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23:30-24:00

22:30-23:30

21:30-22:30

20:30-21:30

19:30-20:30

18:30-19:30

17:30-18:30

16:30-17:30

15:30-16:30

14:30-15:30

13:30-14:30

12:30-13:30

11:30-12:30

10:30-11:30

9:30-10:30

8:30-9:30

7:30-8:30

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2

1

0

daily time slot

num 13:30-14:30 6 99

14:30-15:30 8 99

15:30-16:30 6 95

16:30-17:30 5 99

17:30-18:30 4 95

18:30-19:30 3 96

19:30-20:30 4 100

20:30-21:30 3 100

21:30-22:30 2 94

22:30-23:30 2 100

23:30-24:00 2 100

Comparison of Current and Optimal Staffing (30 minute slot)

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mber

currentoptimal

typestaffing

Current vs. optimal staffing

Current staffingis excessive

Current staffing is too low

Current vs. Optimal Staffing

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2230-2300

2200-2230

2130-2200

2100-2130

2030-2100

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1930-2000

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1200-1230

1130-1200

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1030-1100

1000-1030

0930-1000

0900-0930

0830-0900

0800-0830

0730-0800

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1

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staffing num

Example of a more detailed staffing plan adjusted for seasonal variability and different days of week (2 hours slot)

Monday Jan-May June-Aug Sep-Dec8.-10 3 3 310.-12 5 7 512.-14 6 7 614.-16 7 6 516-18 4 6 618-20 2 3 520-22 2 2 222-22:30 2 2 2

Tue-Thu7:30-9:30 5 4 5

7 7 6

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9:30-11:30 7 7 611:30-13:30 7 7 813:30-15:30 11 7 715:30-17:30 6 9 717:30-19:30 3 4 419:30-21:30 2 2 221:30-23:30 2 2 2

Friday7:30-9:30 4 6 79:30-11:30 8 8 711:30-13:30 7 9 1013:30-15:30 6 8 715:30-17:30 6 6 1017:30-19:30 3 7 519:30-21:30 2 2 221:30-23:30 2 2 2

Optimal Staffing Versus Currently Used

Before implementing PACU optimal staffing plan in 2009 additional nursing cost was:

Overtime $ 5,430

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Implementing optimal staffing plan will result in 80% annual nursing cost saving, i.e. $16,457

Extended shift coverage $15,141

Total $20,571

• The optimal staffing nursing plan development based on management engineering methodology helps managers to take the guesswork out of their daily decision-making.

• The optimal staffing provides the trade-off between the percent of covered patients for the required nurse-to-patient ratio (this improves the quality of care) and nursing staff utilization (this reduces the cost of doing business.)

Conclusions

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doing business.)

• The optimal staffing plan allowed PACU managers making adjustments to the start times, shift length, and the number of required FTEs.

• This allowed, in turn, to place the correct number of nurses in the PACU when they are needed: the right amount of resources in the right place at the right time.

• This methodology and the PACU staffing plans are currently being implemented for planning surgical services at Children’s Hospital of Wisconsin.

Main Take-Away

Management Engineering and System Simulation Modeling is the only methodology that helps to quantitatively address the following typical hospital issues:

Given the variable patient volume:

• How many beds are needed for each unit?

• How many procedure rooms are needed for each service?

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• How many nurses/physicians should each unit schedule for the particular shift?

• What will patient wait time be and how to reduce it to the acceptable level?

• What will an efficient clinic’s schedule look like?

And so on, and so on…

And the Ultimate GoalHow to manage hospital operations to increase profitability (reduce costs, increase revenue) while keeping high quality, safety and outcomes standards for patients?

Summary of Some Fundamental Management Engineering Principles

• Systems behave differently than a combination of their independent components.

• All other factors being equal, combined resources are more efficient than specialized (dedicated) resources with the same total capacity/workload.

• Scheduling appointments (jobs) in the order of their increased

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• Scheduling appointments (jobs) in the order of their increased duration variability (from lower to higher variability) results in a lower overall cycle time and waiting time.

• Size matters. Large units with the same arrival rate (relative to its size) always have a significantly lower waiting time. Large units can also function at a much higher utilization % level than small units with about the same patient waiting time.

• Work load leveling (smoothing) is an effective strategy to reduce waiting time and improve patient flow.

• Because of the variability of patient arrivals and service time, a reserved capacity (sometimes up to 30%) is usually needed to avoid regular operational problems due to unavailable beds/resources.

• Generally, the higher utilization level of the resource (good for the organization) the longer is the waiting time to get this resource

Summary of Some Fundamental Management Engineering Principles – continued

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organization) the longer is the waiting time to get this resource (bad for patient). Utilization level higher than 80% to 85% results in a significant increase in waiting time for random patient arrivals and random service time.

• In a series of dependent activities only a bottleneck defines the throughput of the entire system. A bottleneck is a resource (or activity) whose capacity is less than or equal to demand placed on it.

• An appointment backlog can remain stable even if the average appointment demand is less than appointment capacity.

• The time of peak congestion usually lags the time of the peak arrival rate because it takes time to serve patients

Summary of Some Fundamental Management Engineering Principles – continued

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peak arrival rate because it takes time to serve patients from the previous time periods (service inertia.)

• Reduction of process variability is the key to patient flow improvement, increasing throughput and reducing delays.

APPENDIX

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APPENDIX

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.

What is a Simulation Model?

• 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 on the computer model and test the effectiveness of various solutions (changes) beforeimplementing the change.

How Does a Typical Simulation Model Work?

A simulation model tracks the move of entities through the system at distinct points of time (thus, discrete events.) The detailed track is recorded of all processing times and waiting times. In the end, the system’s statistics for entities and activities is gathered.

Example of Manual Simulation (step by step)

Let’s consider a very simple system that consists of:• A single patient arrival line. • A single server.

1

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A few random numbers sampled from these two distributions are, for example:

Inter-arrival time, minutes Service time, minutes2.6 1.42.2 8.81.4 9.12.4 1.8…. ….and so on… and so on….

Suppose that patient inter-arrival time is uniformly (equally likely) distributed between 1 minute and 3 minutes. Service time is exponentially distributed with the average 2.5 minutes. (Of course, any statistical distributions or non-random patterns can be used instead.)

We will be tracking any change (or event) that happened in the system. A summary of what is happening in the system looks like this:

Event # Time Event that happened in the system

1 2.6 First customer arrives. Service starts that should end at time = 4.

2 4 Service ends. Server waits for patient.

3 4.8 Second patient arrives. Service starts that should end at time = 13.6. Server idle 0.8 minutes.

4 6.2 Third patient arrives. Joins the queue waiting for service.

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5 8.6 Fourth patient arrives. Joins the queue waiting for service.

6 13.6 Second patient (from event 3) service ends. Third patient at the head of the queue (first in, first out) starts service that should end at time 22.7.

7 22.7 Patient #4 starts service…and so on.

In this particular example, we were tracking events at discrete points in time t = 2.6, 4.0, 4.8, 6.2, 8.6, 13.6, 22.7

DES models are capable of tracking hundreds of individual entities, each with its own unique set of attributes, enabling one to simulate the most complex systems with interacting events and component interdependencies.

Basic Elements of a Simulation Model

• Flow chart of the process: Diagram that depicts logical flow of a process from its inception to its completion.

• Entities: Items to be processed (i.e. patients, documents, customers, etc.)

• Activities: Tasks performed on entities (i.e. medical procedures, document approval, customer checkout, etc.)

• Resources: Agents used to perform activities and move entities (i.e. service

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• Resources: Agents used to perform activities and move entities (i.e. service personnel, operators, equipment, nurses, physicians.)

Connections

• Entity arrivals: They define process entry points, time and quantities of the entities that enter the system to begin processing.

• Entity routings: They define directions and logical condition flows for entities (i.e. percent routing, conditional routing, routing on demand, etc.)

Typical Data Inputs Required to Feed the Model

• Entities, their quantities and arrival timesPeriodic, 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.

• The capacity of each activity

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• The capacity of each activity

The maximum 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.