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Problem Statement Solution Approach

Inputs Decisions

Impact/Results

Optimizing Nurse Staffing with Absenteeism Boying Liu1, Kayse Lee Maass1, Zhehui Wang1, Rama Mwenesi1,2, Mary Duck1,2, Hannah Schapiro1, and Mark S. Daskin1

1Department of Industrial and Operations Engineering, University of Michigan, 2University of Michigan Health System

High Variability in Nursing Needs

• Day–to-day

• Among units

Unit and Pool Nurse Absenteeism

• Approximately 20% at UMHS

Why Nurse Staffing

6:1 3.2:1 10:3 40:1

US Economy: 15.7 Trillion

Healthcare: 2.7 Trillion

In-Hospital Nursing:

250 Billion

Hospitals: 847 Billion

U. Mich Budget

6.6 Billion

Effects of Nursing Levels

↑ cost

Already ~10% of HC cost

Increased N:P ratio

Key Issues

Rank Cause Deaths/year Relative

1 Heart disease 652,000 665

2 Cancer 559,000 570

3 Stroke 144,000 147

4 Chronic Lower Respiratory Disease 131,000 134

5 Accidents 118,000 120

6 Preventable Medical Errors 98,000 100

7 Diabetes 75,000 77

8 Alzheimer’s Disease 72,000 73

What is the proper staffing level?

↑ patient care ↑ nurse satisfaction ↓ medication errors

• 5 pools of patient census data

- date range July 2005 - June 2013

- pool size from 3 to 13 units

• Nurse absenteeism: UMHS ~20%; Nationally ~7-10%

Data Analysis Results

• Day of week: Positive correlation

-Monday census is closely correlated to Sunday census

• Monthly: Positive correlation among consecutive months

• Annual: Positive correlation between 07/08 and 10/11

• Unit-to-unit: Positive correlation among most units

• Distributional analysis

-Data does not follow truncated Poisson distribution

Artificially simulating the process will be difficult due to lack of a

distributional form and correlations

2012 Historical Data • 4 Pediatric Units

• Unit Cost: 1

• Pool Cost: 1.0667

• Temp Cost: 1.1555

Cost Savings compared

to 80% staffing: -3.6% savings

- ~$9 billion in savings nationally

UMHS Data STRATEGIC –

How many nurses to hire in each

unit and the pool

TACTICAL –

Which nurses should work each

shift during a week

OPERATIONAL –

How to allocate pool nurses to

units; How many temps to hire

Distribution of nursing

needs by unit

Nurse preferences for

shifts; work rules

Distribution of nursing

needs by unit

Model Description

Solve no absenteeism model (𝑼𝒋 ∀𝒋 ∈ 𝑼𝒏𝒊𝒕𝒔, 𝑷)

Initialize staffing level w/

𝑼 𝒋 = 𝑼𝒋/(𝟏 − 𝑨𝒃𝒔 𝒓𝒂𝒕𝒆) ∀𝒋 and

𝑷 = P/(𝟏 − 𝑨𝒃𝒔 𝒓𝒂𝒕𝒆)

Solve absenteeism model, Sample # absent from binomial

distribution using 𝑼 𝒋 & 𝑷

Converge? Stop Y

Revise staffing level

N

How is Nursing Organized at UMHS?

Spatial and temporal demand correlations

Unit 1 Unit 2 Unit |J|

Temp nurses

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Nu

mb

er o

f D

ay

s E

ach

Ye

ar

Nurses Needed

Unit 2

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Nu

mb

er o

f D

ay

s E

ach

Ye

ar

Nurses Needed

Unit 3

0

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Nu

mb

er o

f D

ay

s E

ach

Ye

ar

Nurses Needed

Unit 4

Pool Nurses

$$$ Flexible

$$ Some Flex

$ Inflexible

Absenteeism

Absenteeism

Optimal Staffing Level Without Absenteeism

0

2

4

6

8

10

12

14

16

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%100%

Nu

mb

er

of

nu

rse

s

Salvage cost as percent of unit cost

Nurse staffing vs. salvage cost

Unit 1

Unit 2

Unit 3

Unit 4

Pool

E(Temp)

E(Salvage)

Conclusions • Optimal staffing must account for variability in demand, differences

in the cost of various types of nurses, and nurse absenteeism rates • Small percentage, but significant amount, of cost savings possible

Future Work • Refine absenteeism rates, perhaps by day of week or time of year • Account for seasonality of nursing demand, perhaps through another

layer of nursing staff between unit and pool nurses • Optimize assignment of units to pools • Work with UMHS nursing staff to implement findings

120

130

140

150

160

170

180

190

200

210

07/0

1/1

2

09/3

0/1

2

12/3

0/1

2

03/3

1/1

3

06/3

0/1

3

Cen

su

s

Date

Mott Census Daily per Fiscal Year: FY13

FY13

30 per. Mov. Avg. (FY13)

7 per. Mov. Avg. (FY13)

Min Unit nurse cost + Pool nurse cost + Temp nurse cost – Benefit of extra nurses s. t. • Hire enough nurses to adequately cover patient demand in each unit each day • All pool nurses are assigned each day

Inputs Decisions

Current Focus

Current Focus

Future Work

Solution Algorithm

• Sample results: Jan 2012- June 2013 • Relative Costs: -Unit Nurse: 1 -Pool Nurse: 1.10

-Temp Nurse: 1.19 -Salvage: 0.45

• 22% increase in total cost with absenteeism

Unit 1 Unit 2 Unit 3 Unit 4 Pool

No Absenteeism 7 6 8 10 1

20% Absenteeism 8 7 9 12 3

No Absenteeism vs. Absenteeism

U: # of unit nurses P: # of pool nurses