optimal staffing modeling with variable patient ...

OPTIMAL STAFFING MODELING WITH VARIABLE PATIENT DEMAND: PRINCIPLES AND EXAMPLES Alexander Kolker, PhD Data Scientist API Healthcare, a GE Healthcare company July 14, 2015

Program Agenda

GE Belief: Deliver Results in an Uncertain World. 1 Business Problem 2 The technology of the Solution & Data needs 3 Business Outcomes 4 Challenges / Future Directions 5 Conclusions

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Program Agenda Analytics  The discipline and practice of using various quantitative methods to aid in solving business /engineering /scientific problems.  The work done during a project that delivers analytics, and reporting results to stakeholders and decision-makers.  Discovery and communication of data patterns in big data sets (“big data”).

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Business Problem

A Big Picture: Nurse Staff Planning Framework Strategic/Budget •

Time period: medium & long-term

•

Capacity Planning and Budgeting staffing needs

•

Scheduling Policies

Focus of this presentation 4

Tactical/Scheduling • Time Period: Biweekly or Monthly • Estimate Staffing Levels on weekly basis • Base Schedule Creation on weekly basis • Preference based SelfScheduling

Operational/Allocation

• Time Period: Daily • Dynamically reacting to variance • Dynamic Allocation based on policies • Floating • Contract • Overtime

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Real Time Staff Assignments

• Time Period: RT • Workload Allocation 4 June 2014

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Business Problem (cont.)

The dynamic nature and inherent uncertainty of the healthcare systems creates two types of problems for the medium & longterm budgeting of the staffing needs:

• Over-staffing Budget , which results in staff idling, frequent sending staff home, and hurting operating margin and

• Under-staffing Budget, which results in overtime and/or premium pay that also hurts operating margin, and causes low quality of care. 5

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Business Problem (cont.)

Take-away : • •

typically staffing is based on the past average census the likelihood that the past average census is equal to the current actual census is very small; hence, frequent over- or under-staffing 6

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Business Problem (cont.) A problem well-defined is half-solved

Problem Statement: Given the variable patient census, predict the optimal planned (budgeted) nursing staffing for mid- to long-term periods, that minimizes the total cost of occurrences of random over- and under-staffing vs. planned (budgeted) value.

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Business Problem (cont.) • Benefit: Labor accounts for typically 50-60% of a unit’s budget. Less deviations from planned ahead budgeted staffing reduces the labor costs and increases staff satisfaction & morale.

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The Technology of the Solution

The type of problem–choosing the minimal cost staffing level with random variable demand in a given time period - is best addressed using a “newsvendor” type framework: If the random demand follows some cumulative probability distribution function in a given time period, F(s), then the optimal staffing level, s*, that balances the cost of “too many” (overage cost, Co) and the cost of “not enough” (underage cost, Cu) is calculated as the solution of the non-linear equation: F(s*)= Cu/(Cu+Co)

(derivation is in Appendix)

Note: A similar type equation is widely used in retail, supply chain management, etc. : F(s*)= (p-w)/(p-v), where p is the retail price, w- is the wholesale price, and v is the salvage price 9

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Data Needs Data required:  One Year of census data per unit 

Patient-to-Nurse ratio or customer’s look-up staffing table



the extra cost ($/hour) of over- & under-staffing (differential over the regular pay rate).

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The Technology of the Solution-Example 1

Cost ratio: Cu/(Cu + Co)

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The Technology of the Solution-Example 2

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The Technology of the Solution: User Interface

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The Technology of the Solution

Annual budgeted FTE

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Business Outcomes The developed technology tested at the following client sites: Baptist Memorial Hospital- Completed Pilot

Key Outcome: Optimal nurse staffing to budget presented to the client

Rehab Institute of Chicago- Pilot in Progress Key Outcome: First pilot of Shift_Predict solution

Methodist Hospital (Houston)- Pilot in Progress

Key Outcome: Defined rough cost savings from Optimal Budgeted Staffing (Initial ~13% of cost savings for client) 15

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Business Outcomes Methodist Hospital-Houston, TX Optimal Budgeted Staffing Day Shift Night Shift # over-staffing deviations from 152 173 optimal # under-staffing deviations from -109 -97 optimal # No Deviation 22 19

Actual Client Day Shift Night Shift

Optimal Budgeted Staffing

362

197

-16

-61

12

23

Actual Client Budgeted

Annual Cost of Understaffing, ($20/hour)

$26,160

$23,184

$3,888

$14,592

Annual Cost Of Overstaffing, ($10/hour) Total over- & understaffing cost

$13,080

$11,592

$43,458

$23,688

$74,016

$85,626

Annual cost saving using optimal budgeted staffing (vs. client cost) – 13.6% 16

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Challenges / Future Directions Next steps: Align engine built with Predix 2.0 Integrate with API Healthcare Solutions: - Shift_Select - Time & Attendance - Staffing & Scheduling

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Conclusions •Proper staffing and scheduling can make the difference between profitability and business failure •There are three main methodology frameworks for modeling optimal staffing with variable demand:  ‘newsvendor’ framework- best for determining the optimal staffing level in the specified time period with random demand– the focus of this presentation  linear optimization - best for determining the optimal staffing if the objective cost function and constraints can be presented as linear functions of the decision variables – in the development  discrete event simulation- best for stochastic systems with multiple staff categories, and shared and cross-trained staff – examples demonstrated 18

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Thank you

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Contact: Alexander Kolker Data Scientist API Healthcare, a GE Healthcare company [email protected]

APPENDIX

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APPENDIX (cont.)

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