Khoon Yu Tan

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Stochastic Healthcare Facility Configuration
Problem Expected Excess Demand Expected Excess
Capacity Study

• Khoon Yu Tan
• Math TeacherJohn H Reagan High School
• Houston Independent School District

Dr. Wilbert WilhelmBarnes Professor Industrial
and Systems Engineering Department Texas AM
University
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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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What is Industrial Systems Engineering?
Design, implement, or improve integrated systems
comprised of people, materials, information, or
energy
Production engineers, supply chain managers,
operations analysts, quality engineers,
information system specialists, management
consultants, etc.
Microelectronics, telecommunications, retail,
transportation, hospitals, government, etc.
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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Dr. Wilbert Wilhelm

• Barnes Professor
• Ph.D. and MS in industrial engineering
  operations research BS in mechanical engineering
• Systems Engineer at IBM Federal Systems Division
• Manufacturing Training Program and other
  positions at General Electric
• Registered professional engineer in Ohio
• Specializes in integer programming, scheduling,
  and supply chain design
• Current research involves healthcare
  configuration problem, supply chain design for
  assembly systems, scheduling surgeries, etc.
  among many areas

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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Research Project Background

• Dr. Wilhelm is directing a research project on
  the Stochastic Healthcare Facility Configuration
  Problem (SHFCP) sponsored by NSF Grant No.
  1129693
• Ph.D. candidate Xue (Lulu) Han, teachers Amy
  Brown and Khoon Yu Tan, and undergraduates David
  Carmona and Brittany Tarin are collaborating
• SHFCP prescribes healthcare facility
  configuration with regards to the location and
  size of each facility, the healthcare services
  each is to offer, and the capacity level of each
  service, all given that patient needs and demand
  are uncertain
• The models objective is to maximize total
  revenue excess while deciding the locations of
  facilities and capacity levels whereby a provider
  can open, expand, contract, or close a facility

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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Research Focus Relevance to Healthcare
Administrators

• A particular difficulty in deciding capacity
  configurations while maximizing total revenue
  excess is uncertainty in patient demand
• To allow the model to deal with patient
  uncertainty, expected excess capacity and
  expected excess demand functions are introduced
  (for further analytical work)
• These functions quantify the recourse cost
• If demand exceeds capacity, excess patients have
  to be referred to competing facilities or have
  their services postponed
• If capacity exceeds demand, staff and expensive
  equipment would be idle

The two scenarios above matter in the
capacity-setting decisions made by healthcare
administrators as cost is at stake in both
scenarios!
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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Connections between the Research and National
Healthcare Development
About 18 of GDP and rising!
Cost matters to providers!
PRUDENCE
OPPORTUNITY
U.S. is expanding healthcare access in
underserved areas
Population aging and government policies and
legislation
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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Research Question
What is the behavior of the expected excess
demand and expected excess capacity functions?
If convex, what are the best possible linear
approximations to the functions?
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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Research Project Activity (Probability
Distribution of Patient Demand)
For a fixed location, service, and time
combination, W, which represents (random)
patient demand, follows the normal distribution
with mean M and variance .
The graph above shows the (probability density)
function of the (standard) normal distribution,
. Here, .
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Research Project Activity (Expected Excess
Demand)
Goal Study the convexity of the expected excess
demand function that represents the shaded region
above. The expected excess demand function,
Eu, is
where K represents capacity.
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Research Project Activity (Expected Excess
Capacity)
Goal Study the convexity of the expected excess
capacity function that represents the non-shaded
region above. The expected excess capacity
function, Eo, is
where K represents
capacity.
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Research Project Activity (Linearizing the
Excess Demand/Capacity Functions)
Motivation Finding the best possible linear
approximations to the functions enables the use
of CPLEX to run the model given its stochastic,
integer nature containing continuous and binary
decision variables

• Xue (Lulu) Han has shown that the expected
  excess functions are convex using Poisson
  distribution, which approximates the normal
  distribution
• Taylor series expansion method does linearly
  (under) approximate the functions but its
  approximation error depends on the choice of
  capacity levels
• Variants of the tangent line method may
  approximate the functions with lower
  approximation error

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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Summary

• The SHFCP is solved via a model that aims to
  maximize total revenue excess, prescribing
  capacity configuration decisions (open, expand,
  contract, or close facilities)
• Part of the model contains the recourse cost
  i.e. the excess demand and excess capacity cost
• By finding the best possible linear
  approximations to the recourse functions if they
  are convex, healthcare providers can make more
  accurate capacity-setting decisions that are
  computationally more efficient

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Content

• Industrial and systems engineering
• Dr. Wilbert Wilhelms background
• Background on the Stochastic Healthcare Facility
  Configuration Problem
• Research focus and relevance to healthcare
  administrators
• Connections between the research project and
  national healthcare development
• Research question
• Research project activity
• Summary
• Acknowledgements

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Acknowledgements

• Texas AM University E3 Program
• Dwight Look College of Engineering
• National Science Foundation
• Nuclear Power Institute
• Chevron
• Dr. Wilbert Wilhelm, faculty adviser
• Xue (Lulu) Han, Ph.D. candidate
• Amy Brown, RET partner
• David Carmona Brittany Tarin, REU partners