Khoon Yu TanMath Teacher

John H Reagan High SchoolHouston Independent

School District

Dr. Wilbert WilhelmBarnes Professor

Industrial and Systems Engineering Department

Texas A&M University

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

Microelectronics,

telecommunications,

retail, transportation,

hospitals, government, etc.

Production engineers, supply chain managers, operations analysts, quality engineers,

information system specialists, management consultants, etc.

Design, implement, or improve integrated systems comprised of people, materials,

information, or energy

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

• 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

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

• 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 model’s 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

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

• 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

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

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

About 18% of GDP and rising!

Cost matters to providers!

U.S. is expanding healthcare access in underserved areas

Population aging and government policies and legislation

PRUDENCEPRUDENCE

OPPORTUNITYOPPORTUNITY

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

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?

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

For a fixed location, service, and time combination, W, which represents (random) patient demand, follows the normal distribution with mean M and variance . 2The graph above shows the (probability density) function of the (standard) normal distribution, . Here, .)(w Ww

Goal: Study the convexity of the expected excess demand function that represents the shaded region above. The expected excess demand

function, E[u], is

where K represents capacity.

MK

KMeMK

1)(2

2

2

2

)(

Goal: Study the convexity of the expected excess capacity function that represents the non-shaded region above. The expected excess

capacity function, E[o], is

where K represents capacity.

MK

MKeMK

)(2

2

2

2

)(

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

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

• 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

• Industrial and systems engineering• Dr. Wilbert Wilhelm’s 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

• Texas A&M 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