1. Khoon Yu Tan Math Teacher John H Reagan High School Houston Independent School District Dr. Wilbert Wilhelm Barnes Professor Industrial and Systems Engineering Department Texas A&M University

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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!

11. 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

12. 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 PRUDENCE OPPORTUNITY

13. 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

14. 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?

15. 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

16. 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,.

17. 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.

18. 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.

19. 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

20. 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

21. 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

22. 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

23. Texas A&M University E 3 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