Khoon Yu Tan Math Teacher John H Reagan High School Houston Independent School District

1. Stochastic Healthcare Facility Configuration Problem: Expected Excess Demand & Expected Excess Capacity Study Dr. Wilbert WilhelmBarnes Professor Industrial and Systems Engineering Department Texas A&M University Khoon Yu Tan Math TeacherJohn H Reagan High School Houston Independent School District

2. Content • 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. Content • 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. 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.

5. Content • 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. 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

7. Content • 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. 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 model’s objective is to maximize total revenue excesswhile deciding the locations of facilities and capacity levels whereby a provider can open, expand, contract, or close a facility

9. Content • 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. 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!

11. Content • 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. 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

13. Content • 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. 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?

15. Content • 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. Research Project Activity (ProbabilityDistribution of PatientDemand) 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. Research Project Activity (ExpectedExcessDemand) 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. Research Project Activity (ExpectedExcessCapacity) 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. Research Project Activity (LinearizingtheExcessDemand/CapacityFunctions) 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. Content • 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. 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

22. Content • 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. 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