1. The Stochastic Healthcare Facility Configuration Problem Amy Brown Math Teacher Taylor High School Alief ISD Dr. Wilbert Wilhelm Barnes Professor Industrial & Systems Engineering Department Texas A & M University

2. Industrial & Systems Engineer determine the most effective ways to use the basic factors of production—people, machines, materials, information, and energy—to make a product. concerned with increasing productivity through the management of people, methods of business organization, and technology. be good at solving problems combine their technical knowledge with a sense of human capabilities and limitations. be able to organize many details into a broad view of the total operations and organization of a company.

3. Industrial & systems engineering is a branch of engineering dealing with the optimization of complex processes or systems.

4. Dr. Wil Wilhelm Ph.D. and MS in industrial engineering and operations research BS in mechanical engineering Registered Professional Engineer in Ohio specializes in integer programming, scheduling, and supply chain design Current research involves: healthcare facility configuration ; scheduling surgeries; rescheduling; locating direction finder, among others

5. Research Team Xue (Lulu) Han, Ph.D. candidate Khoon Yu Tan, teacher, RET Amy Brown, teacher, RET David Carmona, REU Brittany Tarin, REU

6. Project Summary The stochastic healthcare facility configuration problem decides the locations and capacity level for the firm’s facilities in order to maximize total revenue excess. The uncertain demands from population centers place difficulty in evaluating the capacity configuration decisions. Objective to derive models of workload, capacity, and recourse and to optimize SHFCP

7. Research Relevance Healthcare in the United States Underserved areas and populations Improve healthcare effectiveness Healthcare administrators Government officials

8. Patient Behavior Patients decision tree for one service in one time period Probabilistic function Many variables

9. Capacity Configuration Time periods capacity Capacity planning network with opening, expanding, contracting, and closing operations. Nodes sharing a same row denote the same capacity level. Columns denote the time period Arrows(arcs) denote decisions

10. Recourse Evaluation Demands from population centers are random but there is a need to evaluate the recourse cost for the capacity planning decisions.

11. Probability Distribution Function Excess capacity results in idleness and unused resources Excess demand customers waiting and/or choosing competitor for service

12. Objective Function Problem (HFCP a ): Excess demand Excess capacity Cost to adjust capacity Total reimbursement >80% utilization >95% of the time

13. Explicit Recourse Total reimbursement Problem (HFCP b ): maximize excess revenue Cost to adjust capacity Expected recourse cost

14. Research Activities: Recourse cost Assist in determining a piecewise linear approximation using tangent lines method to lower the approximation error. Design a lesson for calculus students to perform a similar activity for a function as they learn about tangent lines and error. Excess capacity Excess demand

15. Summary Probability and statistical techniques are employed to address the SHFCP. Locations and capacity level for the firm’s facilities in order to maximize total revenue excess. Cost to adjust capacity Minimizing expected recourse will allow facilities to make efficient decisions

16. Thank You TAMU E3 program Dr. Wilhelm Xue (Lulu) Han Khoon Yu Tan Brittany Tarin and David Carmona Armando Vital, Marius Maduta, Ashwin Rao, and Cheryl Page