The Stochastic Healthcare Facility Configuration Problem

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

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 capacity Time periods • 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 (HFCPa): Cost to adjust capacity Total reimbursement Excess demand >80% utilization >95% of the time Excess capacity

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

14. Research Activities: Recourse cost Excess demand Excess capacity • 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.

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