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. Research 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

3. Classroom Project Overview: • Introduction of Engineering: • Presentation of E3 experience • Design Process • Fields of Engineering • Engage activity • Evaluate: • Partners present piecewise function • Post test • Exploration activity: • Healthcare configuration • Design Process cont. • Explain: • Share research question PowerPoint • Discuss the advanced mathematics • Elaborate: • Regression analysis of data • Qualitative decision making with justification

4. Day 1 – What is Engineering? Teacher: • Presentation of E3 poster and discussion of the E3 experience. • Show video: TBD • Presentation of Engineering Process and engineering fields. Question and Answer Student: • TLW optimize a flight plan as the variables within the problem change. (TLW = The learner will) • Students will work in pairs on determining the optimal flight that will minimize time of travel while variables change. • Students (pairs) will share out decisions and justifications of those decisions to the whole group.

5. Day 2 – Healthcare Configuration Exploration Student: • TLW develop ideas of parameters involved in a healthcare configuration type problem • Given regional map and population centers students will work with a partner to brainstorm parameters and constraints that will affect decisions as a healthcare administrator • Each student partnership will share their ideas with the whole group.

6. Day 3 – So why? And how? Teacher: • Share my presentation of the healthcare facility configuration problem, the relevance of the research, and discuss the connection to the brainstorming and analysis that they did on the previous day. • Discuss the advanced mathematics that is involved for further analysis and how it will be applied.

7. Day 4 – Data Analysis Student: • TLW make qualitative decisions based on regression analysis for a set of data. • Students will work in pairs with a data set and try different regressions to determine the best model that is continuous. • Students will write and present a piecewise function that best models their data to include justification. Specifically answer the questions: Why is it important to consider the accuracy of the model to be used? How is this accuracy achieved? Is piecewise function an overestimate or underestimate of data?

8. Day 5 – Now I know!! Student: • Partners will present the piecewise function for their data set. Justify reasoning and procedures that lead to their conclusion. • Individually students will take post test (time permitting)

9. Questions for pre/post test • Name two types of discontinuity that a function could have:____________________________ • Is f(x) = • Determine the value of “a” such that f(x) is a continuous function. • The function in the previous question is a ____________ function.

10. Tangent Line Approximation FutureProject - Student: • TLW use tangent line method on a function given certain conditions and determine a piecewise function that will keep the relative error under a given percent of error. • Students will work in pairs with their given function and conditions • Students will graph function on large poster graph paper with tangent lines and calculations • Students will demonstrate that the results are within given relative error

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