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

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

Classroom Project Overview: Introduction of Engineering:  Presentation of E 3 experience  Design Process  Fields of Engineering  Engage activity 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 Evaluate:  Partners present piecewise function  Post test

Day 1 – What is Engineering? Teacher: Presentation of E 3 poster and discussion of the E 3 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.

Day 2 – 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. Healthcare Configuration Exploration

Day 3 – 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. So why? And how?

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?

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)

Questions for pre/post test 1. Name two types of discontinuity that a function could have:____________________________ 2. Is f(x) = 3. Determine the value of “a” such that f(x) is a continuous function. 4. The function in the previous question is a ____________ function.

Future Project - 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 Tangent Line Approximation

Thank You TAMU E 3 program Dr. Wilhelm Xue (Lulu) Han Khoon Yu Tan Brittany Tarin David Carmona Cheryl Page, Ashwin Rao, Tim Chinn, Armondo Vital, and Marius Maduta