Khoon Yu Tan

1
Stochastic Healthcare Facility Configuration
Problem Expected Excess Demand Expected Excess
Capacity Study

• Khoon Yu Tan
• Math TeacherJohn H Reagan High School
• Houston Independent School District

Dr. Wilbert WilhelmBarnes Professor Industrial
and Systems Engineering Department Texas AM
University
2
Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

3
Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

4
Research Overview

• 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
  and analyzed
• The expected excess demand, Eu and expected
  excess capacity, Eo functions are as follow
  respectively
• where K represents capacity, M mean of
• patient demand, standard deviation of
• patient demand, and cummulative
• (probability) density function of patient
  demand.

Credit Xue (Lulu) Han
5
Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

6
Element of Research for Classroom Project

• The key element are the expected excess demand
  and expected excess capacity functions
• Students use analytical and graphical tools of
  Calculus and Pre-Calculus to study the functions
• The study of the functions helps improve the
  model that solves the healthcare facility
  configuration problem, which in turn helps to
  improve capacity-setting decisions, increasing
  cost effectiveness

Credit Xue (Lulu) Han
7
Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

8
College Board AP Calculus Learning Objectives

• Functions, Graphs, and Limits
• a) Analysis of graphs
• b) Asymptotic and unbounded behavior
  understanding asymptotes in terms of graphical
  behavior
• II. Derivatives
• a) Concept of the derivative derivative
  presented graphically, numerically, and
  analytically
• b) Derivative at a point
• i) slope of a curve at a point
• ii) tangent line to a curve at a point
  and local linear approximation
• c) Derivative as a function relationship between
  the increasing and decreasing behavior of f and
  the sign of f
• d) Second derivatives relationship between the
  concavity of f and the sign of f
• e) Applications of derivatives analysis of
  curves, including the notions of monotonicity and
  concavity

Asymptotes credit Wolfram MathWorld
Derivatives credit http//clas.sa.ucsb.edu/staff/
lee
9
Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

10
Day One of Project

• ENGAGE

• E3 experience industrial engineering,
  healthcare data, mathematical model
• Students inquire pre-day one about their or
  their parents healthcare spending insurance,
  out-of-pocket cost
• Poster, pictures, video,
• authentic data from students

EXPLORE

• Engineering fields and what engineers do in each
• Matching-cards game using pictures of
  engineering work from students everyday life
  names of engineering fields
• Think-pair-share and class sharing
• Shortest flight time discuss variables e.g.
  distance, route,
• time, speed, airport location

Engage credit http//www.dreamstime.com
Explore credit http//selinasvintage.blogspot.com
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Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

12
Days Two Three of Project

• EXPLAIN

• Students are to investigate the convexity of the
  expected excess demand capacity functions
• Students are to linearly approximate the
  functions within a certain percentage error
• Students follow the engineering design process

Design Process credit Project Lead The Way
Explain credit http//rikowski.wordpress.com/
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Days Two Three of Project

• ELABORATE

• Students are grouped in threes
• Groups are differentiated by tasks investigate
  convexity with respect to different variables
• Each group builds approximation models after
  selecting its approach
• The models differ in terms of approximation
  error, complexity (piecewise), computational cost
  (time)
• Each group selects its best model and presents
  its findings to the class

Design Process credit Project Lead The Way
Elaborate credit http//activedabawenya.blogspot.
com/
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Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

15
Days Four of Project

• EVALUATE

• When a group presents, other groups and teacher
  evaluate based on a rubric
• Within each group, members anonymously evaluate
  each others contribution
• Rubric clarifies assignment of points for
  different steps of the design process, reasoning,
  conclusion, and presentation
• Post-test

Evaluate credit http//www.strategicinteractions.
com/
16
Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

17
Sample Pre-Test Post-Test

• QUALITATIVE

QUANTITATIVE

• Why is excess demand an important factor in
  deciding where to open a healthcare facility, or
  to expand, contract or close an existing
  facility?
• Excess demand is costly
• Excess demand influences the decision to open a
  new facility or expand an existing one
• Excess demand causes loss of business (patients)
• Some patients may be unhappy
• I and II only b) II and III only
• c) I, II, and III only d) all of them

Differentiate the function with respect to
capacity level assuming other variables are held
constant? Four multiple-choice responses but
correct response is
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Content

• Research overview
• Element of research for classroom project
• College Board AP Calculus learning objectives
• Day one of project
• Days two and three of project
• Day four of project
• Sample pre-test and post-test
• Acknowledgements

19
Acknowledgements

• Texas AM 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 participant
• David Carmona Brittany Tarin, REU participants