Post on 27-Jan-2016
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The Stochastic Healthcare Facility
Configuration Problem
Amy Brown Math Teacher
Taylor High School Alief ISD
Dr. Wilbert WilhelmBarnes Professor
Industrial & Systems Engineering DepartmentTexas A & M University
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.
Industrial & systems engineering is a branch of engineering dealing with the optimization of complex processes or systems.
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
Research Team
Xue (Lulu) Han, Ph.D. candidate Khoon Yu Tan, teacher, RET Amy Brown, teacher, RET David Carmona, REU Brittany Tarin, REU
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
Research Relevance
Healthcare in the United States Underserved areas and populations Improve healthcare
effectiveness Healthcare administrators Government officials
Patient Behavior
• Patients decision tree for one service in one time period• Probabilistic function• Many variables
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
Recourse Evaluation
Demands from population centers are random but there is a need to evaluate the recourse cost for the capacity planningdecisions.
Probability Distribution Function
• Excess capacity results in idleness and unused resources
• Excess demand customers waiting and/or choosing competitor for service
Objective Function
Problem (HFCPa):
2 2
2 2
max
( / 2 )exp (2 )
( / 2 )exp (2 )
ls
st lst als alsl L s S t T l L s S a A
u lst lstlst lst lst lst lst lst lst
l L s S t T lst
o lst lstlst lst lst lst lst lst lst
lst
c K b x
Kc K K
Kc K K
l L s S t T
Excess demand
Excess capacity
Cost to adjust capacity Total reimbursement
>80% utilization >95% of the time
Explicit Recourse
Total reimbursement
1max [ ( ,..., , , )]ls
Tst lst als als
l L s S t T l L s S a A
c K b x E g N N x K
EEEEEEEEEEEEE E
• Problem (HFCPb): maximize excess revenue
Cost to adjust capacity
Expected recourse cost
Research Activities: Recourse cost
• Assist in determining a piecewise linear approximation using tangentlines 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
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
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