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