Advanced Optimization Techniques in Healthcare Delivery Analysis

This assignment delves into the application of advanced optimization techniques within the healthcare sector. It highlights various methods, including stochastic programming and discrete convex analysis, and their use in solving complex problems such as healthcare facility location, capacity planning, disease screening, treatment delivery planning, and appointment scheduling. The assignment emphasizes the significance of these techniques in providing systematic and flexible tools for healthcare professionals to make informed decisions. Two specific optimization problems are presented: a pharmaceutical company's production of NasaMist drug and a brain tumor treatment scenario, with detailed results from solver analyses. The document underscores the importance of optimization in enhancing patient outcomes and improving administrative policies in healthcare, supported by relevant references.

Running head: ADVANCED OPTIMIZATION TECHNIQUES 1
Advanced Optimization Techniques in Healthcare Delivery
(Name of Student)
(Institutional Affiliation)
(Date of Submission)

Advanced Optimization Techniques in Healthcare Delivery 2
More Advanced Optimization Techniques in Healthcare Delivery and their Application
In healthcare, many different optimization techniques and methods have been applied
which have been ranging from the decisions of the operational levels to the design of the policies
of the national healthcare. These techniques in healthcare includes stochastic programming,
approximate dynamic programming and discrete convex analysis. They have been applied to
solve problems such healthcare facility location, capacity planning, disease screening, disease
prediction, treatment delivery planning, medical human resource scheduling, organ allocation
and transplantation, appointment scheduling, workforce scheduling, and even in designing of the
vaccines.
Optimization techniques have been considered to be superior to other systems in
providing systematic, rich and flexible equipment for the drug practitioners to critically do the
analysis and make informed decisions based on the complex problems under concern. The
optimization problems in healthcare are known to have certain significant characteristics than
those that arise from other industries (Pierskalla and Brailler, 1994). For instance we need to
apply discrete convex analysis in disease screening in the decision making problem to increase
the chances of patients’ life and thus prevents death. Consequently, the application of stochastic
programming in the allocation of medical facilities will greatly influence the administrative
policies and the rights of the patients. Therefore, decision makers in healthcare sector such as
nurses, physicians and the administrators should participate in decision making problems using
these optimization techniques.
Problem 80 (Pharmaceutical Company)
The total amount of NasaMist drug to be produced = 1000 pounds.
The ingredients:
Engine: Simplex LP
Solution Time: 0.031 Seconds.
Iterations: 0 Sub problems: 0
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Sub problems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume Nonnegative
NON
E

Advanced Optimization Techniques in Healthcare Delivery 3
Cell Name
Original
Value Final Value Integer
$B$2
Chemical
1 $0 $0 Contin
$B$3
Chemical
2 $0 $0 Contin
$B$4
Chemical
3 $0 $0 Contin
$B$5
Chemical
4 $0 $0 Contin
Cell Name Cell Value Formula Status Slack
$D$9
Chemical
1 C 0.01 $D$9<=60
Not
Binding 59.99
$D$10
Chemical
2 C 0.01 $D$10<=60
Not
Binding 59.99
$D$11
Chemical
3 C 0.04 $D$11<=60
Not
Binding 59.96
$D$12
Chemical
4 C 0.04 $D$12<=60
Not
Binding 59.96
$L$25 0 $L$25<=43263
Not
Binding
4326
3
Problem 90 (Brain Tumor)
Microsoft Excel 15.0 Answer Report
Worksheet: [1949908_990730870_P1490.xlsx]Data 60
Report Created: 1/14/2018 2:37:49 AM 0
Result: Solver found a solution. All Constraints and optimality conditions are
satisfied. 0
Solver Engine 0
Engine: Simplex LP 0
Solution Time: 0.015 Seconds. 0
Iterations: 0 Sub problems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001
Max Sub problems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume

Advanced Optimization Techniques in Healthcare Delivery 4
Nonnegative
Objective Cell (Max)
Variable Cells
Cell Name Original Value Final Value Integer
$G$2 Tumor 1 9 23 Contin
$G$3 Tumor 2 12 10 Contin
$G$4 Tumor 3 26 0 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$A$2 Beam 1 $A$2<=60 Binding 59
$B$2 Normal 1 24 $B$2<=60 Binding 36
$C$2 Normal 2 18 $C$2<=60 Binding 42
$D$2 Normal 3 12 $D$2<=60 Binding 48
$E$2 Tumor 1 30 $E$2<=60 Binding 30
$F$2 Tumor 2 18 $F$2<=60 Binding 42
$G$2 Tumor 3 0 $G$2<=60 Binding 60
$A$3 Beam 2 $A$3<=60 Not Binding 58
$B$3 Normal 1 18 $B$3<=60 Not Binding 42
$C$3 Normal 2 15 $C$3<=60 Not Binding 45
$D$3 Normal 3 9 $D$3<=60 Not Binding 51
$E$3 Tumor 1 27 $E$3<=60 Not Binding 33
$F$3 Tumor 2 23 $F$3<=60 Not Binding 37
$G$3 Tumor 3 0 $G$3<=60 Not Binding 60
$A$4 Beam 3 $A$4<=60 Not Binding 57
$B$4 Normal 1 14 $B$4<=60 Not Binding 46
$C$4 Normal 2 12 $C$4<=60 Not Binding 48
$D$4 Normal 3 20 $D$4<=60 Not Binding 40
$E$4 Tumor 1 20 $E$4<=60 Not Binding 40
$F$4 Tumor 2 15 $F$4<=60 Not Binding 45
$G$4 Tumor 3 0 $G$4<=60 Not Binding 60
$A$5 Beam 4 $A$5<=60 Not Binding 56
$B$5 Normal 1 6 $B$5<=60 Not Binding 54
$C$5 Normal 2 18 $C$5<=60 Not Binding 42
$D$5 Normal 3 18 $D$5<=60 Not Binding 42
$E$5 Tumor 1 9 $E$5<=60 Not Binding 51

Advanced Optimization Techniques in Healthcare Delivery 5
$F$5 Tumor 2 27 $F$5<=60 Not Binding 33
$G$5 Tumor 3 0 $G$5<=60 Not Binding 60
$A$6 Beam 5 $A$6<=60 Not Binding 55
$B$6 Normal 1 14 $B$6<=60 Not Binding 46
$C$6 Normal 2 6 $C$6<=60 Not Binding 54
$D$6 Normal 3 17 $D$6<=60 Not Binding 43
$E$6 Tumor 1 20 $E$6<=60 Not Binding 40
$F$6 Tumor 2 8 $F$6<=60 Not Binding 52
$G$6 Tumor 3 0 $G$6<=60 Not Binding 60
$A$7 Beam 6 $A$7<=60 Not Binding 54
$B$7 Normal 1 12 $B$7<=60 Not Binding 48
$C$7 Normal 2 11 $C$7<=60 Not Binding 49
$D$7 Normal 3 11 $D$7<=60 Not Binding 49
$E$7 Tumor 1 15 $E$7<=60 Not Binding 45
$F$7 Tumor 2 15 $F$7<=60 Not Binding 45
$G$7 Tumor 3 0 $G$7<=60 Not Binding 60
Therefore, beam one should be used

Advanced Optimization Techniques in Healthcare Delivery 6
References
Adan, I., &Bekkers, J., &Dellaert, N., &Vissers, J., &Yu, X (2009). Patient mix Optimization
And Stochastic Resource Requirements: A case study in cardiothoracic surgery planning.
Health Care Management Science.
Begen, M., (2010). Appointment scheduling with discrete random durations and applications.
Ph.D. Thesis, University of British Columbia. Retrieved from
http://hdl.handle.net/2429/23332
Begen, M., &Cochran, J., & Keskinocak, P (2011). Stochastic Dynamic Programming models
And applications. Wiley Encyclopedia of operations research and management Science.
Retrieved from http://ca.wiley.com/WileyCDA/Section/id-380199.html.