This document discusses optimization techniques used in pharmaceutical formulations. It begins with defining optimization and describing how experimental design can be used to shorten experimentation time. It then covers various optimization parameters, classic optimization methods using calculus, and common optimization methods like factorial designs, response surface methodology, and simplex lattice designs. Applications mentioned include improving process yield, reducing costs and development time. Finally, some commonly used software for optimization is listed along with references.

1. Presented by :
PRASHIK S SHIMPI
M. Pharm 2nd Semester
Department of Quality Assurance
R.C.Patel Institute of Pharmaceutical
Education & Research, Shirpur.
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2. Contents
 Introduction
 Optimization parameters
 Classic optimization
 Optimization methods
 Application
 Reference
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3. Introduction
 Optimize:
To make as perfect, effective or functional as possible.
 Optimization :
It is the process of finding the best way of using the existing
resources while taking into account all of the factors that
influence decisions in any experiment.
 The composition of pharmaceutical formulation is often subject
to trial & error.
 Optimization by means of an experimental design may be
helpful in shortening the experimenting time.
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4. Optimization Parameters
A. Problem type
i) Constrained – Restrictions placed on the system due to
physical limitations or perhaps due to simple practicality.
ii) Unconstrained- No restrictions, but almost nonexistent in
pharmaceuticals.
B. Variable type
i) Independent variable:-
ii) Dependent variable:-
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5. Classic Optimization
 Result from application of calculus to the basic problem of
finding the maximum or minimum of a function.
 Useful for problems that are not too complex and do not
involve more than a few variables.
 Y=f (X)
 Y=f(X1, X2)
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6. Input Real System Output
Response
Mathematical
Model of
System
Input Factor
Levels
Optimization
Procedure
Applied Optimization Methods
 These general optimization techniques can be described
by following flowchart-
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7. Design of experiment
 Factorial designs
 Full Factorial designs
 Fractional Factorial designs
 Plackett-Burman design
 Response surface(second order) designs
• Central Composite designs
• Box-Behnken designs
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8. Factorial Design
 A full factorial design for n factors requires runs; with 10
factors that would mean 1024 runs!
 In fractional factorial designs the number of runs N is a power
of 2 (N = 4, 8, 16, 32, and so forth)
 In Plackett-Burman designs the number of runs N is a multiple
of 4 (N = 4, 8, 12, 16, 20, 24, and so forth)
 Plackett-Burman designs fill in the gaps in the run sizes
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9. Factorial Experiments
3-FACTOR
 3 main effects
(A, B, C)
 3, 2-way Interactions
A X B, A X C, B X C
 1, 3-way Interaction
A X B X C
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4-FACTOR
 4 main effects
(A, B, C, D)
 6, 2-way Interactions
A X B, A X C, A X D,
B X C, B X D, C X D
 4, 3-way Interactions
A X B X C, A X B X D,
A X C X D, B X C X D
 1, 4-way Interaction
A X B X C X D

10. - 23 level Factorial Design
- Full / Fractional Factorial Design
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2 level Full Factorial Design Fractional Factorial Design
Classifications
x1 x1
x2
x2
x3 x3
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11. Plackett-Burman Design
 Plackett and Burman (1946) showed how full factorial designs
can be fractionalized in a different manner than traditional 2k
fractional factorial designs, in order to screen the max number
of (main) effects in the least number of experimental runs.
 Fractional factorial designs for studying k = N – 1 variables in
N runs, where N is a multiple of 4.
 Only main effects are of interest.
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12. When to use PB designs:
 Screening
 Possible to neglect higher order interactions
 2-level multi-factor experiments.
 More than 4 factors, since for 2 to 4 variables a full factorial
can be performed.
 To economically detect large main effects.
 Particularly useful for N = 12, 20, 24, 28 and 36.
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13. Box-Behnken Design
 Box-Behnken designs are the equivalent
of Plackett-Burman designs for the case
of 3-level multi-factor.
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x1
x2
x3
 When to use Box-Behnken designs:
• With three-level multi-factor experiments.
• When it is required to economically detect large main effects,
especially when it is expensive to perform all the necessary runs.
• When the experimenter should avoid combined factor extremes.
This property prevents a potential loss of data in those cases.

14. Number of runs required by Central
Composite and Box-Behnken designs
Number
of factors
Box Behnken Central Composite
2 - 13 (5 center points)
3 15 20 (6 center point runs)
4 27 30 (6 center point runs)
5 46 33 (fractional factorial) or
52 (full factorial)
6 54 54 (fractional factorial) or
91 (full factorial)
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15. Example: Improving Yield of a
Chemical Process
Factor
Levels
– 0 +
Time (min) 70 75 80
Temperature (°C) 127.5 130 132.5
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16. Use a 23 Factorial Design With
Central Points
Run Factors in original
units
Factors in coded
units
Response
Time(min.)
X1
Temp.(°C)
X2 X1 X2
Yield(gms)
Y
1 70 127.5 - - 54.3
2 80 127.5 + - 60.3
3 70 132.5 - + 64.6
4 80 132.5 + + 68.0
5 75 130.0 0 0 60.3
6 75 130.0 0 0 64.3
7 75 130.0 0 0 62.3
Results From First Factorial Design
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18. Results of Second Factorial Design
Run Factors in original
units
Factors in coded
units
Response
Time(min.)
X1
Temp.(°C)
X2 X1 X2
Yield(gms)
Y
11 80 140 - - 78.8
12 100 140 + - 84.5
13 80 150 - + 91.2
14 100 150 + + 77.4
15 90 145 0 0 89.7
16 90 145 0 0 86.8
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20.  Improve process yield
 Reduce variability
 Reduce development time
 Reduce overall costs
 Evaluate and compare alternatives
 Evaluate material alternatives
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Applications of Optimization Techniques

21. Applications of Optimization Techniques
Optimization techniques are widely used in pharmacy especially
used in-
 Pharmaceutical suspension
 Controlled release formulations
 In tablet coating operation
 In Enteric film coating
 In HPLC analysis
 To study formulation of culture medium in virology
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22. Softwares for Optimization Techniques
 Design Expert 7.1.3
 SYSTAT SigmaStat 3.11
 SPSS 13
 DeltaGraph 5.6
 EquivTest
 PASS 2005 Quickstart manual
 Prism GraphPad 4.03
 CYTEL East 3.1
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23. Reference
1. Banker GS & Rhodes TS. Modern Pharmaceutics. 2nd ed.
vol-40, p. 803-828.
2. Hirmath SR. Industrial Pharmacy. Orient Longman Private
Ltd. p. 158-168.
3. Lewis GA, Roger DM, Phan-Tan-Luu. Pharmaceutical
Experimental Design. vol-92. p.247- 292.
4. Parikh DM. Handbook Of Pharmaceutical Granulation
Technology. vol-81. p.253-258.
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24. 5. Alderborn GF & Nystrom CS. Pharmaceutical Powder
Compaction Technology. vol-71. p.580-590.
6. Banker GS & Rhodes CT. Modern Pharmaceutics.4th ed. Vol-
121, p. 606-625.
7. Bolton SA. Pharmaceutical Statistics Practical & Clinical
Application. 3rd ed. vol-80. p. 590-625.
8. Nielloud F & Marti-Mestres G. Pharmaceutical Emulsion
&Suspensions. vol-105, p.51,540,543,549.
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25. Thank You
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