It is the process of finding the best way of using the existing resources while taking in to the account of all the factors that influences decisions in any experiment. The objective of designing quality formulation is achieved by various optimization techniques. In Pharmacy word “optimization” is found in the literature referring to study of the formula. In formulation development process generally experiments by a series of logical steps, carefully controlling the variables and changing one at a time until satisfactory results are obtained.

1. OPTIMIZATION TECHNIQUES IN PHARMACEUTICAL FORMULATION AND
PROCESSING: PLACKETT BURMAN DESIGN AND D-OPTIMAL
Presented by:-
Dau Ram Chandravanshi
M.Pharma. 1st sem.

2. Contents
 Introduction
General optimization techniques
 Optimization parameter
 Design of experiments
 Basic Principles of experimental design.
• Randomization
• Replication
• Local control
Types of optimization techniques.
Application
Software for optimization and design
References

3. Introduction
It is the process of finding the best way of using the existing resources
while taking in to the account of all the factors that influences decisions
in any experiment.
The objective of designing quality formulation is achieved by various
optimization techniques.
In Pharmacy word “optimization” is found in the literature referring to
study of the formula. In formulation development process generally
experiments by a series of logical steps, carefully controlling the
variables and changing one at a time until satisfactory results are
obtained.

4. REAL
SYSTEM
MATHEMATICAL
MODEL OF
SYSTEM
RESPONSE
OPTIMIZATION
PROCEDURE
INPUT
FACTOR
LEVEL
INPUT
OUTPUT
General Optimization Technique

5. Optimization Parameters
PARAMETERS
PROBLEM
TYPE
CONSTRAINED
UNCONSTRAI
NED
VARIABLE
DEPENDENT INDEPENDENT

6. Problem Types
Unconstrained
• In unconstrained optimization problems there are no restrictions.
• For a given pharmaceutical system one might wish to make the
hardest tablet possible.
• The making of the hardest tablet is the unconstrained optimization
problem.
Constrained
• The constrained problem involved in it, is to make the hardest tablet
possible, but it must disintegrate in less than 15 minutes.

7. (a) Variables
The development procedure of the pharmaceutical formulation involve
several variables.
The independent variables are under the control of the formulator. These
might include Ingredients, compression force or the die cavity filling or the
mixing time.
The dependent variables are the responses or the characteristics that are
developed due to the independent variables. The more the variables that
are present in the system the more the complications that are involved in
the optimization
(b) Factor:- It is Assigned and Independent variables, which affect the
product or output of the process. It is an assigned quantitative and
qualitatively like this

8. Quantitative: Numerical factor assigned to it. Ex; Concentration- 1%,
2%, 3% etc.
Qualitative: These are not numerical. Ex; Polymer grade, humidity
condition etc.
(c) Level:- Levels of a factor are the values or designations assigned to
the factor.
(d) Response surface:- Response surface representing the
relationship between the independent variables X1 and X2 and the
dependent variable Y.
(e) Run or trials:- Experiments conducted according to the selected
experimental design
(g) Contour Plot:- Geometric illustration of a response obtained by
plotting one independent variable against another, while holding the
magnitude of response and other variables as constant.
(h) Interaction:- It gives the overall effect of two or more variables
means lack of additivity of factor effects Ex: Combined effect of
lubricant and glidant on hardness of the tablets.

9. Basic Principles of experimental
design
 Randomization- Randomization is the random process of assigning
treatments to the experimental units. The random process implies that
every possible allotment of treatments has the same probability.
 Replication- By replication we mean that repetition of the basic
experiments. For example, If we need to compare the grain yield of two
varieties of wheat then each variety is applied to more than one
experimental units. The number of times these are applied to experimental
units is called their number of replication. It has two important properties:
• It allows the experimenter to obtain an estimate of the experimental error.
• The more replication would provide the increased precision by reducing
the standard errors.

10. It has been observed that all extraneous source of variation is not
removed by randomization and replication, i.e. unable to control the
extraneous source of various.
Thus we need to a refinement in the experimental technique. In
other words, we need to choose a design in such a way that all
extraneous source of variation is brought under control. For this
purpose we make use of local control, a term referring to the amount
of (i) balancing, (ii) blocking.
 Local control

11. Types of optimization techniques
1. Plackett-burman designs.
2. Factorial designs.
3. Fractional factorial design (FFD).
4. Response surface methodology.
5. Central composite design (box-wilson design).
6. Box-behnken designs.

12. 1. Plackett Burman Design
In 1946, R.L. Plackett and J.P. Burman published their now famous paper
"The Design of Optimal Multifactorial Experiments" in Biometrika (vol.
33).
This paper described the construction of very economical designs with
the run number a multiple of four (rather than a power of 2). Plackett-
Burman designs are very efficient screening designs when only main
effects are of interest.
These designs have run numbers that are a multiple of 4. Plackett-
Burman (PB) designs are used for screening experiments because, in a
PB design main effects are in general heavily confounded with two-
factor interactions. The PB design in 12 runs for example may be used
for an experiment containing up to 11 factors.

13. Plackett-Burman Design in 12 Runs for up to 11 Factors
Pattern X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11
1 +++++++++++ +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1
2 -+-+++---+- -1 +1 -1 +1 +1 +1 -1 -1 -1 +1 -1
3 --+-+++---+ -1 -1 +1 -1 +1 +1 +1 -1 -1 -1 +1
4 +--+-+++--- +1 -1 -1 +1 -1 +1 +1 +1 -1 -1 -1
5 -+--+-+++-- -1 +1 -1 -1 +1 -1 +1 +1 +1 -1 -1
6 --+--+-+++- -1 -1 +1 -1 -1 +1 -1 +1 +1 +1 -1
7 ---+--+-+++ -1 -1 -1 +1 -1 -1 +1 -1 +1 +1 +1
8 +---+--+-++ +1 -1 -1 -1 +1 -1 -1 +1 -1 +1 +1
9 ++---+--+-+ +1 +1 -1 -1 -1 +1 -1 -1 +1 -1 +1
10 +++---+--+- +1 +1 +1 -1 -1 -1 +1 -1 -1 +1 -1
11 -+++---+--+ -1 +1 +1 +1 -1 -1 -1 +1 -1 -1 +1
12 +-+++---+-- +1 -1 +1 +1 +1 -1 -1 -1 +1 -1 -1

14. 20-Run Plackett-Burman Design
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19
1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1
2 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1
3 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1
4 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1
5 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1
6 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1
7 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1
8 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1
9 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1
10 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1 -1
11 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1 +1
12 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1 -1
13 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1 +1
14 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1 +1
15 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1 +1
16 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1 +1
17 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1 -1
18 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1 -1
19 -1 -1 +1 +1 +1 +1 -1 +1 -1 +1 -1 -1 -1 -1 +1 +1 -1 -1 +1

15. 24-Run Plackett-Burman Design
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1
3 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1
4 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1
5 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1
6 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1
7 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1
8 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1
9 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1
10 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1
11 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1
12 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1
13 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1
14 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1
15 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1
16 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1
17 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1
18 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1
19 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1 -1

16. 20 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 1
21 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1 1
22 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1 1
23 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1 1
24 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 -1
These designs do not have a defining relation since interactions are not identically equal
to main effects. With the 2 k=pIII designs, a main effect column Xi is either orthogonal
to XiXj or identical to plus or minus Xi Xj. For Plackett-Burman designs, the two-factor
interaction column XiXj is correlated with every Xk (for k not equal to i or j).
Economical for detecting large main effects. However, these designs are very useful for
economically detecting large main effects, assuming all interactions are negligible when
compared with the few important main effects.

17. D- Optimal design
D-optimal designs are one form of design provided by a computer
algorithm. These types of computer-aided designs are particularly useful
when classical designs do not apply.
Unlike standard classical designs such as factorials and fractional
factorials, D-optimal design matrices are usually not orthogonal and
effect estimates are correlated.
These types of designs are always an option regardless of the type of
model the experimenter wishes to fit (for example, first order, first order
plus some interactions, full quadratic, cubic, etc.) or the objective
specified for the experiment (for example, screening, response surface,
etc.). D-optimal designs are straight optimizations based on a chosen
optimality criterion and the model that will be fit. The optimality
criterion used in generating D-optimal designs is one of maximizing
|X'X|, the determinant of the information matrix X'X.

18. Cont..
This optimality criterion results in minimizing the generalized variance
of the parameter estimates for a pre-specified model. As a result, the
'optimality' of a given D-optimal design is model dependent. That is, the
experimenter must specify a model for the design before a computer
can generate the specific treatment combinations. Given the total
number of treatment runs for an experiment and a specified model, the
computer algorithm chooses the optimal set of design runs from
a candidate set of possible design treatment runs.
This candidate set of treatment runs usually consists of all possible
combinations of various factor levels that one wishes to use in the
experiment.
In other words, the candidate set is a collection of treatment
combinations from which the D-optimal algorithm chooses the
treatment combinations to include in the design. The computer
algorithm generally uses a stepping and exchanging process to select
the set of treatment runs.

19. Cont..
D-optimal designs are useful when resources are limited or there are
constraints on factor settings.
The reasons for using D-optimal designs instead of standard classical
designs generally fall into two categories:
1. Standard factorial or fractional factorial designs require too many
runs for the amount of resources or time allowed for the experiment.
2. The design space is constrained (the process space contains factor
settings that are not feasible or are impossible to run).
Example: Suppose an industrial process has three design variables (k =
3), and engineering judgment specifies the following model as an
appropriate representation of the process.

20. Cont..
The levels being considered by the researcher are (coded)
X1: 5 levels (-1, -0.5, 0, 0.5, 1)
X2: 2 levels (-1, 1)
X3: 2 levels (-1, 1)
Due to resource limitations, only n = 12 data points can be collected.
Create the candidate set - Given the experimental specifications, the
first step in generating the design is to create a candidate set of points.
The candidate set is a data table with a row for each point (run) to be
considered for the design, often a full factorial. For our problem, the
candidate set is a full factorial in all factors containing 5*2*2 = 20
possible design runs.

21. Candidate Set for Variables X1, X2, X3
X1 X2 X3
-1 -1 -1
-1 -1 +1
-1 +1 -1
-1 +1 +1
-0.5 -1 -1
-0.5 -1 +1
-0.5 +1 -1
-0.5 +1 +1
0 -1 -1
0 -1 +1
0 +1 -1
0 +1 +1
0.5 -1 -1
0.5 -1 +1
0.5 +1 -1
0.5 +1 +1
+1 -1 -1
+1 -1 +1
+1 +1 -1
+1 +1 +1

22. Generating a D-optimal design
D-optimal designs maximize the D-efficiency, which is a volume criterion
on the generalized variance of the parameter estimates.
The D-efficiency values are a function of the number of points in the
design, the number of independent variables in the model, and the
maximum standard error for prediction over the design points. The best
design is the one with the highest D-efficiency. Other reported
efficiencies (e.g. A, G, I) help choose an optimal design when various
models produce similar D-efficiencies.
The D-optimal design (D=0.6825575, A=2.2, G=1, I=4.6625) using 12 runs
is shown in Table in standard order. The standard error of prediction is
also shown. The design runs should be randomized before the treatment
combinations are executed.

23. Final D-optimal Design
X1 X2 X3 OptStdPred
-1 -1 -1 0.645497
-1 -1 +1 0.645497
-1 +1 -1 0.645497
-1 +1 +1 0.645497
0 -1 -1 0.645497
0 -1 +1 0.645497
0 +1 -1 0.645497
0 +1 +1 0.645497
+1 -1 -1 0.645497
+1 -1 +1 0.645497
+1 +1 -1 0.645497
+1 +1 +1 0.645497

24. Applications
Formulation and Processing.
Clinical Chemistry.
Medicinal Chemistry.
High Performance Liquid Chromatographic Analysis.
Study of Pharmacokinetic Parameters.
Allow large number of variables to be investigated in compact trial.

25. Software for Designs and
Optimization
Software’s dedicated to experimental designs
 DESIGN EXPERT
 ECHIP
 MULTI-SIMPLEX
 NEMRODW
 Software for general statistical nature
 SAS
 MINITAB
 SYSTAT
 GRAPHPAD PRISM

26. References
1. Badawi MA, El-Khordagui LK. A quality by design approach to optimization of
emulsions for electrospinning using factorial and D-optimal designs. Eur J Pharm
Sci. 2014;58:44-54.
2. Garg Rahul Kumar* and Singhvi Indrajeet, Optimization techniques: an overview
for formulation development, Asian J. Pharm. Res. Vol 5, Issue 3, 217-221, 2015.
3. Fukuda I.M, Pinto C.F.F, Moreira C.S, Saviano A.M, Lourenço F.R. Design of
experiments (DOE) applied to pharmaceutical and analytical quality by design
(QBD) Braz. J. Pharm. Sci. 2018;54(Special):e01006.
4. https://www.itl.nist.gov/div898/handbook/index.htm
5. Sahira N. Muslim, Alaa N. Mahammed, Hadeel K. Musafer, Israa M. S. AL_Kadmy,
and Shatha A. Shafiq, Sraa N. Muslim “Detection of the Optimal Conditions for
Tannase Productivity and Activity by Erwinia Carotovora”, Journal of Medical and
Bioengineering Vol. 4, No. 3, June 2015.