This document discusses optimization methods in pharmaceutical product development. It introduces the simplex method, which uses geometric figures to optimize formulations based on multiple variables. For two variables, the simplex is a triangle, and for three variables it is a tetrahedron. The basic simplex method replaces the worst performing vertex with a new point, while the modified simplex method allows the shape and size of the simplex to vary. The modified method uses reflection, expansion, contraction exterior, and contraction interior operations to move away from worst responses and find the optimal formulation.

1. Presented by:
KARANAM RANJITH KUMAR
REG No. 130617011
SUB: PCE-604 PHARMACEUTICAL PRODUCT DEVELOPMENT
M. PHARM INDUSTRIAL PHARMACY PART-1
DEPT. OF PHARMACEUTICS
MCOPS, MANIPAL.

2. INTRODUCTION:
 The term Optimize is defined as to make perfect , effective , or
functional as possible.
 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.
 Traditionally, optimization in pharmaceuticals refers to
changing one variable at a time, so to obtain solution of a
problematic formulation.
 Final product not only meets the requirements from the bio-
availability but also from the practical mass production criteria.

3.  Simplex Method was introduced by Spendley et.al, which has
been applied more widely to pharmaceutical systems.
 A simplex is a geometric figure, that has one more point than
the No. of factors.
SIMPLEX METHOD OPTIMIZATION:

4.  For two factors or independent variables the simplex is
represented by triangle.
 If three independent variables are under study, then the
simplex would be a tetrahedron.
a b
c

5.  The strategy is to move towards a better response by moving
away from worst response.
 It is of two types
A. Basic Simplex Method
B. Modified Simplex Method.

6.  Number of initial trials is equal to the number of control
variables plus one.
 These initial trials form the first simplex.
A. Basic Simplex Method

7. W B
N R
 Rule 1 :
The new simplex is formed by keeping
the two vertices from preceding simplex with best results,
and replacing the rejected vertex (W) with its mirror
image across the line defined by remaining two vertices.
Conc.Ofdisintegrant
Conc. Of binder

8. Rule 2 :
When the new vertex in a simplex
is the worst response, the second lowest response in the
simplex is eliminated and its mirror image across the
line; is defined as new vertices to form the new simplex.
R
Conc.Ofdisintegrant
Conc. Of binder

9. W B
N R
Rule 3 :
When a certain
point is retained in three
successive simplexes, the
response at this point or
vertex is re determined
and if same results are
obtained, the point is
considered to be the best
optimum that can be
obtained.
Conc.Ofdisintegrant
Conc. Of binder

10. Rule 4 :
If a point falls outside the
boundaries of the chosen range of factors, an
artificially worse response should be assigned to it and
one proceeds further with rules 1 to 3. This will force
the simplex back into the boundaries.

11. B. Modified Simplex Method:
 It was introduced by Nelder-Mead in 1965.
 It can adjust its shape and size depending on the response
in each step. This method is also called the variable-size
simplex method.
 This method involves the expansion or contraction of the
simplex formed in order to determine the optimum value
more effectively.

12. The set of operations which allow us to move away
from the worst response are as follows
 Reflection (R)
 Expansion (E)
 Contraction Exterior (Cr)
 Contraction Interior (Cw)

13. Reflection (R):
Conc.Ofdisintegrant
Conc. Of binder
W B
N R
valid if :
Best response > reflection response > next worst response Or
Reflection response > best response and Expansion < best
response i.e. B > R > N Or R > B and E < B

14. When R > B, expansion has to be checked out. If
expansion response is less than B, then reflection is valid. The
other 3 operations are checked out only when reflection is not
valid.
Expansion (E)
W B
N R
E
Conc.Ofdisintegrant
Conc. Of binder
valid if: R > B and E > B

15.  Contraction Exterior (Cr)
Conc.Ofdisintegrant
Conc. Of binder
W B
N RCr
It will be chosen if: N > R > W
Contraction exterior is to come half way back from reflection
point

16.  Contraction Interior (Cw)
W B
N R
Cw
Conc.Ofdisintegrant
Conc. Of binder
It would be chosen if W > R

17. W B
N R
E
Cr
Cw
Modified Simplex Method
Conc.Ofdisintegrant
Conc. Of binder
Once the new simplex is formed by one of the above
operations, the worst response in the newly formed reflex has
to be considered for the further reflection and other
operations.