INTEGER LINEAR PROGRAMMING
There are many LP problems in which the decision
variables will take only integer values. If all the
decision variables will only take integer values it is
called a pure integer LPP; otherwise the problem is
called a mixed integ
Dual Problem of an LPP
Given a LPP (called the primal problem),
we shall associate another LPP called the
dual problem of the original (primal)
problem. We shall see that the Optimal
values of the primal and dual are the same
provided both have finite fea
Dualitytheorems
Findingthedualoptimal
solutionfromtheprimaloptimal
tableau
Dual problem in Matrix form
In this lecture we shall present the primal
and dual problems in matrix form and
prove certain results on the feasible and
optimal solutions of the prim
CLASSICAL OPTIMIZATION THEORY
Quadratic forms
Let
x1
x
2
X .
.
xn
be a n-vector.
Let A = ( aij) be a nn symmetric matrix.
We define the kth order principal minor as
the kk determinant
a11 a12 . a1k
a21 a22 . a2 k
.
.
ak 1 ak 2 . akk
Then the q
Iterativecomputationsofthe
Transportationalgorithm
Iterative computations of the Transportation algorithm
After determining the starting BFS by any one of the
three methods discussed earlier, we use the following
algorithm to determine the optimum solutio
DeterminationofStarting
BasicFeasibleSolution
Determination of the starting Solution
In any transportation model we determine a starting
BFS and then iteratively move towards the optimal
solution which has the least shipping cost.
There are three methods
Explanationoftheentriesin
anysimplextableauinterms
oftheentriesofthestarting
tableau
In this lecture we explain how the
starting Simplex tableau (in matrix
form) gets transformed after some
iterations. We also give the meaning of
the entries in the new ta
TheTransportationModel
Formulations
The Transportation Model
The transportation model is a special class of LPPs
that deals with transporting(=shipping) a
commodity from sources (e.g. factories) to
destinations (e.g. warehouses). The objective is to
deter
QUADRATIC
PROGRAMMING
Quadratic Programming
A quadratic programming problem is a non-linear
programming problem of the form
Maximize
Subject to
T
z c X X DX
A X b , X 0
Here
x1
b1
x
b
2 2
X . , b . , c c1 c2 . . . cn
.
.
xn
bm
a11 a12
MATRIXFORMULATION
OFTHELPps
In this lecture we shall look at the matrix
formulation of the LPPs. We see that the
Basic feasible solutions are got by solving
the matrix equation BX =b
where B is a mm nonsingular submatrix
of the contraint matrix of the LPP
Addition of a new constraint
The addition of a new constraint to an existing
model can lead to one of two cases:
1. The new constraint is redundant, meaning
that it is satisfied by the current optimal
solution and hence can be dropped
altogether from the
PERT Networks
In PERT the duration of any activity is
indeterministic. It bases the duration of an
activity on three estimates:
Optimistic Time, a
Most Likely Time, m
Pessimistic Time, b
The range [a, b] is assumed to enclose all
possible estimates of
Deterministic Dynamic Programming
Dynamic Programming (DP) determines the
optimum solution to an n-variable problem by
decomposing it into n stages with each stage
constituting a single-variable sub problem.
Recursive Nature of Computations in DP
Computat
Your write-up should introduce your solution to the project by describing the
problem. Correctly identify what type of problem this is. For example, you should
note if the problem is a maximization or minimization problem, as well as identify
the resource