1. SUBMITTED TO
HULAS PATHAK
Asstt. Professor
Deptt. Of Agricultural
Economics
SUBMITTED BY
Manisha Sonwani
M.Sc.(Ag.) Previous year
Deptt.of Agricultural Economics
2. Linear programming is that branch of mathematical
programming which is designed to solve
optimization problem where all the constraint as well
as objective are expressed as linear function.
APPLICATION OF LP
1. Choice of investment from a variety of shares &
debenture so as to maximize return on investment.
2. Selection of product mix to make the best use of
available resources like machine, man house etc.
3. Designing, routing & assignment problems.
4. Transportation problems.
5. Manufacturing problems.
3.
4. A recursive linear programming (RLP) model belongs to a
mathematical system whose members consist of a sequence of
linear programming problems in which one or more of the
coefficients of each problem depend on the solution vectors of
preceding problems in the sequence. Their explicit use has
been confined to the construction of various economic theories
and to the development of empirical models of economic
behavior. This paper reviews and summarizes the theory
concerning the existence and character of solutions for RLP
models, and attempts to extend their domain of application by
demonstrating their implicit use in certain decomposing &non
linear programming algorithms.
5. Dynamic Programming refers to a very large class of
algorithms. The idea is to break a large problem down (if
possible) into incremental steps so that, at any given
stage, optimal solutions are known to sub-problems.
When the technique is applicable, this condition can be
extended incrementally without having to alter previously
computed optimal solutions to sub problems. Eventually
the condition applies to all of the data and, if the
formulation is correct, this together with the fact that
nothing remains untreated gives the desired answer to the
complete problem.
6. Method for problem solving used in math and computer
science in which large problems are broken down into
smaller problems. Through solving the individual smaller
problems, the solution to the larger problem is discovered.
Examples of dynamic programming include
1. [edit-distance], longest common subsequence, spelling
correction, and similar problems on strings; also
Hirschberg's space-efficient [version], a functional
programming [version] and a longest common
subsequence (LCS) (LCSS), algorithm using bit
operations for speed-up [HTML],
2. shortest path algorithms on [graphs],
[segmentation] of a time series,
3. Some [spanning-tree] algorithms.
7. The dynamic programming can be applied to many
real life situations.
1. Capital budgeting problem.
2. Reliability improvement problem.
3. Stage-coach problem.
4. Optimal subdividing problem.
5. Linear programming problem
8. DEFINITION
Transportation problem is one of the subclass
of LP in which the objective to transport
various quantity of a single homogenous
commodity which is initially stored at various
origin , to different destination in a such a way
the total transport cost would be minimize.
9. All the relationship in transport problem in linear
1. Component of the problem.
2. Set up the objective function.
3. Set up the linear structural constraint.
4. Set up the non negativity constraint.
10. 1. The total supply available at the origin.
2. The total quantity demanded by the destination.
3. The total cost of transportation problem per unit
from origin to destination.
11. Example 1. The sources & four destination
represent the cost of transportation per unit.
LEST COST METHOD
Destination
ORIGIN D1 D2 D3 D4 CAPACITY
O1 3 1 7 4 300
O2 2 6 5 9 400
O3 8 3 3 2 500
DEMAND 250 350 400 200 1200
19. The transportation problem is only a special
topic of the linear programming problems. It
would be a rare instance when a linear
programming problem would actually be
solved by hand. There are too many
computers around and too many LP software
programs to justify spending time for manual
solution.
