Topic 3: Linear Programming– Part 1
Outline
I.
Introduction to Linear Programming (LP)
II.
LP Model Formulation
Structure of LP model
Assumptions of LP model
Learning Outcomes
At the end of the class, you will learn the followings:
1.
The basic approach of linear programming.
2.
The types of management problems that can be analyzed by linear programming.
3.
The formulation of various types of problems as linear programming problems.
4.
The meaning of the terms
Linear programming
Decision variables
Objective function
Constraints
Linear equality
Linear inequality
I.
Introduction to Linear Programming
Linear programming is a mathematical programming and optimization technique that has been
widely used by business and industry for many years. It involves allocating scarce resources on
the basis of a given criterion of optimality. Most often, this criterion is either maximum profit or
minimum cost.
LP is a mathematical method to allocate limited resources in an optimal way.
Examples
include allocation of production facilities, production mix determination, blending, manpower
allocation
and
assignment, personnel
allocation,
transportation
planning,
scheduling,
advertising budget allocation, etc.
LP uses mathematical model to describe the problem of concern.
The word
linear
implies that all mathematical relationships in the model have linear
relationships.
The word
programming
does not refer to computer programming; it refers to
planning
.
II. Model Formulation
Every LP problem involves the following:
decisions
that must be made
an
objective
that we need to optimize (maximize or minimize)
a set of
restrictions (or constraints)
that the solution must satisfy
The linear programming model consists of an objective function and a set of constraints. The
quantifiable goal that is to be maximized or minimized is the "objective function." This function
measures the effectiveness of a particular solution for a linear programming problem. The
constraints are mathematical statements that specify elements of the problem such as the
limitations of available resources or a demand level that must be met.
QMT437 Operations Research
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 Spring '12
 pn.wanfaezah
 Operations Research, Linear Programming, Optimization, lp model

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