Linear Programming in Business

1. Presentation on
Management Science
KEEN ORBITKEEN ORBIT
Presented to
S M Salamotullah Bhuiyan
Adjunct Professor,
FBA, USTC

2. Name of group members
Md. Abdul Motaleb
Roll- 1126
Md. Omar Faruq
Roll- 1120
Md. Jahirul Islam
Roll- 1128
Suhail Mahmud Shakil
Roll- 1121
Shanjida Afroz
Roll- 1119
Mehedi Hasan
Roll-1114

3. What is Management Science?
Management science (MS), is an interdisciplinary
branch of applied science including
mathematical modeling;
Engineering;
Statistics; and
algorithms
improve an organization's ability to enact rational
and meaningful management decisions.
The discipline is typically concerned with maximizing
profit, assembly line performance, crop yield,
bandwidth, etc. or minimizing expenses, loss, risk,
etc.

4. Applications
Applications of management science are abundant in industry
such as airlines, manufacturing companies, service organizations,
military branches, and in government. The range of problems and
issues to which management science has contributed insights and
solutions is vast. It includes:
scheduling airlines, both planes and crew,
deciding the appropriate place to place new facilities such as a
warehouse or factory,
managing the flow of water from reservoirs,
identifying possible future development paths for parts of the
telecommunications industry,
establishing the information needs and appropriate systems to
supply them within the health service, and
identifying and understanding the strategies adopted by
companies for their information systems.

6. Linear programming
Linear programming (LP; also
called linear optimization)
ois a method to achieve the best
outcome (such as maximum profit
or lowest cost) in a mathematical
model whose requirements are
represented by linear
relationships.
ois a special case of
mathematical
programming (mathematical
optimization).

7. Linear programming is used to solve
problems in many aspects of business
administration including:

8. Linear programming in Business
• Linear programming methods
to determine the best ways to
increase profits and decrease
operational costs.
• Linear programming methods
enable businesses to identify
the solutions they want for their
operational problems,
• Define the issues that may
alter the desired outcome and
• Figure out an answer that
delivers the results they seek.

9. Linear programming in Business
Production Planning
Linear programming methods
are often helpful at solving
problems related to production.
For instance, a custom
furniture shop that makes chairs
and tables can calculate how
many of each item they must sell
to maximize their profits by
looking at the numbers of each
item previously sold and their
prices.

10. Linear programming in Business
 Marketing Mix
• A key aspect of marketing strategy is the
"marketing mix." The marketing mix
determines how much of a company's
marketing budget will go toward various
advertising and marketing channels by
linear programming.
 For example, the custom furniture store
can use a linear programming method to
examine how many leads come from TV
commercials, newspaper display ads and
online marketing efforts. The solution will
also compare the relative prices of each
medium to find the most economical mix.

11. Linear programming in Business
 Product Distribution
• Manufacturers and
distributors can use linear
programming methods to
solve distribution problems.
• These models can also
ensure that warehouses
maintain an optimal amount
of each product in stock as
demand fluctuates.

12. Personnel Assignments
Human resources planners can use linear
programming methods to determine
when to hire more workers,
which skill sets the company needs and
how much they can offer in compensation.
also be used to anticipate times of
increased demand for available workers.
For example, a department store can use
linear programming methods to calculate
how many new hires they will make for the
busy holiday shopping season, as well as
which departments will see higher traffic
and require more staff.

13. Charactaristics of Linear programming
 Branch of mathematics
 Branch statistics
 To determine solutions to
problems of optimization.
Linear programming
problems are distinctive
 An extremely useful field
ranging from logistics to
industrial planning.

14. Charactaristics
• Optimization
 All linear programming
problems are problems of
optimization means either
maximize or minimize some
value.

15. Charactaristics
• Linearity
 As the name hints, linear programming problems all
have the trait of being linear.
 Linearity does not, however, mean that the functions
of a linear programming problem are only of one
variable.
 Linearity allows the variables to relate to each other
as coordinates on a line, excluding other shapes and
curves.

16. Charactaristics
• Objective Function
The result of a linear
programming problem will be
given in terms of the objective
function.

17. Charactaristics
• Constraints
All linear programming problems have
constraints on the variables inside the
objective function. These inequalities define
how the objective function can be
maximized or minimized, as together they
determine the "domain" in which an
organization can make decisions about
resources.

18. Advantages
 Linear programming has a
versatile technique that can be
used to represent a number of
real-world situations.
 Businesses use techniques to
solve problems that involve
multiple variables and
constraints.
 The use of computers has made
this technique easier to apply.
 Linear programming is one of the
widely used modeling techniques.

19. Limitation
 The linear programming approach
is based on an assumption that
the world is linear. In the real
world, this is not always the case.
 There are certain ways of mixing
the inputs that a linear
programming approach doesn't
permit.
 Linear models also don't account
for factors such as increased
production efficiency as the level
of production rises.
Assumption of Linearity

20. Limitation
Fractional Values
 The linear programming model
assumes that inputs and outputs can
be fractional.
 If even one variable involved has to be
in integer form, linear programming is
not a suitable technique.

22. Thank You