Quantitative analysis for business decision (QABD)- Linear programming problem (LLP)

1. QUANTITATIVE ANALYSIS
FOR
BUSINESS DECISION
First semester ---
Mid One PPT
IMMANI CHANDRA SHEKAR
REGD. NO. :19K61E0020
SUBJECT CODE :18MS01T5
1

2. LINEAR PROGRAMMING PROBLEM
(LPP)
Mid Topic
2

3. Introduction:
 Linear Programming is an optimization technique.
 It is “a technique for specifying how to use limited
resources or capacities of a business to obtain a
particular objective, such as least cost, highest
margin or least time, when those resources have
alternate uses”. 3

4. Definition Of Linear Programming:
In the words of William M. Fox,
“Linear programming is a planning
technique that permits some objective
function to be minimized or maximized
within the framework of given situational
restrictions.” 4

5. Application Areas of Linear Programme:
In practice linear programming
has proved to be one of the most
widely used technique of
managerial decision making in
business, industry and numerous
other fields.
5

6. 1. Industrial Applications :
Linear programming is extensively used to solve a variety of industrial
problems.
Few examples of industrial applications are as follows:
 Product Mix-Problem.
 Production Scheduling.
 Production Smoothing Problem.
 Transportation Problems.
 Production distribution problems.
 Linear programming is also used by oil refineries to determine the
optimal mix of products to be produced by the refinery during a given
period.
 Communication Industry: LP methods are used in solving problems
involving facilities for transmission, switching, relaying etc.
6

7. Rail Road Industry: An LP model for optimal programming of
railway freight, and train movements has been formulated to handle
scheduling problems as found at large terminal switching rail points.
2. Management Applications:
 Portfolio Selection.
 Financial Mix Strategy.
 Profit Planning.
 Travelling Salesmen Problem.
 Determination of equitable salaries.
 Staffing problem. 7

8. 3. Miscellaneous Applications:
The additional application of Linear Programming are
as follows:
a. Farm planning. -The particular crops to be grown
or cattle to keep during a period
b. Airline routine.
c. Administration, Education and Politics have
also employed linear programming to solve their
problems.
d. Diet Problems: The diet problem, one of the earliest
applications of linear programming was originally
used by hospitals to determine the most economical
diet for patients. 8

9. 4. Administrative applications of Linear Programming:
 Linear programming can be used for administrative
applications. Administrative applications of Linear
Programming are concerned with optimal usage of resources
like men, machine and material.
5. Non-Industrial applications of linear programming:
Examples of the use of L.P techniques for non-industrial
applications are given below:
 Agriculture.
 Environmental Protection.
 Urban Department.
 Facilities Location.
9

10. 6. Further applications of Linear
Programming are:
 In scheduling of a military tanker
fleet.
 In determining which parts to make
and which to buy to obtain
maximum profit margin.
 In design of optimal purchasing
policies.
10

11. Advantages of Linear Programming:
 Improves quality decision
 Cost-benefit analysis
 Flexibility
 Number of possible solutions
 Use of productive factors
 Scientific approach 11

12. Limitations of Linear Programming:
 where the constraints and the objective function can be
stated in terms of linear expressions.
 Linear programming will fail to give a solution if
management have conflicting multiple goals.
 Does not take into consideration the effect of time and
uncertainty
 Parameters appearing in the model are assumed to be
constants but in real-life situations they are frequently
neither known nor constants.
12

13. Methods of Solving Linear programming Problems:
Linear Programming problem (LPP) can
be basically solved by two methods.
1.Graphical Method (LLP which involves only two variables)
2.Simplex Method (LLP which involves two or more than two
variables) 1. Big-M Method
2. Two Phase Method
13

14. 14