Salient features of linear programming and its applications

This presentation explores the salient features of linear programming and its applications in resource allocation, production planning, transportation logistics, finance, marketing scheduling, supply chain management, network flow problem, environmental management, healthcare.

1. PRESENTATION FOR CA#1
TOPIC: SALIENT FEATURES OF LINEAR
PROGRAMMING AND ITS APPLICATIONS
Name: SomnilPaul
Roll: 18700721013
Stream: ME
Sem: 6th
Paper name: Humanities II(Operations Research)
Paper code: HM HU 601

2. WHAT IS LINEAR PROGRAMMING
Optimization Method:Linear
programming is a method for
optimizing (maximizing or minimizing)
a linear objective function.
Linear Relationships:It deals with
linear relationships among decision
variables and constraints.
Decision Variables:Variables
representing quantities to be
determined or optimized.
Objective Function:Linear equation
representing the goal, either
maximizing or minimizing.

3. Constraints:Linear relationships restricting the possible
values for decision variables.
Feasible Region:Set of values satisfying all constraints.
Non-negativity Constraints:Typically, decision variables
are constrained to non-negative values.
Mathematical Modelling:Involves setting up a
mathematical model to represent real-world problems with
linear relationships.

4. SALIENT FEATURES OF LINEAR
PROGRAMMING
Versatility:Widely applicable
across various domains like
operations, finance, and logistics.
Optimization:Efficiently
optimizes resource allocation and
decision-making processes.
Mathematical Clarity:Clear and
manageable mathematical
formulation.
Efficiency:Algorithms like
simplex method handle large-
scale problems effectively.
Sensitivity Analysis:Allows
understanding how parameter
changes impact optimal solutions.

5. Quantitative Decision-Making:Provides a quantitative
basis for decision-makers.
Resource Optimization:Optimizes resource use,
minimizing costs or maximizing profits.
Easy Interpretation:Results are often easy to understand
and interpret.
Software Integration:Easily integrated into software tools
for automated solutions.
Proven Track Record:Successfully applied in various
industries for real-world problem-solving.

6. APPLICATIONS OF LINEAR PROGRAMMING
Resource Allocation:Optimal
allocation of resources like labour,
materials, and machines to maximize
production or minimize costs.
Production Planning:Determining
the optimal production quantities for
different products to maximize profit
or minimize costs.
Transportation and Logistics:
Optimizing the transportation of
goods from multiple sources to
multiple destinations, considering
costs and capacities.
Finance:Portfolio optimization,
where investors seek to maximize
returns for a given level of risk.

7. Marketing:Determining the optimal mix of advertising
channels to maximize reach or sales while considering
budget constraints.
Scheduling:Assigning tasks to resources efficiently,
considering time and resource constraints.
Supply Chain Management:Optimizing supply chain
activities, including inventory management, production
planning, and distribution.
Network Flow Problems:Maximizing or minimizing flow
through a network, such as in the design of communication
or transportation networks.
Environmental Management:Optimizing resource use and
waste disposal to minimize environmental impact.
Healthcare:Resource allocation in healthcare facilities, such
as staff scheduling or bed allocation, to optimize efficiency.

8. THANK YOU