The document provides an overview of operations research, including: - Operations research developed during World War II to allocate scarce military resources efficiently. It has since been applied to optimize operations in many industries. - Mathematical modeling involves representing real-world problems mathematically to enable analysis and optimization using tools like linear programming. - Linear programming formulates problems as mathematical models to find optimal solutions while respecting constraints, and was pioneered in the 1930s-40s. It has become one of the most important developments in 20th century mathematics.

1. Operations Research
Safi Ur Rehman

2. Outline
• Introduction to Operations Research
• Mathematical Modeling
– Concepts and Formulations
• Linear Programming
– Examples
– Geometry of Linear Programs / Graphical Solution
• Mathematical Programming
– Solving Linear & Integer Programming Problems
• Excel Solver & GNU Linear Programming Kit (GLPK)

3. Operations Research
“The discipline of applying advanced analytical
methods to help make better decisions”
✦✦✦
• World War II :
British Military leaders asked scientists and
engineers to analyze several military problems
• Deploying of radar
• Management of convoy, bombing,
antisubmarine and mining operations
• The result was called Operations Research
• Management Science is also used as a synonym,
sometimes for OR.

4. Operations Research - Definitions
“The science of better”
✦✦✦
“The use of mathematical models, statistics and
algorithms to aid in decision-making with the goal
of improving or optimizing performance”
✦✦✦
“Research designed to determine the most
efficient way to do something”
✦✦✦
“The application of scientific methods to
improve the effectiveness of operations,
decisions and management”

5. • During WWII, OR developed to allocate scarce resources to
military operations
• After the war, OR introduced into industry
• Improvements in techniques
• Computer revolution
• OR techniques may be used to solve problems
• Related to how to coordinate the activities of an organization
• Type of organization is irrelevant.
• OR successfully applied to a wide range of industries
Operations Research

6. • Skills for Operations Researchers
• Modeling Skills
• Take a real world situation, and model it using
mathematics
• Methodological Toolkit
• Optimization
• Probabilistic Models
Operations Research

7. • Phases of an OR study
• Define the problem of interest and gather relevant data
• Formulate a mathematical model to represent the problem
• Develop a computer-based procedure for deriving solutions
to the problem from the model
• Test the model and refine it as needed
• Prepare for the ongoing application of the model as
prescribed by management
• Implement
• Data, Models, Algorithms, Insights and Decisions
(DMAID)
• Optimization
Operations Research

8. • Personal choices
• Best career choices,
• Best use of our time
• Best strategies,
• Best value for the dollar
• Company choices
• Maximize value to shareholders
• Determine optimal mix of products or services
• Minimize production costs
• Minimize cost of getting product to customers
• Maximize value of advertising
• Hire the best workers
Optimization is Every where

9. Mathematical Modeling
&
Linear Programming

10. • Mathematical modeling is describing a real-world
problem in a mathematical way by what is called a
model, such that it becomes possible to deploy
mathematical tools for its solution.
• The model should be based on first principles and
elementary relations and it should be accurate
enough to have reasonable claims to predict both
quantitative and qualitative aspects of the original
problem.
Mathematical Modelling

11. Linear Programming
• 1939 - L. V. Kantorovitch : Foundations of Linear
Programming
• 1947 G. B. Dantgiz : Invention of the Simplex
Algorithm
• Today: Some people say and believe that:
Linear programming is the most important
development of mathematics in the 20th century

12. Optimal Use of Scarce Resources
Foundation and Economics Interpretation of LP
Leonid V. Kantorovich Tjalling C. Koopmans
Nobel Prize for Economics 1975

13. Stigler’s Diet Problem
The First Linear Program
George J. Stigler
Nobel Prize for Economics 1982

14. George Dantgiz and Ralph Gomory

25. Class Break
Discussion about Mini Project

39. Mathematical Programming

40. Mathematical Programming