Operations Research

Safi Ur Rehman

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)

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.

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”

• 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

• Skills for Operations Researchers

• Modeling Skills• Take a real world situation, and model it

using mathematics

• Methodological Toolkit• Optimization • Probabilistic Models

Operations Research

• 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

• 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

Mathematical Modeling &

Linear Programming

• 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

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

Optimal Use of Scarce ResourcesFoundation and Economics Interpretation of LP

Leonid V. Kantorovich Tjalling C. Koopmans Nobel Prize for Economics 1975

Stigler’s Diet ProblemThe First Linear Program

George J. StiglerNobel Prize for Economics 1982

George Dantgiz and Ralph Gomory

Class Break

Discussion about Mini Project

Mathematical Programming

Mathematical Programming