Introduction to Operations Research

Operations Research (OR)

Definition

Operations Research is the representation of real world systems by mathematical models together with the use of quantitative methods (Algorithms) for solving such models, with a view of optimising. - (J.E Beasley)

“The attack of modern science on complex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government and defence. The distinctive approach is to develop a scientific model of the system incorporating measurements of factors such as change and risk, with which to predict and compare the outcome of alternative decisions, strategies or controls. The purpose is to help management determine its policy and action scientifically”. - (T. Lucey)

Other definitions

• The discipline of applying advanced analytical methods to help make better decisions. • Using techniques such as mathematical modelling to analyse complex situations, OR gives executives the power to make more effective decisions and build more productive systems.

OR methods include :

1. Simulation: Giving you the ability to try out approaches and test ideas for improvement. 2. Optimisation : Narrowing your choices to the very best when there are virtually innumerable feasible options and comparing them is difficult. 3. Probability and Statistics : Helping you measure risk, mine data to find valuable connections and insights, test conclusions and make reliable forecasts 4. Mathematical modelling

5. Complex algorithms

6. Visualisation

7. Neural networks

8. Pattern recognition

9. Data mining, Data warehousing.

OR can be used to support an indefinite number of business decisions.

Typical application of OR

• Capital Budgetting

• Asset allocation

• Fraud prevention, Anti money laundering

• Benchmarking

• Market channel optimisation

• Customer segmentation

• Direct market campaigns

• Predicting customer response

• Supply chain planning

• Distribution, Routing and Scheduling

• Traffic flow optimisation

• Resource allocation

• Staff allocation

• Inventory planning

• Product mix and blending.

Some OR techniques explained.

(1)Simulation

Discrete event system simulation.

Mathematical imitation of a system over time. A discrete event might be the movement of a truck from point A to point B, or the receipt of an order.

Queuing Theory

The application of probability, statistics and other mathematical methods to simulate the flow and queuing of objects eg cars at a toll gate – often in view to reducing congestion.

(2)Optimisation

Linear Programming

Mathematical techniques for optimising an “objective function” subject to certain constraints all expressed as linear equations. Eg. Maximising revenue subject to plant capacity and transportation constraints could be an LP problem.

3) Decision analysis

Decision trees

Branched diagrams whose endpoints reflect various financial outcomes and whose branching points represent choices (we build a new plant or we do not) or outcomes determined by probabilities. (there is a 40% chance that our workforce will strike) The financial outcomes can be combined with the probabilities to yield expected value of a decision.

Bayesian probability

It is a statistical approach to decision making that quantifies uncertainty, often combining probabilities from subjective judgements (our employees won’t strike this year) with probabilities derived from prior observations. (0.01% of our products are defective)

Bayesian logic : is a type of statistical analysis that can quantify an uncertain outcome by determining its probability of occurrence using previously known related data.

Bayesian logic offers a way to measure things that were previously...