Operations Research Intro

Week 1

Overview of Operations Research

Michael Ajani

Introduction

• Operations Research (OR) involves the research on operations of organizations. OR is thus applied to problems that concern how to conduct and coordinate the operations of an organization. • The research part of the name means that operations research uses the scientific approach in its methods, techniques and analysis.

Nature of Operations Research A typical OR study normally follows the following steps:

1.Define the problem and gather data 2.Formulate a mathematical model to represent the problem 3.Develop a computer-based model (such as Spreadsheet modeling) based on the mathematical model to derive solutions to the problem. 4.Test the model and refine it as needed. 5.Apply the model to analyze the problem and develop recommendations for management. 6.Help to implement the OR recommendations that are adapted by management.

Mathematical Modeling

• A mathematical model of an OR problem is a system of equations and related mathematical expressions that describes the essence of the problem. • Generally, a model is defined as an abstract mathematical representation of a problem situation.

Mathematical Modeling

A typical mathematical model comprises of four parts:

Decision Variables: These are the variables in the mathematical model. The decision variables are derived from the decision to be made by management. Parameters: These are the constants in the mathematical model. The parameters are the estimates of quantities which affects the decision to be made. Objective Function: This is a mathematical expression that gives the measure of performance for the problem in terms of the decision variables. Constraints: These are inequalities or equations that express some restrictions on the values that can be assigned to the decision variables. We have the functional constraints and the non-negativity constraints.

Mathematical Modeling

The form of the mathematical model may...