Operation Research Chapter 1

Operation Research Definition

• Operation Research (OR) is a scientific discipline that deals with the analysis and solution of complex decision-making problems
• OR uses a wide range of skills, including math, statistics, probability theory, economics, business, computers, engineering, and physical and behavioral sciences

Difficulty in Decision Making

• Decisions can be difficult to make due to complexity, uncertainty, multiple objectives, and multiple decision makers

Application Areas

• Education
• Production
• Natural resources
• Health care
• Transportation
• Finance
• Marketing
• Human resources management
• Sports

Application Examples

• Scheduling airline crews
• Catalog sales and telemarketing operations
• Transportation planning
• Portfolio management
• Fast-food restaurant operations

Decision Making Phases

• Intelligence: searching for conditions that call for decisions, examining reality, identifying and defining the problem
• Design: generating, developing, and analyzing possible courses of action, constructing a representative model, validating and evaluating the model
• Choice: selecting a course of action from available alternatives, proposing a solution to the model/problem
• Implementation: implementing the solution to the original problem, and possibly backtracking or cycling throughout the process

Intelligence Phase

• Scanning the environment to identify problem situations or opportunities
• Identifying organizational goals and objectives
• Determining whether goals are being met
• Defining the problem explicitly
• Distinguishing between problem and symptoms of problem

Design Phase

• Generating, developing, and analyzing possible courses of action
• Understanding the problem
• Testing solutions for feasibility
• Constructing, testing, and validating a model
• Identifying evaluation criteria

Principle of Choice

• Criteria for selecting a solution, including what makes a solution best or good enough
• Decision regarding the acceptability of a solution approach
• Principles of choice can be normative, descriptive, or political

Management Science Process

• Classification of management science techniques
• Characteristics of optimization problems, including decisions, constraints, and objectives

Optimization Models

• Optimization problems involve satisfying objectives subject to constraints
• Examples of constraints include time, budget, space, capacity, energy, and demand
• Optimization models aim to find the optimal decision

General Form of an Optimization Problem

• MAX (or MIN) of the objective function f0(X1, X2, …, Xn) subject to constraints f1(X1, X2, …, Xn)=bk, …, fm(X1, X2, …, Xn)=bm

General Form of a Linear Programming (LP) Problem

• MAX (or MIN) of the objective function c1X1 + c2X2 + … + cnXn subject to constraints a11X1 + a12X2 + … + a1nXn, …