## Operations Research by P. Mariappan

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2.1 introduction.

Linear Programming constitutes a set of Mathematical Methods specially designed for the Modelling and solution of certain kinds of constrained optimization problems.

The Mathematical presentation of a Linear Programming Problem in the form of a linear objective function and one or more linear constraints with equations or inequations constitutes a Linear Programming Problem. The process leading to the construction of this model is referred to as the Model Building or Mathematical formulation of Business problem given. In this model, a linear objective function of the decision variables are maximized/minimized subject to a set of linear constraints with equations/inequations. This technique ...

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## Operations Research

Itgd4207 operations research course text book and other references: hamdy a. taha, operations research an introduction , fourth edition, ... – powerpoint ppt presentation.

- Assistant Professor
- Dr. Sanaa Wafa Al-Sayegh
- 2nd Semester 2008-2009
- Course Description
- Operations Research is a very important area of study, which tracks its roots to business applications. It combines the three broad disciplines of Mathematics, Computer Science, and Business Applications. This course will formally develop the ideas of developing, analyzing, and validating mathematical models for decision problems, and their systematic solution. The course will involve programming and mathematical analysis
- Course Objectives
- Upon completion of this course, the students will be able to
- - Solve business problems and apply it's applications by using computer programming and mathematical analysis.
- - Develop the ideas of developing, analyzing, and validating mathematical models for decision problems, and their systematic solution.
- - Understand the main concepts of OR .
- Course Text Book and Other References
- Hamdy A. Taha, Operations Research An Introduction , Fourth Edition, Macmillan publishing company, 1982.
- Fredrik S. Hillier, "Introduction to Operations Research", Seventh Edition, McGraw-Hill, 2001
- Admitham B. Rao " Operations Research", Jaico Publishing House, 2006
- Introduction
- The Origins of Operations Research
- The Nature of OR
- What is Operations Research
- OR/MS What is It?
- Differences Between OR and IT
- Terminology
- Model Types
- Phases of an OR Study
- OR Software Packages
- The formal activities of Operations Research (OR) were initiated in England during World War II when a team of British scientists set out to make decisions regarding the best utilization of war material. Following the end of the war, the ideas advanced in military operations were adapted to improve efficiency and productivity in the civilian sector. Today, OR is a dominant decision making tool.
- As its name implies, operations research involves research on operations. Thus, operations research is applied to problems that concern how to conduct and coordinate the operations (i.e., the activities) within an organization .The nature of the organization is essentially immaterial, and, in fact, OR has been applied extensively in such diverse areas as manufacturing, transportation, construction, telecommunications, financial planning, health care, the military, and public services, to name just a few. Therefore, the breadth of application is unusually wide.
- The research part of the name means that operations research uses an approach that resembles the way research is conducted in established scientific fields. To a considerable extent, the scientific method is used to investigate the problem of concern. (In fact, the term management science sometimes is used as a synonym for operations research.)
- Operations Research ( OR) Is the application of scientific methods in solving problems facing management and to help to taking decisions.
- A rose by any other name
- Management Science
- Systems Engineering
- Industrial Engineering
- Operations Management
- Applied Mathematics
- Operations research (also known as management science) is a collection of techniques based on mathematics and other scientific approaches that finds solutions to your problems.
- Focuses on data as a corporate resource
- Stores, retrieves, formats, displays data
- Understands business process and transactions
- Uses data as input
- Provides improved solutions
- Gives global focus
- Multiple objectives
- Multiple criteria
- Evaluates tradeoffs
- Decision VariableRepresents an alternative available to the decision- Maker
- Objective FunctionA (usually real-valued) function measuring the goodness of alternatives
- ConstraintAn restriction on the set of alternatives that may be considered
- FeasibleAn alternative (value) is feasible if it satisfies all constraints
- OptimalAn alternative (value) is optimal if it yields the most favorable value of the objective function over all feasible solutions considered
- Linear Program (LP)
- Integer Linear Program (IP or ILP)
- Non-Linear Program (NLP)
- Dynamic Program (DP)
- Goal Program (GP)
- Queuing Models
- Simulations
- Network models
- Game theory
- Definition of the Problem
- Construction of the Model(s)
- Solution of the Model(s)
- Validation of the Model(s)
- Implementation of Recommended actions based on the solution(s)
- A very popular approach now is to use todays premier spreadsheet package, Microsoft Excel, to formulate small OR models in a spreadsheet format. The Excel Solver then is used to solve the models.
- LINDO (and its companion modeling language LINGO) continues to be a dominant OR software package. Student versions of LINDO and LINGO now can be downloaded free from the Web.
- CPLEX is a state-of-the-art software package that is widely used for solving large and challenging OR problems
- MPL is a user-friendly modeling system that uses CPLEX as its main solver.

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## What is Operations Research?

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## Lecture 1 – Operations Research

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Lecture 1 – Operations Research. Topics What is OR? Modeling and the problem solving process Deterministic vs. stochastic models OR techniques Using the Excel add-ins to find solutions Solving real problems. What is Operations Research?. Operations

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- deterministic models stochastic models
- scheduling equipment
- computer models
- define variables
- stochastic models
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Lecture 1 – Operations Research Topics • What is OR? • Modeling and the problem solving process • Deterministic vs. stochastic models • OR techniques • Using the Excel add-ins to find solutions • Solving real problems J. Bard and J. W. Barnes Operations Research Models and Methods Copyright 2004 - All rights reserved

What is Operations Research? Operations The activities carried out in an organization. Research The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. Model An abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.

Systems Approach Include broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered. Optimal Solution A solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. Team A group of individuals bringing various skills and viewpoints to a problem. Operations Research Techniques A collection of general mathematical models, analytical procedures, and algorithms.

Definition of OR? OR professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.

Problem Solving Process Goal: solve a problem • Model must be valid • Model must be tractable • Solution must be useful

The Situation • May involve current operations or proposed expansions due to expected market shifts • May become apparent through consumer complaints or through employee suggestions • May be a conscious effort to improve efficiency or response to an unexpected crisis. Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.

Define variables Define constraints Data requirements Problem Formulation • Describe system • Define boundaries • State assumptions • Select performance measures Example: Maximize individual nurse preferences subject to demand requirements.

Personnel Planning and Scheduling: Example of Bounding a Problem

Problem statement Formulate the Problem Construct a Model Model Constructing a Model • Problem must be translated from verbal, qualitative terms to logical, quantitative terms • A logical model is a series of rules, usually embodied in a computer program • A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. Example: Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources.

Model Find a solution Solution Tools Solving the Mathematical Model • Many tools are available as discussed in this course • Some lead to “optimal” solutions • Others only evaluate candidates trial and error to find “best” course of action Example: Read nurse profiles and demand requirements, apply algorithm, post-processes results to get monthly schedules.

Implementation • A solution to a problem usually implies changes for some individuals in the organization • Often there is resistance to change, making the implementation difficult • User-friendly system needed • Those affected should go through training Example: Implement nurse scheduling system in one unit at a time. Integrate with existing HR and T&A systems. Provide training sessions during the workday.

Components of OR-Based Decision Support System • Data base (nurse profiles, external resources, rules) • Graphical User Interface (GUI); web enabled using java or VBA • Algorithms, pre- and post- processor • What-if analysis • Report generators

Problems, Models and Methods Real World Situation Problems Models Methods

Operations Research Models Deterministic Models Stochastic Models • Linear Programming • Discrete-Time Markov Chains • Network Optimization • Continuous-Time Markov Chains • Integer Programming • Queueing • Nonlinear Programming • Decision Analysis

Deterministic vs. Stochastic Models Deterministic models – 60% of course Stochastic (or probabilistic) models – 40% of course Deterministic models assume all data are known with certainty Stochastic models explicitly represent uncertain data via random variables or stochastic processes. Deterministic models involve optimization Stochastic models characterize / estimate system performance.

Examples of OR Applications • Rescheduling aircraft in response to groundings and delays • Planning production for printed circuit board assembly • Scheduling equipment operators in mail processing & distribution centers • Developing routes for propane delivery • Adjusting nurse schedules in light of daily fluctuations in demand

Steps in OR Study

Activate Excel Add-ins Tools Menu: Add ORMM or Individual Add-ins

Available OR_MM Add-ins

What you Should Know about Operations Research • How decision-making problems are characterized • OR terminology • What a model is and how to assess its value • How to go from a conceptual problem to a quantitative solution • How to find solutions with the Excel add-ins

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## COMMENTS

Chapter Two Linear Programming: Application and Model Formulation. 2. Introduction (We first detail discuss the theory of LP) The term linear implies that all the mathematical relations used in the problem are linear or straight-line relations, while the term programming refers to the method of determining a particular program or plan of action, i., the use of algorithms that is a well defined ...

Download ppt "Introduction Hamdy A. Taha, Operations Research: An introduction, 8th Edition." Similar presentations 1 1 Slide Chapter 1 & Lecture Slide Body of Knowledge n Management science Is an approach to decision making based on the scientific method Is.

speaking, an O.R. project comprises three steps: (1) building a model, (2) solving it, and. (3) implementing the results. The emphasis of this chapter is on the first and third steps. The second step typically involves specific methodologies or techniques, which could be.

Operations Research (OR) is the study of mathematical models for complex organizational systems. Optimization is a branch of OR which uses mathematical techniques such as linear and nonlinear programming to derive values for system variables that will optimize performance. Introduction to Operations Research - p.5

Operation Research Chapter 2 Part II. Chapter 2 Outline: Part II • Introduction • The Linear Programming Model • Examples of Linear Programming Problems • Developing Linear Programming Models • Graphical Solution to LP Problems • Slack, Surplus and unrestricted variables • Graphical LP Sensitivity Analysis Operation Research: An Introduction By Dr: AlaaSagheer

2.1 INTRODUCTION. Linear Programming constitutes a set of Mathematical Methods specially designed for the Modelling and solution of certain kinds of constrained optimization problems. The Mathematical presentation of a Linear Programming Problem in the form of a linear objective function and one or more linear constraints with equations or ...

1 , Introduction to Operations Research, 7th ed. McGraw Hill, Frederick S. Hillier and Gerald J. Lieberman. 2 History of Operations Research: Chapter 1 Introduction History of Operations Research: Research on Radar: This work involved the closest possible cooperation between the scientists and the officers and men of the (English) Royal Air ...

List of Lecture Slides. Course organization , text, etc. One/Page. Solving Systems of Linear Equations One/Page or HANDOUT. Linear Programming: optimization of a linear function of several variables, with the restriction that these variables satisfy certain linear equations or inequalities. Formulating LP Models One/Page or HANDOUT.

6 DEFINITION OF OPERATIONAL RESEARCH. It is an Act of winning wars without actually fighting. -Aurther Clark It is a Scientific Approach to problem solving for executive management. -H.M. Wagner It is Art of giving bad answers to problem which otherwise have worse answers.

Title: 456556 Introduction to Operations Research 1 456/556 Introduction to Operations Research. Chapter 1 Introduction ; Chapter 2 Overview of the Operations Research Modeling Approach; 2 Origins of Operations Research. Operations Research (OR) or Management Science can be defined as the use of quantitative methods to assist analysts and ...

Operations Research is a very important area of. study, which tracks its roots to business. applications. It combines the three broad. disciplines of Mathematics, Computer Science, and. Business Applications. This course will formally. develop the ideas of developing, analyzing, and.

2 CHAPTER 1. MATHEMATICAL MODELING BY EXAMPLE Constraints: •producing x1 toy soldiers and x2 toy trains requires (a) 1x1 +1x2 hours in the carpentry shop; there are 80 hours available (b) 2x 1 +1x2 hours in the ﬁnishing shop; there are 100 hours available •the number x1 of toy soldiers produced should be at most 40 Variable domains: the numbers x 1, x2 of toy soldiers and trains must be ...

The activities carried out in an organization. Research The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. Model An abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.

Operations The activities carried out in an organization. Research The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. Model An abstract representation of reality. Mathematical, physical, narrative, set of rules in ...