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This book, intended for the course on operations research, is particularly useful for UG/PG degree programmes in engineering and computer applications and may also suit other streams such as management, sciences, etc. The content is designed to address the requirements of the engineering programmes in Indian universities. The systems engineering approach is unique and is expected to receive appreciation especially from the academic community. Operations research is related to the analytical part of systems engineering. This book discusses the operations research techniques using the fundamental concepts of systems engineering to make a difficult but important subject easy to understand. This course in systems engineering concepts coupled with the application of operations research techniques shall help engineers and managers to develop the viewpoint and tools necessary for handling real-life problems.
Difficult analytical techniques and mathematical procedures are explained from first principles assuming bare minimum pre-requisites, to encourage the learner and to make learning enjoyable. A step-by-step explanation presents the concepts and principles and a clear link is established to the already-digested concepts to keep the student involved.
Features
Basic concepts of systems engineering integrated with operations research techniques to enhance real-life problem solving.
Simple, everyday-life examples are used to facilitate a smooth transfer of knowledge in an interesting manner.
High-quality diagrams illustrate the subject matter.
A comprehensive collection of solved examples in a chronological order with increasing level of difficulty help to assimilate the concepts and induce problem-solving skills.
Extensive end-of-chapter key concepts and exercises help to review the learning.
About the Author
Prasanna Devidas Dahe
Prasanna Devidas Dahe is Professor in the Department of Civil Engineering at SGGSIE&T Nanded. A PhD from IIT Roorkee, he has more than 31 years of experience teaching undergraduate as well as postgraduate students. Prof. Dahe has published and presented more than 30 papers in national and international journals and conferences. His primary research interest areas are the applications of systems engineering and operations research techniques to planning and management of surface water resources. One of his taught courses is water resources systems engineering.
Table of Contents:
PART I SYSTEMS ENGINEERING
1. Introduction to Systems Engineering
1.1 Background
1.2 Nature of Real-life Engineering Systems
1.3 Necessity, Significance, and Scope of Systems Engineering
1.4 Role of Systems Engineering
1.5 Justification for Systems Engineering
1.6 An Example: Proposal for Constructing a House for Oneself
2. The Concept of System
2.1 Introduction and Definition
2.2 System Concepts
2.3 Characteristics of a System
2.4 Examples of Systems
2.4.1 A Computer System
2.4.2 The Hydrologic Cycle
2.5 Types of Systems
2.6 Hierarchy of Systems
2.6.1 Subsystems and Suprasystems
2.7 Identification and Formulation of Systems
2.7.1 Building Systems from Subsystems
2.7.2 An Example
3. Systems Engineering
3.1 Introduction to Systems Engineering
3.1.1 Definition
3.2 Systems Approach and Systems Analysis
3.2.1 Systems Approach
3.2.2 Systems Analysis
3.3 System Models and Their Role
3.3.1 Models
3.3.2 Development of System Models
3.3.3 Role of System Models
3.3.4 Types of System Models
3.3.5 An Example
3.4 Examples: Informal Applications of Systems Engineering
4. Systems Analysis
4.1 Introduction
4.2 Systems Analysis Techniques
4.3 The Concept and Process of Optimization
4.4 Optimization by Method of Calculus
4.4.1 Function of a Single Variable
4.4.2 Function of Multiple Variables
4.4.3 Unconstrained Systems
4.4.4 Constrained Systems
4.5 Terminology and Definition of Terms
4.6 Non-linear Programming
PART II DETERMINISTIC MODELS
5. Linear Programming
5.1 Introduction
5.2 General Form of Linear Programming Model
5.3 Assumptions in Linear Programming
5.4 Solution of Linear Programming Models by Graphical Method
5.5 Solution of Linear Programming Models by Simplex Method
5.5.1 The Simplex Algorithm
5.6 Handling Artificial Variables: The Big-M and Two-phase Methods
5.6.1 The Big-M Method
5.6.2 The Two-phase Method
5.7 Introduction to the Theory of Duality
5.8 Applications of Linear Programming Models
5.9 Limitations of Linear Programming
5.10 Examples: Formulation of Linear Programming Problems
5.10.1 The Crop Planning Problem
5.10.2 The Product Mix Problem
6. Transportation, Transshipment, and Assignment Problems
6.1 Introduction
6.2 The Transportation Problem
6.2.1 Formulation and Discussion
6.2.2 Solution to the Transportation Problem
6.2.3 Transportation Algorithm: Finding the Initial Basic Feasible Solution
6.2.4 Transportation Algorithm: The Check for Optimality
6.2.5 Transportation Algorithm: Iterating the Algorithm
6.2.6 Degeneracy
6.2.7 Closure
6.2.8 Exercises
6.3 The Transshipment Problem
6.3.1 Steps in Solving the Transshipment Problem
6.3.2 Closure
6.3.3 Exercises
6.4 The Assignment Problem
6.4.1 The Hungarian Method
6.4.2 Algorithm for the Hungarian Method
6.4.3 Closure
6.4.4 Exercises
7. Dynamic Programming
7.1 Introduction
7.2 Approach and Methodology
7.3 Applications of Dynamic Programming
7.3.1 Shortest Route Problem 1
7.3.2 Shortest Route Problem 2
7.3.3 Shortest Route Problem 3
7.3.4 Resource Allocation Problem 1
7.3.5 Resource Allocation Problem 2
7.4 Curse of Dimensionality in Dynamic Programming
7.5 Formulation of Dynamic Programming Problems
8. Inventory Models
8.1 Introduction
8.2 Selective Inventory Control
8.2.1 ABC Analysis
8.2.2 VED Analysis
8.2.3 SDE Analysis
8.2.4 FSN Analysis
8.3 General Inventory Model
8.3.1 Inventory Parameters
8.3.2 Cost Considerations in Inventory Problem
8.3.3 Assumptions
8.4 Infinite Delivery Rate with No Backordering
8.4.1 Derivation of the Economic Order Quantity Formula
8.4.2 Price Breaks
8.5 Finite Delivery Rate with No Backordering
8.6 Infinite Delivery Rate with Backordering
8.7 Finite Delivery Rate with Backordering
9. Sequencing Models
9.1 Introduction
9.2 Elements and Assumptions
9.2.1 Elements of Sequencing Problems
9.2.2 Assumptions in Sequencing Problems
9.3 Processing N Jobs Through One Machine
9.4 Processing N Jobs Through Two Machines
9.5 Processing N Jobs Through Three Machines
PART III PROBABILISTIC MODELS
10. Probability Concepts and Forecasting Techniques
10.1 Introduction
10.2 Basic Concepts of Probability and Statistics
10.2.1 Probability of an Event
10.2.2 Random Variables
10.2.3 Discrete Random Variables
10.2.4 Important Probability Distributions of a Discrete Random Variable
10.2.5 Continuous Random Variables
10.2.6 Important Probability Distributions of Continuous Random Variables
10.3 Forecasting Techniques
10.3.1 Forecasting Process
10.3.2 Classification of Forecasting Techniques
10.3.3 Qualitative Forecasting Techniques
10.3.4 Quantitative Forecasting Techniques
10.3.5 Regression and Correlation Analysis
10.3.6 Accuracy and Control of Forecasts
11. Queuing Theory—Waiting Line Models
11.1 Introduction
11.2 Approaches to Resolve the Queuing Problem
11.3 Queuing Parameters
11.3.1 The Input Process
11.3.2 The Service Mechanism
11.3.3 Queue Discipline
11.3.4 Customer Behaviour
11.4 Assumptions, Concepts, and Definitions
11.4.1 Assumptions
11.4.2 Transient and Steady-state System
11.4.3 Traffic Intensity
11.4.4 The Queue System
11.4.5 Notation
11.4.6 Kendall’s Notation
11.4.7 Balance Diagram and Balance Equations
11.5 Queuing Model M/M/1/∞
11.6 Queuing Model M/M
11.7 Queuing Model M/M/s/∞
11.8 Queuing Model M/M/s/N
12. Replacement Models
12.1 Introduction
12.2 Replacement of Items that Deteriorate with Time
12.2.1 Time Value of Money is Not Considered
12.2.2 Time Value of Money is Considered
12.3 Replacement of Items that Fail Suddenly
12.4 Replacement Policies
12.4.1 Individual Replacement Policy
12.4.2 Group Replacement Policy
12.4.3 Mortality
12.4.4 Group Replacement
12.4.5 Preventive Replacement
13. Decision Theory and Games
13.1 Introduction
13.2 Decision-making Under Risk
13.2.1 Expected Value Criterion
13.2.2 Decision Procedure with Bayes Probabilities
13.3 Decision Trees
13.4 Decision-making Under Uncertainty
13.4.1 Maximax and Minimin Criteria
13.4.2 Minimax and Maximin Criteria
13.4.3 Laplace Criterion
13.4.4 Hurwicz Criterion
13.5 Game Theory—Competitive Strategy
13.5.1 Concepts and Terminology
13.5.2 Solution of Two-person Zero-sum Games with Pure Strategies
13.5.3 Mixed Strategies
14. Simulation
14.1 Introduction
14.2 The Concept of Simulation
14.2.1 Classification of Simulation Models
14.2.2 Advantages and Limitations of Simulation Models
14.2.3 Application of Simulation Models
14.3 Monte Carlo Simu
14.4 Examples of Monte Carlo Simulation
14.4.1 To Create Cumulative Probability of Demand Based on Normal Distribution
15. Project Management
15.1 Introduction
15.1.1 Cost of Delays in Implementation of Projects
15.1.2 Projects and the Planning Process
15.1.3 Project Life Cycle
15.1.4 Role of Project Management Techniques—Critical Path Method and Performance Evaluation and Review Technique
15.2 Principles of Network Technique
15.2.1 Activities and Events
15.2.2 Event and Activity Numbering
15.2.3 Developing a Network
15.3 Project Time Analysis for Network Techniques—Critical Path Method and Performance Evaluation and Review Technique
15.3.1 Activity Duration
15.3.2 Event Time and Activity Time
15.3.3 Time Analysis for a Project
15.3.4 Event Slack and Activity Float
15.3.5 Critical Path
15.4 Performance Evaluation and Review Technique
15.4.1 Performance Evaluation and Review Technique Statistics
15.4.2 Probability of Completing a Project on Schedule
15.4.3 Criticism of Performance Evaluation and Review Technique and Its Utility
15.5 Project Time–Cost Relationship
15.5.1 Shortening Project Duration
15.5.2 Activity Time–Cost relationship
15.5.3 Project Time–Cost Relationship
15.5.4 Time–Cost Trade-off Analysis
15.6 Resource Allocation and Scheduling
15.6.1 Project Resources
15.6.2 Resource Usage
15.6.3 Resources Smoothening
15.6.4 Resources Leveling
15.7 Project Scheduling and Monitoring
15.7.1 Methods for Scheduling
15.7.2 Presenting the Project Schedule
15.7.3 Monitoring and Control of a Project
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