Operational research books title

1. A Short Introduction to Queueing Theory  Author : Andreas Willig, Technical University Berlin, Telecommunication Networks Group  Publication Date : July 21, 1999  Book Excerpts:  This document is intended to be a short introduction to the field of queueing theory, serving as a module within the lecture Leistungsbewertung von Kommunikationsnetzen of Prof. Adam Woliszfrom the Telecommunication Networks Group at Technical University Berlin. It covers the most important queueing systems with a single service center, for queueing networks only some basics are mentioned. This script is neither complete nor error free.  In this script most of the mathematical details are omitted, instead often "intuitive" (or better: prosaic) arguments are used. Most of the formulas are only used during a derivation and have no numbers, however, the important formulas are numbered. The author does not annotate all statements with a reference, since most of the material can be found in the standard literature.  2.   Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis and Computation  Author : Floyd B. Hanson, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago  Publication Date : May 24, 2006  Book Excerpts:  The aim of this book is to be a self-contained, practical, entry level text on stochastic processes and control for jump-diffusions in continuous time, technically Markov processes in continuous time.  The book is intended for graduate students as well as a research monograph for researchers in applied mathematics, computational science and engineering. Also, the book may be useful for financial engineering practicians who need fast and efficient answers to stochastic financial problems. Hence, the exposition is based upon integrated basic principles of applied mathematics, applied probability and computational science. The target audience includes mathematical modelers and students in many areas of science and engineering seeking to construct models for scientific applications subject to uncertain environments. The prime interest is in modeling and problem solving. The utility of the exposition, based upon systematic derivations along with essential proofs in the spirit of classical applied mathematics, is more important to setting up a stochastic model of an application than abstract theory. However, a lengthy last chapter is intended to bridge the gap between the applied world and the abstract world in order to enable applied students and readers to understand the more abstract literature.  3. Markov Chains and Stochastic Stability  Authors : Sean Meyn, Dept. of Electrical and Computer Engineering, University of Illinois and Richard Tweedie, Division of Biostatistics, University of Minnesota  ISBN : 0387198326  Pages : 548  Publication Date : 1993, recompiled September 2005  Publisher : Springer-Verlag  Book Excerpts:  This book describes the modern theory of general state space Markov chains, and the application of that theory to operations research, time series analysis, and systems and control theory. It is intended as an advanced graduate text in any of these areas, as well as being a research monograph incorporating a new and thorough treatment of the stability of general Markov chains.  There are several key themes in this book which interweave to a surprising extent in both the mathematics and its implementation. There is the use of the splitting technique, which provides an approach to general state space chains through regeneration methods; the systematic use of "Foster-Lyapunov" drift criteria, both in improving the theory and in enabling the classification of individual chains; the delineation of appropriate continuity conditions to link the general theory with the properties of chains on, in particular, Euclidean space; and the development of control model approaches, enabling analysis of models from their deterministic counterparts.  The applications cover storage systems, including some networks models as well as more traditional GI/G/1 queues and dam models; vector ARMA models including those with random coefficients and bilinear models; and both linear and non-linear state space systems with and without controls. To enhance accessibility, each chapter begins with a development of countable state space chains if appropriate. The general state space theory is then developed in close analogy, and where possible the theory is then specialized to chains on a topological state space, such as Euclidean space, so that the special structure of such spaces can be explored.  Queueing Theory  Authors : Ivo Adan and Jacques Resing, Department of Mathematics and Computing Science, Eindhoven University of Technology  Publication Date : February 28, 2002  Book Excerpts:  This document has been used as lecture notes for the Queueing Theory course at Department of Mathematics and Computing Science, Eindhoven University of Technology.  This course discusses a number of elementary queueing models. Attention is paid to methods for the analysis of these models, and also to applications of queueing models. Important application areas of queueing models are production systems, transportation and stocking systems, communication systems and information processing systems. Queueing models are particularly useful for the design of these system in terms of layout, capacities and control.  In these lectures the attention is restricted to models with one queue. Situations with multiple queues are treated in the course "Networks of queues." More advanced techniques for the exact, approximative and numerical analysis of queueing models are the subject of the course "Algorithmic methods in queueing theory."  The organization is as follows. Chapter 2 first discusses a number of basic concepts and results from probability theory that will be used. The most simple interesting queueing model is treated in chapter 4, and its multi server version is treated in the next chapter. Models with more general service or interarrival time distributions are analysed in the chapters 6, 7 and 8. Some simple variations on these models are discussed in chapter 10. Chapter 9 is devoted to queueing models with priority rules. The last chapter discusses some insentive systems.  The text contains a lot of exercises and the reader is urged to try these exercises. This is really necessary to acquire skills to model and analyse new situations.  Probabilistic Design  Author : John Browne, School of Engineering and Science, Swinburne University of Technology  Publication Date : October 2001  Document Excerpts:  This document has been used for teaching Design for Quality course in Swinburne University of Technology, Australia. The course aim is to explore advanced quantitative methodologies for the design of mass-produced products in an environment where time-to-market and quality are critical.  Design for Quality, as it is just starting to be practised world wide, comprises a collection of analytical and experimental techniques for determining and optimizing reliabilities and making design decisions which will result in a product or process which is insensitive to tolerances and other 'noise' influences.        6.  Reversibility and Stochastic Networks           Author : Prof. Frank P. Kelly, Statistical Laboratory, University of Cambridge           ISBN : 0471276014           Pages: 238           Publisher : John Wiley and Sons           Publication Date : 1979, reprinted 1987, 1994  Source: http://www.freetechbooks.com/operations-research-f54.html

Applications of Operational Research (queuing theory)

Basics of Operational Research

Operations research (also referred to as decision science, or management science) is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations. In contrast, many other science & engineering disciplines focus on technology giving secondary considerations to its use.

Employing techniques from other mathematical sciences — such as mathematical modeling, statistical analysis, and mathematical optimization — operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Operations Research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective.

Operational research encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency. Some of the tools used by operational researchers are statistics, optimization, probability theory, queuing theory, game theory, graph theory, decision analysis, mathematical modeling and simulation. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power

Problems addressed with OR are-

·        Critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project

·        Floorplanning: designing the layout of equipment in a factory or components on a computer chip to reduce manufacturing time (therefore reducing cost)

·        Bayesian search theory : looking for a target

·        Automation: automating or integrating robotic systems in human-driven operations processes.

QUEUEING MODEL

Adopting queuing theory to estimate network traffic becomes the important way of network performance prediction, analysis and estimation; through this we can imitate the true network, its reliable and useful for organizing, monitoring and defending the network.

In queuing theory, a queuing model is used to approximate a real queueing situation or system, so the queuing behavior can be analyzed mathematically. Queuing models allow a number of useful steady state performance measures to be determined, including:

• the average number in the queue, or the system,
• the average time spent in the queue, or the system,
• the statistical distribution of those numbers or times,
• the probability the queue is full, or empty, and

the probability of finding the system in a particular state

Basic Operations Research Models/Techniques

·     Linear programming or Allocation Models

·     Inventory Models

·     Waiting(or queuing) Models

·     Competitive(Game Theory)

·     Network Models

·     Sequencing Models

·     Replacement Models

·     Dynamic Programming Models

·     Markov-Chain Models

·     Simulation Models

·     Decision Analysis Models

Optimization Theory Sample paper

1. What is operations research? Explain the scope of OR.                                    [3]
2. List the phases of OR and explain them.                                                           [3]
3. Discuss the guideline of formulation of Linear Programming model and for 

       converting it into standard form?                                                                          [3]     

4. Define the following:                                                                                         [3]

            a.  Optimal solution.

                   b. Unbounded solution.

c.   Artificial variable.

      5. A paper mill produces 2 grades of paper namely X and Y. Because of raw  material restrictions, it cannot produce more than 400 tonnes of grade X and 300            tonnes of grade Y in a week. There are 160 production hours in a week. It requires 0.2 and 0.4 hours to produce a ton of products X and Y respectively with corresponding profits of Rs.200 and Rs. 500 per ton. Formulate the above as a LPP to maximize profit and find the optimum product mix.                                     [3]

6. What conditions must exist in a simplex table to establish the existence of an alternative solution? Unbounded solution?  Degeneracy?                                     [3]

7.  Solve following LP problem using Big M method:

Maximize Z=3x₁ + 5x₂

subject to constraints

                        x₁-2x₂ ≤6

                               x₁≤10

                               x₂≥1

                          x_1, x₂ ≥0                                                                                    [3]

8. What are artificial variables? Why do we need them? Describe two- phase

     method of solving LP problem with artificial variables.                                   [3]

9.  XYZ company produces automobile spare part. The contract that it has signed

     with a large truck manufacturer calls for the following 4-month shipping   

     schedule:

        

Month	Number of parts to be shipped
January	3000
Feburary	4000
March	5000
April	5000

           The company can manufacture 3000 parts per month on a regular time basis             

           and  2000 parts per month on overtime basis. Its production cost is Rs 15000 for

           a part  produced in regular time and 25000 for part produced in overtime.            

           Formulate   problem as LP model to minimize overall cost.                            [3]

     10.  What are unrestricted variables? How can we solve a Linear Programming

          problem having unrestricted variable using simple method? Explain with 

          example.                                                                                                             [3]

Introduction to operational research

Operations research (also referred to as decision science, or management science) is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations. In contrast, many other science & engineering disciplines focus on technology giving secondary considerations to its use.
Employing techniques from other mathematical sciences — such as mathematical modeling, statistical analysis, and mathematical optimization — operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Operations Research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective.
Operational research encompasses a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency. Some of the tools used by operational researchers are statistics, optimization, probability theory, queuing theory, game theory, graph theory, decision analysis, mathematical modeling and simulation. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power
Problems addressed with OR are-

·       Critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project

·       Floorplanning: designing the layout of equipment in a factory or components on a computer chip to reduce manufacturing time (therefore reducing cost)

·       Bayesian search theory : looking for a target

·       Automation: automating or integrating robotic systems in human-driven operations processes.