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Operations research

Author: S R Yadav; A K Malik
Publisher: New Delhi, India : Oxford University Press, 2014.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This text starts with basic topics, such as formulation and graphical solution of linear programming problems, simplex and revised simplex method, duality and sensitivity analysis, transportation and assignment models, and then moves on to advance topics, such as sequencing and scheduling, dynamic, integer and goal programming, game and decision theories, queuing and replacement models, simulation, inventory models,  Read more...
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Document Type: Book
All Authors / Contributors: S R Yadav; A K Malik
ISBN: 9780198096184 0198096186
OCLC Number: 896901482
Description: xvi, 691 pages : illustrations ; 24 cm
Contents: 1. Introduction to Operations Research ; 1.1 INTRODUCTION ; 1.2 HISTORICAL DEVELOPMENT ; 1.3 DEFINITIONS ; 1.4 MODELS ; 1.5 SCOPE AND APPLICATIONS ; 1.6 PHASES ; 2. Linear Programming Problem I-Formulation ; 2.1 INTRODUCTION ; 2.2 LINEAR PROGRAMMING PROBLEM ; 2.3 BASIC ASSUMPTIONS OF LINEAR PROGRAMMING PROBLEM ; 2.4 FORMULATION OF LINEAR PROGRAMMING MODEL ; 2.5 LIMITATIONS OF LINEAR PROGRAMMING PROBLEM ; 2.6 APPLICATIONS OF LINEAR PROGRAMMING PROBLEM IN BUSINESS AND INDUSTRIES ; 3. Linear Programming Problem II-Graphical Method ; 3.1 INTRODUCTION ; 3.2 SOME DEFINITIONS ; 3.3 SOME IMPORTANT THEOREMS ; 3.4 GRAPHICAL METHOD ; 3.4.1 Corner Point Method ; 3.4.2 Iso-profit Method or Isovalue Line Method ; 3.5 SPECIAL CASES IN GRAPHICAL METHOD ; 3.5.1 Alternate Optimal Solution ; 3.5.2 No Feasible Solution ; 3.5.3 Unbounded Solution Space but Bounded Optimal Solution ; 3.5.4 Unbounded Solution Space and Unbounded Solution ; 3.6 LIMITATIONS OF GRAPHICAL METHOD ; 4. Linear Programming Problem III-Simplex Method ; 4.1 INTRODUCTION ; 4.2 STANDARD FORM OF LINEAR PROGRAMMING PROBLEM ; 4.3 SOME IMPORTANT TERMINOLOGIES ; 4.4 SOME IMPORTANT RESOLUTIONS USED IN LPP FOR SIMPLEX METHOD ; 4.5 SIMPLEX METHOD ; 4.6 SIMPLEX TABLE ; 4.7 CRITERIA OF OPTIMALITY ; 4.8 COMPUTATIONAL OR ITERATIVE PROCEDURE FOR SOLVING LINEAR PROGRAMMING PROBLEM USING SIMPLEX METHOD ; 4.9 SPECIAL CASES IN SIMPLEX METHOD ; 4.9.1 Infeasibility ; 4.9.2 Unboundedness ; 4.9.3 Degeneracy ; 4.9.4 Alternate or More Than One Optimal Solution ; 4.9.5 Cycling ; 4.10 ARTIFICIAL VARIABLE TECHNIQUE FOR SOLVING LINEAR ; PROGRAMMING PROBLEMS ; 4.10.1 Big-M Method ; 4.10.2 Two-phase Method ; 4.10.3 Comparison between Big-M and Two-phase Methods ; 4.11 SOLVING SIMULTANEOUS LINEAR EQUATIONS USING SIMPLEX METHOD ; 4.12 FINDING INVERSE OF SQUARE MATRIX USING SIMPLEX METHOD ; 5. Linear Programming Problem IV-Revised Simplex Method ; 5.1 INTRODUCTION ; 5.2 REVISED SIMPLEX METHOD ; 5.3 COMPUTATIONAL PROCEDURE FOR SOLVING LPP BY REVISED SIMPLEX METHOD ; 6. Duality in Linear Programming ; 6.1 INTRODUCTION ; 6.2 SYMMETRIC FORM ; 6.3 DEFINITION OF DUAL OF LINEAR PROGRAMMING PROBLEM ; 6.4 PRIMAL-DUAL RELATIONSHIP ; 6.5 ECONOMIC INTERPRETATION OF DUALITY ; 6.6 IMPORTANT THEOREMS ; 6.7 DUAL SIMPLEX METHOD ; 6.7.1 Procedure for Solving a Linear Programming Problem ; 7. Post-optimality Analysis or Sensitivity Analysis ; 7.1 INTRODUCTION ; 7.2 CHANGES AFFECTING FEASIBILITY AND OPTIMALITY ; 7.3 GRAPHICAL SENSITIVITY ANALYSIS ; 7.4 CHANGES IN COST CJ IN OBJECTIVE FUNCTION ; 7.5 CHANGES IN BI'S AVAILABILITIES ; 7.6 ADDITION OF NEW VARIABLE ; 7.7 DELETION OF CONSTRAINTS ; 7.8 DELETION OF VARIABLES ; 7.9 ADDITION OF CONSTRAINTS ; 7.10 CHANGE IN AIJ'S ; 7.11 PARAMETRIC LINEAR PROGRAMMING ; 7.11.1 Parametric Changes in Cost Vector c ; 7.11.2 Parametric Changes in Requirement Vector b ; 7.12 DIFFERENCE BETWEEN SENSITIVITY ANALYSIS AND PARAMETRIC LINEAR PROGRAMMING ; 8. Transportation Problems ; 8.1 INTRODUCTION ; 8.2 FORMULATION OF TRANSPORTATION PROBLEM ; 8.3 DEVELOPMENT OF TRANSPORTATION ALGORITHM ; 8.4 SOLUTION OF TRANSPORTATION PROBLEM ; 8.4.1 North-west Corner Method ; 8.4.2 Least Cost Entry or Matrix Minima Method ; 8.4.3 Vogel's Approximation Method ; 8.5 TEST OF OPTIMALITY ; 8.5.1 MODI Method ; 8.5.2 Stepping Stone Method ; 8.6 DEGENERACY IN TRANSPORTATION PROBLEM ; 8.7 UNBALANCED TRANSPORTATION PROBLEM ; 8.8 TRANSSHIPMENT PROBLEM ; 9. Assignment Problems ; 9.1 INTRODUCTION ; 9.2 SOLVING ASSIGNMENT PROBLEMS USING HUNGARIAN METHOD ; 9.3 MINIMAL ASSIGNMENT PROBLEM ; 9.4 MAXIMAL ASSIGNMENT PROBLEM ; 9.5 UNBALANCED ASSIGNMENT PROBLEM ; 9.6 ASSIGNMENT PROBLEMS UNDER CERTAIN RESTRICTIONS ; 9.7 TRAVELLING SALESMAN PROBLEM ; 9.8 DIFFERENCE BETWEEN ASSIGNMENT AND TRANSPORTATION PROBLEMS ; 10. Sequencing ; 10.1 INTRODUCTION ; 10.2 ASSUMPTIONS, NOTATIONS, AND TERMINOLOGIES ; 10.2.1 Assumptions ; 10.2.2 Notations ; 10.2.3 Terminologies ; 10.3 JOHNSON'S ALGORITHM FOR PROCESSING N JOBS THROUGH TWO MACHINES ; 10.4 JOHNSON'S ALGORITHM FOR PROCESSING N JOBS THROUGH K MACHINES ; 10.5 PROCESSING TWO JOBS THROUGH K MACHINES ; 11. Project Scheduling ; 11.1 NTRODUCTION ; 11.2 PROJECT SCHEDULING ; 11.2.1 Planning ; 11.2.2 Scheduling ; 11.2.3 Controlling ; 11.3 NETWORK ; 11.3.1 Notations ; 11.3.2 Fulkerson's Rule for Numbering Events ; 11.4 CRITICAL PATH METHOD ; 11.5 PROGRAM EVALUATION AND REVIEW TECHNIQUE ; 11.6 OPTIMUM SCHEDULING BY CRITICAL PATH METHOD ; 11.7 TIME-COST OPTIMIZATION ALGORITHM ; 12. Dynamic Programming ; 12.1 INTRODUCTION ; 12.2 TERMINOLOGY USED IN DYNAMIC PROGRAMMING ; 12.3 MULTI-DECISION PROCESS ; 12.4 BELLMAN'S PRINCIPLE OF OPTIMALITY ; 12.5 CHARACTERISTICS OF DYNAMIC PROGRAMMING PROBLEMS ; 12.6 DYNAMIC PROGRAMMING ALGORITHM ; 12.7 DETERMINISTIC AND PROBABILISTIC DYNAMIC PROGRAMMING ; 12.8 MODELS OF DYNAMIC PROGRAMMING ; 12.8.1 Model I-Shortest Route Problem ; 12.8.2 Model II-Solving Dynamic Programming using Calculus Method ; 12.8.3 MODEL III ; 12.9 SOLVING LINEAR PROGRAMMING PROBLEMS USING DYNAMIC PROGRAMMING ; 12.10 APPLICATIONS OF DYNAMIC PROGRAMMING ; 13. Integer Programming ; 13.1 INTRODUCTION ; 13.2 MATHEMATICAL FORMULATION OF INTEGER PROGRAMMING ; PROBLEMS ; 13.3 TYPES OF INTEGER PROGRAMMING PROBLEMS ; 13.4 GOMORY'S CUTTING PLANE METHOD FOR AIPP ; 13.4.1 Algorithm for Gomory's Cutting Plane Method ; 13.5 GOMORY'S CUTTING PLANE METHOD FOR MIPP ; 13.6 DIFFERENCE BETWEEN GOMORY'S CUTTING PLANE METHOD FOR AIPP AND MIPP ; 13.7 BRANCH AND BOUND TECHNIQUE TO FIND SOLUTION OF IPP () ; 13.8 ZERO-ONE INTEGER PROGRAMMING PROBLEM ; 13.8.1 Format of Balas-Zero-One Additive Algorithm ; 13.8.2 Some Important Terms used in Balas Additive Algorithm ; 13.8.3 Solution Procedure of Zero-One IPP ; 14. Queuing Theory ; 14.1 INTRODUCTION ; 14.2 BASIC ELEMENTS OF QUEUING SYSTEMS ; 14.2.1 State of Systems ; 14.3 MARKOVIAN QUEUES ; 14.4 TERMINOLOGY AND NOTATIONS USED IN QUEUING SYSTEMS ; 14.5 SYMBOLIC REPRESENTATION OF QUEUING MODELS ; 14.6 PROBABILITY DISTRIBUTION OF N ARRIVALS IN TIME INTERVAL (T, T+ IN PURE BIRTH PROCESSES ; 14.7 DISTRIBUTION OF INTER-ARRIVALS TIME ; 14.8 DISTRIBUTION OF DEPARTURES IN PURE DEATH PROCESSES ; 14.9 BIRTH AND DEATH PROCESS ; 14.10 VARIOUS QUEUING MODELS WITH THEIR CHARACTERISTIC PROPERTIES ; 14.10.1 Model-I-(M/M/1):(FCFS/?) ; 14.10.2 Finite Storage Queue System with One Server (M/M/1):(FCFS/N) ; 14.10.3 S-Server case (M/M/S):(FCFS/?) ; 14.10.4 S-Server Case with Finite Accommodation Capacity (M/M/S):(FCFS/N) ; 14.11 ADVANTAGES OF QUEUING THEORY ; 15. Goal Programming ; 15.1 INTRODUCTION ; 15.2 FORMULATION OF GOAL PROGRAMMING ; 15.3 BASIC TERMINOLOGIES ; 15.4 SINGLE-GOAL MODELS ; 15.5 GP ALGORITHM OR MODIFIED SIMPLEX METHOD ; 15.6 MULTIPLE-GOAL MODELS ; 15.6.1 Multiple-goal Models with Equal or No Priorities ; 15.6.2 Multiple-goal Models with Priorities ; 15.6.3 Multiple-goal Models with Priorities and Weights ; 15.7 GRAPHICAL SOLUTION OF GOAL PROGRAMMING PROBLEMS ; 16. Game Theory ; 16.1 INTRODUCTION ; 16.2 CHARACTERISTICS OF GAMES ; 16.3 BASIC TERMINOLOGY USED IN GAME THEORY ; 16.4 LOWER AND UPPER VALUE OF GAME-'MINIMAX' PRINCIPLE WITH PURE STRATEGIES ; 16.5 PROCEDURE TO DETERMINE SADDLE POINT ; 16.6 MATRIX REDUCTION BY DOMINANCE PRINCIPLE ; 16.7 GAMES WITHOUT SADDLE POINT ; 16.7.1 2 x 2 Game Without Saddle Point ; 16.8 (3 x 3) GAMES WITH NO SADDLE POINT ; 16.9 GRAPHICAL METHOD FOR (2 X N) AND (M X 2) GAMES ; 16.9.1 Graphical Method for n x 2 Games ; 16.9.2 Graphical Method for m x 2 Games ; 16.10 METHOD OF SUBMATRICES OR SUBGAMES FOR (2 X N) OR (M X 2) GAMES WITH NO SADDLE POINT ; 16.11 TWO-PERSON ZERO-SUM GAME WITH MIXED STRATEGIES OR LINEAR PROGRAMMNING METHOD ; 16.12 LIMITATIONS OF GAME THEORY ; 17. Decision Theory (Analysis) ; 17.1 INTRODUCTION ; 17.2 DECISION MODELS ; 17.2.1 Decision Alternatives ; 17.2.2 States of Nature or Events ; 17.2.3 Payoff ; 17.3 DECISION-MAKING SITUATIONS ; 17.3.1 Decision-making Under Certainty ; 17.3.2 Decision-making Under Risk ; 17.3.3 Decision-making Under Uncertainty (Fuzzy Environment) ; 17.3.4 Posterior Probability and Bayesian Analysis ; 17.3.5 DECISION-MAKING UNDER CONFLICT (GAME THEORY) ; 18. Networking ; 18.1 INTRODUCTION ; 18.2 DEFINITIONS AND NOTATIONS USED IN NETWORKING ; 18.3 SHORTEST ROUTE PROBLEM ; 18.4 MINIMUM SPANNING TREE PROBLEM ; 18.5 MAXIMUM FLOW PROBLEMS ; 19. Replacement Models ; 19.1 INTRODUCTION ; 19.2 REPLACEMENT POLICY MODELS ; 19.3 REPLACEMENT POLICY WHEN THE VALUE OF MONEY DOES NOT CHANGE WITH TIME ; 19.4 REPLACEMENT POLICY WHEN THE VALUE OF MONEY CHANGES WITH TIME ; 19.5 PROCEDURE TO SELECT THE BETTER EQUIPMENT ; 19.6 REPLACEMENT OF EQUIPMENT THAT FAILS SUDDENLY ; 19.7 GROUP REPLACEMENT THEOREM ; 20. Simulation ; 20.1 INTRODUCTION ; 20.2 BASIC TERMINOLOGIES ; 20.3 RANDOM NUMBERS AND PSEUDO-RANDOM NUMBERS ; 20.3.1 Mid-square Method or Technique of Generating Pseudo-random Numbers ; 20.3.2 Limitations of Mid-square Method ; 20.3.3 Multiplicative Congruential or Power Residual Technique ; 20.3.4 Mixed Congruential Method ; 20.4 MONTE CARLO SIMULATION ; 20.5 GENERATION OF RANDOM VARIATES ; 20.5.1 Continuous Random Variate X ; 20.5.2 Discrete Case ; 20.6 APPLICATIONS OF SIMULATION IN QUEUING MODELS ; 20.7 ADVANTAGES AND DISADVANTAGES OF SIMULATION ; 20.8 SIMULATION LANGUAGES ; 21. Inventory Models ; 21.1 INTRODUCTION ; 21.2 INVENTORY ; 21.3 SOME BASIC TERMINOLOGIES USED IN INVENTORY ; 21.4 INVENTORY CONTROL ; 21.5 INVENTORY COSTS ; 21.6 INVENTORY MANAGEMENT AND ITS BENEFITS ; 21.7 ECONOMIC ORDER QUANTITY ; 21.7.1 Deterministic Inventory Models With No Shortages ; 21.8 DETERMINISTIC INVENTORY MODELS WITH SHORTAGES ; 21.9 EOQ PROBLEM WITH PRICE BREAKS OR QUANTITY DISCOUNT ; 21.10 PROBABILISTIC INVENTORY MODELS ; 21.10.1 Single Period Problem without Set-up Cost and Uniform Demand ; 21.10.2 Single Period Problems without Set-up Cost and Instantaneous Demand ; 21.11 SOME IMPORTANT INVENTORY CONTROL TECHNIQUES ; 22. Classical Optimization Techniques ; 22.1 INTRODUCTION ; 22.2 UNCONSTRAINED OPTIMIZATION PROBLEMS ; 22.2.1 Single-variable Unconstrained Optimization Problems ; 22.2.2 Conditions for Local Maxima or Minima of Single-variable Function ; 22.2.3 Procedure to Find Extreme Points of Functions of Single Variables ; 22.3 MULTIVARIABLE OPTIMIZATION PROBLEMS ; 22.3.1 Working Rule to Find Extreme Points of Functions of Two Variables ; 22.3.2 Working Rule to Find Extreme Points of Functions of n Variables ; 22.4 MULTIVARIABLE CONSTRAINED OPTIMIZATION PROBLEMS WITH EQUALITY CONSTRAINTS ; 22.4.1 Direct Substitution Method ; 22.4.2 Lagrange Multipliers Method ; 22.5 MULTIVARIABLE CONSTRAINED OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS ; 23. Non-Linear Programming Problem 1-Search Techniques ; 23.1 INTRODUCTION ; 23.2 UNCONSTRAINED NON-LINEAR PROGRAMMING PROBLEM ; 23.3 DIRECT SEARCH METHODS ; 23.4 SEARCH TECHNIQUES OR ONE DIMENSION ; 23.4.2 Golden Section Method arch ; 23.4.3 Univariate Method ; 23.4.4 Pattern Search Methods ; 23.5 INDIRECT SEARCH METHODS ; 23.5.1 Steepest Descent or Cauchy's Method ; 23.6 CONSTRAINED NON-LINEAR PROGRAMMING PROBLEMS ; 23.7 DIRECT METHODS ; 23.7.1 Complex Method ; 23.7.2 Zoutendijk Method or Method of Feasible Direction ; 23.8 INDIRECT METHODS ; 23.8.1 Transform Techniques ; 23.8.2 Penalty Function Methods ; 23.9 ROSEN'S GRADIENT PROJECTION METHOD ; 24. Non-Linear Programming 2-Quadratic and Separable Programming ; 24.1 INTRODUCTION ; 24.2 KUHN-TUCKER CONDITIONS ; 24.3 QUADRATIC PROGRAMMING ; 24.3.1 Wolfe's Modified Simplex Method ; 24.3.2 Beale's Method ; 24.4 SEPARABLE PROGRAMMING ; Appendix A: Linear Algebra ; Appendix B: Matrices ; Appendix C: Calculus ; Appendix D: Probability ; Appendix E: Poisson Probability Distribution X Table ; Appendix F: Area under the Standard Normal Distribution Z ; Appendix G: Table of Random Nu
Responsibility: S.R. Yadav, A.K. Malik.

Abstract:

Operations Research is designed as a textbook for undergraduate students of Mechanical Engineering. It is intended to help them understand and apply operations research techniques to industrial  Read more...

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