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Full Description
The book starts with basic topics, such as formulation and graphical solution of Linear Programming Problems (LPP), 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 (CPM &PERT), dynamic, integer and goal programming, game and decision theories, queuing and replacement models, simulation, inventory (deterministic and probabilistic)models, non-linear programming, classical optimization techniques, etc. Further, seven appendices have been provided which discuss a few preliminary mathematical concepts in brief, and also provide a few tables that would be helpful in solving certain problems provided in the book.
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 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 SIMPLEX METHOD ; 4.5 SIMPLEX METHOD ; 4.6 SIMPLEX TABLE ; 4.7 CRITERIA OF 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 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 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 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 North-west Corner Method ; 8.4.2 Least Cost Entry or Matrix Minima Method ; 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 ; ALGORITHM ; 12. Dynamic Programming ; 12.1 INTRODUCTION ; 12.2 TERMINOLOGY PROBLEMS ; 12.6 DYNAMIC PROGRAMMING ALGORITHM ; 12.7 DETERMINISTIC AND 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 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 () ; 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 State of Systems ; 14.3 MARKOVIAN QUEUES ; 14.4 TERMINOLOGY AND NOTATIONS 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) ; 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 PRINCIPLE ; 16.7 GAMES WITHOUT SADDLE POINT ; 16.7.1 2 x 2 Game Without METHOD FOR (2 X N) AND (M X 2) GAMES ; 16.9.1 Graphical Method for n x 2 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 18.4 MINIMUM SPANNING TREE PROBLEM ; 18.5 MAXIMUM FLOW PROBLEMS ; 19. Replacement Models ; 19.1 INTRODUCTION ; 19.2 REPLACEMENT POLICY MODELS ; 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 VARIATES ; 20.5.1 Continuous Random Variate X ; 20.5.2 Discrete Case ; 20.6 Models ; 21.1 INTRODUCTION ; 21.2 INVENTORY ; 21.3 SOME BASIC TERMINOLOGIES 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 ; 23.4.3 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
