Operations Research
Sen, Rathindra P
Operations Research Algorithms and Applications - New Delhi PHI Learning Private Limited 2011 - 789p
includes index and biblioraphy
PARTI DETERMINISTIC OPERATIONS RESEARCH MODELS Linear Programming I: Problem Formulation, Graphical Solution and the Simplex Method Introduction Operational Definitions Formulation of a Linear Programming Problem Formulation of a Linear Programming Problem in General Terms Formulation with Different Types of Constraints Graphical Solution Exceptional Cases of the Solution The Simplex Method Computational Aspect of the Simplex Method Maximization (All Constraints of the Type <) Minimization (Constraints of Mixed Type) Multiple, Unbounded, and Infeasible Solutions Linear Programming II: Duality Concept and Post-optimality Analysis Duality Concept Dual Formulation Procedure Duality Theorems Utility of the Dual Post-optimality Analysis Changes in Coefficients of Objective Function Changes in Right Hand Side Values of Constraint Inequalities Addition of a New Variable Changes in Technological Coefficient Linear Programming Extensions: Transportation and Assignment Models The Transportation Model: An Introduction Formulation of a Transportation Problem Methods of Initial Feasible Solution The North-West Corner Rule Least-Cost (or Matrix-Minima) Method Vogel`s Approximation Method (VAM) or Penalty Method Methods of Optimum Solution Stepping-Stone Method Modified Distribution (MODI) Method or u-v Method Unbalanced Transportation Problem Degenerate Transportation Problem Degeneracy at the Initial Solution Degeneracy during the Testing of the Optimum Solution Transhipment Problem The Assignment Model: An Introduction Solution of an Assignment Problem Hungarian Method of Assignment Problem (Minimization Case) Hungarian Algorithms Variations in the Assignment Problem Maximization in an Assignment Problem Multiple Optimization Solution Unbalanced Assignment Problem Infeasible Assignment Problem Travelling Salesman Problem HYBRID OPERATIONS RESEARCH MODELS Project Management: PERT and CPM Introduction PERT/CPM: Background and Development Comparison of PERT/CPM PERT and Gantt Chart Assumptions of PERT/CPM Algorithms of PERT/CPM Techniques Network Analysis 5.6.1 Objectives of Network Analysis Fundamentals of Network Model Events Activity Dummy Activity Predecessor Activities Successor Activities Concurrent Activities Restraints and Ladders Network Adjacent Operations Adjacent Activities Chain Path and Cycle Connected Graph Tree Spanning Tree Oriented Graph Flow Capacity Source Sink Circuit Guidelines for Network Construction Errors in Network Diagramming Formation of a Loop Dangling Redundancy Critical Path Analysis (Time Estimates) Changes in the Duration of Critical Path . Notations Methods Based on Time Estimates to Find the Critical Path Forward Pass Method (for Earliest Event Time) Backward Pass Method (for Latest Allowable Event Time) The Concepts of Slack and Floats in Network Analysis Slack Use of Float Information in Decision-Making Three-estimate Approach of PERT Resource Levelling and Time-cost Trade-off Analysis Project Time-cost Trade-off Analysis Resource Allocation and Scheduling in a Project Project Control Reviews and Updating of a Project GERT Line of Balance (LoB) Choosing between PERT and CPM Concluding Observations
425
P30 / SE551
Operations Research Algorithms and Applications - New Delhi PHI Learning Private Limited 2011 - 789p
includes index and biblioraphy
PARTI DETERMINISTIC OPERATIONS RESEARCH MODELS Linear Programming I: Problem Formulation, Graphical Solution and the Simplex Method Introduction Operational Definitions Formulation of a Linear Programming Problem Formulation of a Linear Programming Problem in General Terms Formulation with Different Types of Constraints Graphical Solution Exceptional Cases of the Solution The Simplex Method Computational Aspect of the Simplex Method Maximization (All Constraints of the Type <) Minimization (Constraints of Mixed Type) Multiple, Unbounded, and Infeasible Solutions Linear Programming II: Duality Concept and Post-optimality Analysis Duality Concept Dual Formulation Procedure Duality Theorems Utility of the Dual Post-optimality Analysis Changes in Coefficients of Objective Function Changes in Right Hand Side Values of Constraint Inequalities Addition of a New Variable Changes in Technological Coefficient Linear Programming Extensions: Transportation and Assignment Models The Transportation Model: An Introduction Formulation of a Transportation Problem Methods of Initial Feasible Solution The North-West Corner Rule Least-Cost (or Matrix-Minima) Method Vogel`s Approximation Method (VAM) or Penalty Method Methods of Optimum Solution Stepping-Stone Method Modified Distribution (MODI) Method or u-v Method Unbalanced Transportation Problem Degenerate Transportation Problem Degeneracy at the Initial Solution Degeneracy during the Testing of the Optimum Solution Transhipment Problem The Assignment Model: An Introduction Solution of an Assignment Problem Hungarian Method of Assignment Problem (Minimization Case) Hungarian Algorithms Variations in the Assignment Problem Maximization in an Assignment Problem Multiple Optimization Solution Unbalanced Assignment Problem Infeasible Assignment Problem Travelling Salesman Problem HYBRID OPERATIONS RESEARCH MODELS Project Management: PERT and CPM Introduction PERT/CPM: Background and Development Comparison of PERT/CPM PERT and Gantt Chart Assumptions of PERT/CPM Algorithms of PERT/CPM Techniques Network Analysis 5.6.1 Objectives of Network Analysis Fundamentals of Network Model Events Activity Dummy Activity Predecessor Activities Successor Activities Concurrent Activities Restraints and Ladders Network Adjacent Operations Adjacent Activities Chain Path and Cycle Connected Graph Tree Spanning Tree Oriented Graph Flow Capacity Source Sink Circuit Guidelines for Network Construction Errors in Network Diagramming Formation of a Loop Dangling Redundancy Critical Path Analysis (Time Estimates) Changes in the Duration of Critical Path . Notations Methods Based on Time Estimates to Find the Critical Path Forward Pass Method (for Earliest Event Time) Backward Pass Method (for Latest Allowable Event Time) The Concepts of Slack and Floats in Network Analysis Slack Use of Float Information in Decision-Making Three-estimate Approach of PERT Resource Levelling and Time-cost Trade-off Analysis Project Time-cost Trade-off Analysis Resource Allocation and Scheduling in a Project Project Control Reviews and Updating of a Project GERT Line of Balance (LoB) Choosing between PERT and CPM Concluding Observations
425
P30 / SE551