Operations Research

5.

Network Optimization Models

5.1.

Graph Theory Fundamentals

5.1.1.

Basic Definitions

5.1.1.1.

5.1.1.2.

Directed and Undirected Graphs

5.1.1.3.

Paths and Cycles

5.1.2.

Network Representation

5.1.3.

Graph Properties

5.1.4.

Network Flow Concepts

5.2.

Shortest Path Problems

5.2.1.

Single-Source Shortest Path

5.2.1.1.

Dijkstra's Algorithm

5.2.1.2.

Bellman-Ford Algorithm

5.2.2.

All-Pairs Shortest Path

5.2.2.1.

Floyd-Warshall Algorithm

5.2.3.

Applications in Routing and Navigation

5.3.

Minimum Spanning Tree Problems

5.3.1.

Problem Definition and Applications

5.3.2.

Prim's Algorithm

5.3.3.

Kruskal's Algorithm

5.3.4.

Properties of Minimum Spanning Trees

5.4.

Maximum Flow Problems

5.4.1.

Problem Definition and Formulation

5.4.2.

Flow Conservation Constraints

5.4.3.

Capacity Constraints

5.4.4.

Max-Flow Min-Cut Theorem

5.4.5.

Ford-Fulkerson Algorithm

5.4.6.

Edmonds-Karp Algorithm

5.4.7.

Applications in Network Capacity

5.5.

Minimum Cost Flow Problems

5.5.1.

Problem Formulation

5.5.2.

Network Simplex Method

5.5.3.

Applications in Supply Chain Optimization

5.5.4.

Relationship to Other Network Problems

5.6.

Project Scheduling Networks

5.6.1.

Project Network Representation

5.6.2.

Activity-on-Node Networks

5.6.3.

Activity-on-Arrow Networks

5.6.4.

Critical Path Method

5.6.4.1.

Forward Pass Calculations

5.6.4.2.

Backward Pass Calculations

5.6.4.3.

Slack Calculations

5.6.4.4.

Critical Path Identification

5.6.5.

Program Evaluation and Review Technique

5.6.5.1.

Probabilistic Time Estimates

5.6.5.2.

Expected Project Duration

5.6.5.3.

Project Variance Calculations

5.6.6.

Project Crashing

5.6.7.

Resource Allocation and Leveling

Previous

4. Transportation and Assignment Problems

Go to top

Next

6. Integer Programming