Chapter 6 - Distribution & Network Models

Network Model

A mathematical representation of a system where items flow between locations.

Node

A point in a network representing a location (e.g., factory, warehouse, store).

Arc

A connection between nodes representing a path, road, or route.

Transportation Problem

A model that minimizes shipping costs between multiple suppliers and demand points.

Balanced Transportation Problem

A transportation problem where total supply = total demand.

Unbalanced Transportation Problem

A transportation problem where total supply ≠ total demand. Requires a dummy source/destination.

Dummy Source/Destination

A fictitious node added to balance an unbalanced transportation problem.

Transshipment Problem

A transportation problem that allows shipments to pass through intermediate nodes.

Flow Conservation

In a transshipment model, total inflow = outflow at an intermediate node.

Assignment Problem

A special case of transportation where workers are assigned to tasks at minimum cost.

Hungarian Algorithm

A specialized method to solve assignment problems optimally.

Shortest-Route Problem

A model that finds the shortest path between two nodes in a network.

Dijkstra’s Algorithm

A method to find the shortest path in a network with non-negative weights.

Bellman-Ford Algorithm

A method to find the shortest path that works with negative weights.

Maximal Flow Problem

A model that determines the maximum possible flow from a source node to a sink node.

Source Node

The starting point of flow in a maximal flow problem.

Sink Node

The final destination where flow is collected.

Flow Capacity

The maximum amount of flow allowed through an arc.

Ford-Fulkerson Algorithm

A method used to find the maximum flow in a network.