Module5

Question 1

What is a node (vertex)?

Answer 1

A junction point in a network.

• Represents locations like plants, warehouses, terminals
• Shown as a labeled circle

Question 2

What is an arc (edge/link)?

Answer 2

A channel through which flow may occur from one node to another.

• Represents roads, rail tracks, trade lanes, etc.
• Shown as an arrow indicating the direction of flow

Question 3

Define flow (weight) in a network.

Answer 3

Objects passing through nodes and arcs.

• Can be freight, cargo, passengers, etc.
• Measured in quantity, e.g., volume or cost

Question 4

List the types of nodes in a supply chain network.

Answer 4

• Source: All flow originates (no predecessors)
• Sink: All flow ends (no successors)
• Supply: Outflow - Inflow > 0
• Demand: Outflow - Inflow < 0
• Transshipment: Outflow - Inflow = 0

Question 5

What is the objective in a minimum-cost flow problem?

Answer 5

To minimize the total cost of flow from sources to sinks.

• Subject to capacity constraints and flow conservation

Question 6

What is the feasibility condition for min-cost flow?

Answer 6

Sum of supplies = Sum of demands.

• Otherwise, there’s no feasible solution

Question 7

What is the integer solutions property for min-cost flow?

Answer 7

If all supplies, demands, and capacities are integer, then there is an optimal solution with integer flow values.

Question 8

Give the LP formulation (objective) for min-cost flow.

Answer 8

Minimize ∑_i ∑_j c_i,j x_i,j

• c_i,j: cost per unit flow
• x_i,j: flow on arc (i,j)

Question 9

What is the transportation problem?

Answer 9

Minimize total shipping cost from multiple origins to multiple destinations.

• Each origin has a supply
• Each destination has a demand

Question 10

What is the assignment problem?

Answer 10

Assign agents to tasks at minimum cost.

• Each agent performs exactly one task
• Each task is done by exactly one agent

Question 11

What is a transshipment problem?

Answer 11

An extension of the transportation problem with intermediate nodes.

• These nodes can both receive and send flow

Question 12

What is the maximum flow problem?

Answer 12

Maximize the amount of flow from a single source to a single sink.

• Subject to arc capacities

Question 13

What is the shortest path problem?

Answer 13

Find the path with minimum distance (or cost) from an origin to a destination.

• Often used for routing and travel

Question 14

List the basic supply chain models discussed. (Module 5)

Answer 14

• Transportation problem
• Assignment problem
• Transshipment problem
• Maximum flow problem
• Shortest path problem

Question 15

What is a hub-and-spoke network?

Answer 15

A design where flows go through central hubs.

• Reduces the number of direct routes
• Increases efficiency and frequency