## 28 Questions

What is the goal of the formulation described in the text?

Minimize the cost of satisfying demand

In the context of the formulation, what do the constraints (7b) represent?

Flow balance equations

What does the notation ∑𝑗∶(𝑖,𝑗)∈𝐴 represent in the text?

Summing over all nodes 𝑗 such that the arc (𝑖, 𝑗) belongs to 𝐴

What is the role of 𝑙𝑖𝑗 and 𝑢𝑖𝑗 in the formulation?

They represent lower and upper bounds for flow on each arc

What is the significance of the notation ⎧> 0, { 𝑏𝑖 is ⎨< 0, {= 0, ⎩ if supply node, if demand node, if transshipment node?

It indicates whether a node is a supply, demand, or transshipment node

What does the objective function (7a) aim to minimize in the formulation?

Cost of satisfying demand

In the context of the formulation, what does 𝑐𝑖𝑗 represent?

Cost of each arc

Which term is used to collectively refer to the constraints (7b) in the context of the formulation?

"Flow balance equations/constraints"

What does the notation ∑ 𝑥𝑖𝑗 − ∑ 𝑥𝑗𝑖 = 𝑏𝑖 , ∀𝑖 ∈ 𝑉 in constraint (7b) represent?

Flow balance equations

What problem type does the above formulation represent?

Minimum Cost Network Flow (MCNF) problem

Which type of problems can be solved as LPs and will produce integer optimal solutions?

Shortest path and max flow problems

What happens to the MCNF structure if additional constraints or variables are added that break the structure?

It no longer has the special LP property

In which type of problems is it obvious that they can be written with a source node 𝑠 and sink nodes 𝑡?

Shortest path and max flow problems

What is the main idea behind the illustration in Figure 23?

To demonstrate how to convert the transportation problem to have a source and sink

What do all red arcs with cost 𝑐𝑖𝑗 = 0 represent in the context of the text?

Main transportation routes

What does it mean for a supply node if 𝑏𝑖 is ⎧> 0?

It means the supply node has excess inventory

What type of problems are covered in MCNF problems?

Network flow problems

What do the constraints (7b) represent in the context of the formulation?

Capacity constraints

What is the role of the 'capacity' attribute in the function maximum_flow?

To identify the attribute representing the capacity of the graph's arcs

What is the main goal of solving the shortest path problem?

To minimize the distance between the source and target vertex

In the context of the formulation, what does 𝑐𝑖𝑗 represent?

The cost associated with arc (i, j)

What type of problems are covered in MCNF problems?

Minimum Cost Network Flow problems

What happens to the MCNF structure if additional constraints or variables are added that break the structure?

It becomes infeasible to solve

What does it mean for a supply node if 𝑏𝑖 is ⎧> 0?

The node has excess supply that needs to be distributed

Which term is used to collectively refer to the constraints (7b) in the context of the formulation?

Flow conservation constraints

What do all red arcs with cost 𝑐𝑖𝑗 = 0 represent in the context of the text?

Optimal paths with no cost associated

What is the significance of the notation ⎧> 0, { 𝑏𝑖 is ⎨< 0, {= 0, ⎩ if supply node, if demand node, if transshipment node?

It determines whether nodes are source, sink, or transshipment points

What does the notation ∑𝑗∶(𝑖,𝑗)∈𝐴 represent in the text?

The sum of costs for all arcs connected to node i

This quiz covers the bus route assignment problem in logistics and transportation systems, focusing on the allocation of drivers to specific routes based on duration and vertices. It involves formulating the problem and understanding the network sketch for bus route assignment example.

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