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Questions and Answers
What is the goal of the formulation described in the text?
What is the goal of the formulation described in the text?
- Minimize the flow on each arc
- Maximize the flow on each arc
- Minimize the cost of satisfying demand (correct)
- Maximize the cost of satisfying demand
In the context of the formulation, what do the constraints (7b) represent?
In the context of the formulation, what do the constraints (7b) represent?
- Maximum flow on each arc
- Minimum flow on each arc
- Flow balance equations (correct)
- Cost of each arc
What does the notation ∑𝑗∶(𝑖,𝑗)∈𝐴 represent in the text?
What does the notation ∑𝑗∶(𝑖,𝑗)∈𝐴 represent in the text?
- Summing over all arcs entering node 𝑖
- Summing over all nodes 𝑗 such that the arc (𝑖, 𝑗) belongs to 𝐴 (correct)
- Summing over all arcs in the graph
- Summing over all arcs leaving node 𝑗
What is the role of 𝑙𝑖𝑗 and 𝑢𝑖𝑗 in the formulation?
What is the role of 𝑙𝑖𝑗 and 𝑢𝑖𝑗 in the formulation?
What is the significance of the notation ⎧> 0, { 𝑏𝑖 is ⎨< 0, {= 0, ⎩ if supply node, if demand node, if transshipment node?
What is the significance of the notation ⎧> 0, { 𝑏𝑖 is ⎨< 0, {= 0, ⎩ if supply node, if demand node, if transshipment node?
What does the objective function (7a) aim to minimize in the formulation?
What does the objective function (7a) aim to minimize in the formulation?
In the context of the formulation, what does 𝑐𝑖𝑗 represent?
In the context of the formulation, what does 𝑐𝑖𝑗 represent?
Which term is used to collectively refer to the constraints (7b) in the context of the formulation?
Which term is used to collectively refer to the constraints (7b) in the context of the formulation?
What does the notation ∑ 𝑥𝑖𝑗 − ∑ 𝑥𝑗𝑖 = 𝑏𝑖 , ∀𝑖 ∈ 𝑉 in constraint (7b) represent?
What does the notation ∑ 𝑥𝑖𝑗 − ∑ 𝑥𝑗𝑖 = 𝑏𝑖 , ∀𝑖 ∈ 𝑉 in constraint (7b) represent?
What problem type does the above formulation represent?
What problem type does the above formulation represent?
Which type of problems can be solved as LPs and will produce integer optimal solutions?
Which type of problems can be solved as LPs and will produce integer optimal solutions?
What happens to the MCNF structure if additional constraints or variables are added that break the structure?
What happens to the MCNF structure if additional constraints or variables are added that break the structure?
In which type of problems is it obvious that they can be written with a source node 𝑠 and sink nodes 𝑡?
In which type of problems is it obvious that they can be written with a source node 𝑠 and sink nodes 𝑡?
What is the main idea behind the illustration in Figure 23?
What is the main idea behind the illustration in Figure 23?
What do all red arcs with cost 𝑐𝑖𝑗 = 0 represent in the context of the text?
What do all red arcs with cost 𝑐𝑖𝑗 = 0 represent in the context of the text?
What does it mean for a supply node if 𝑏𝑖 is ⎧> 0?
What does it mean for a supply node if 𝑏𝑖 is ⎧> 0?
What type of problems are covered in MCNF problems?
What type of problems are covered in MCNF problems?
What do the constraints (7b) represent in the context of the formulation?
What do the constraints (7b) represent in the context of the formulation?
What is the role of the 'capacity' attribute in the function maximum_flow?
What is the role of the 'capacity' attribute in the function maximum_flow?
What is the main goal of solving the shortest path problem?
What is the main goal of solving the shortest path problem?
In the context of the formulation, what does 𝑐𝑖𝑗 represent?
In the context of the formulation, what does 𝑐𝑖𝑗 represent?
What type of problems are covered in MCNF problems?
What type of problems are covered in MCNF problems?
What happens to the MCNF structure if additional constraints or variables are added that break the structure?
What happens to the MCNF structure if additional constraints or variables are added that break the structure?
What does it mean for a supply node if 𝑏𝑖 is ⎧> 0?
What does it mean for a supply node if 𝑏𝑖 is ⎧> 0?
Which term is used to collectively refer to the constraints (7b) in the context of the formulation?
Which term is used to collectively refer to the constraints (7b) in the context of the formulation?
What do all red arcs with cost 𝑐𝑖𝑗 = 0 represent in the context of the text?
What do all red arcs with cost 𝑐𝑖𝑗 = 0 represent in the context of the text?
What is the significance of the notation ⎧> 0, { 𝑏𝑖 is ⎨< 0, {= 0, ⎩ if supply node, if demand node, if transshipment node?
What is the significance of the notation ⎧> 0, { 𝑏𝑖 is ⎨< 0, {= 0, ⎩ if supply node, if demand node, if transshipment node?
What does the notation ∑𝑗∶(𝑖,𝑗)∈𝐴 represent in the text?
What does the notation ∑𝑗∶(𝑖,𝑗)∈𝐴 represent in the text?
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