Question 1

A node which can both send to and receive from other nodes is a

Accepted Answer

A)  demand node. 
B)  supply node. 
C)  random node. 
D)  transshipment node. 
A)  demand node. 
B)  supply node. 
C)  random node. 
D)  transshipment node. D

Question 2

A railroad needs to move the maximum amount of material through its rail network. Formulate the LP model to determine this maximum amount based on the following network diagram.

Accepted Answer

$\text { MAX: } \quad X_{61}$

Subject to:
$
\begin{array}{ll}
X_{61}-X_{12}-X_{13}=0 & \
\mathrm{X}_{12}-\mathrm{X}_{25}=0 & \
\mathrm{X}_{13}-\mathrm{X}_{35}-\mathrm{X}_{34}=0 & \
\mathrm{X}_{34}-\mathrm{X}_{46}=0 & \
\mathrm{X}_{25}+\mathrm{X}_{35}-\mathrm{X}_{56}=0 & \
\mathrm{X}_{56}+\mathrm{X}_{46}-\mathrm{X}_{61}=0 & \
0 \leq \mathrm{X}_{12} \leq 5 & 0 \leq \mathrm{X}_{13} \leq 4 \
0 \leq \mathrm{X}_{25} \leq 6 & 0 \leq \mathrm{X}_{35} \leq 6 \
0 \leq \mathrm{X}_{34} \leq 6 & 0 \leq \mathrm{X}_{56} \leq 8 \
0 \leq \mathrm{X}_{46} \leq 2 & 0 \leq \mathrm{X}_{61} \leq \infty
\end{array}
$

Question 3

How many constraints are there in a transshipment problem which has n nodes and m arcs?

Accepted Answer

A)  n 
B)  m 
C)  n + m 
D)  m - n 
A)  n 
B)  m 
C)  n + m 
D)  m - n A

Question 4

The following network depicts a transportation/distribution problem for Clifton Distributing. Formulate the LP for Clifton assuming they wish to minimize the total product-miles incurred.

Accepted Answer

The answer of The following network depicts a transportation/distribution problem...

Question 5

Draw the network representation of this LP model. What type of problem is it?
 MAX $\quad $ $X_{41} $ 
Subject to:
$
\begin{array}{l}
\mathrm{X}_{41}-\mathrm{X}_{12}-\mathrm{X}_{13}=0 \
\mathrm{X}_{12}-\mathrm{X}_{24}=0 \
\mathrm{X}_{13}-\mathrm{X}_{34}=0 \
\mathrm{X}_{24}+\mathrm{X}_{34}-\mathrm{X}_{41}=0 \
0 \leq \mathrm{X}_{12} \leq 5 \
0 \leq X_{13} \leq 4 \
0 \leq X_{24} \leq 3 \
0 \leq X_{34} \leq 2 \
0 \leq X_{41} \leq \infty
\end{array}
$

Accepted Answer

It is a ma

Question 6

The minimal spanning tree solution algorithm works by defining a subnetwork and

Accepted Answer

A)  adding the least expensive arc which connects any node in the current subnetwork to any node not in the current subnetwork. 
B)  adding the most expensive arc which connects any node in the current subnetwork to any node not in the current subnetwork. 
C)  adding the least expensive arc which connects unconnected nodes in the current subnetwork. 
D)  adding the least expensive arc which connects the most recently added node in the current subnetwork to the closest node not in the current subnetwork. 
A)  adding the least expensive arc which connects any node in the current subnetwork to any node not in the current subnetwork. 
B)  adding the most expensive arc which connects any node in the current subnetwork to any node not in the current subnetwork. 
C)  adding the least expensive arc which connects unconnected nodes in the current subnetwork. 
D)  adding the least expensive arc which connects the most recently added node in the current subnetwork to the closest node not in the current subnetwork.

Question 7

A company needs to ship 100 units from Seattle to Denver at the lowest possible cost. The costs associated with shipping between the cities are:
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\underline{\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad To\quad\quad\quad\quad\quad}}$
$\begin{array}{lcccc}
\text { From } & \text { Portland } & \text { Spokane } & \text { Salt Lake City } & \text { Denver } \
\hline \text { Seattle } & 100 & 500 & 600 & - \
\text { Portland } & - & 350 & 300 & - \
\text { Spokane } & - & - & 250 & 200 \
\text { Salt Lake City } & - & - & - & 200
\end{array}$
 What values should go into cells G6:L13 in the following Excel spreadsheet?

Accepted Answer

The answer of A company needs to ship 100 units...

Question 8

In generalized network flow problems

Accepted Answer

A)  solutions may not be integer values. 
B)  flows along arcs may increase or decrease. 
C)  it can be difficult to tell if total supply is adequate to meet total demand. 
D)  all of these. 
A)  solutions may not be integer values. 
B)  flows along arcs may increase or decrease. 
C)  it can be difficult to tell if total supply is adequate to meet total demand. 
D)  all of these.

Question 9

A company wants to manage its distribution network which is depicted below. Identify the supply, demand and transshipment nodes in this problem.

Accepted Answer

The answer of A company wants to manage its distribution...

Question 10

If a side constraint for a network flow model cannot be avoided, and non-integer solutions result, how can the solution be expressed as an integer solution?

Accepted Answer

A)  Force all the arc flow decision variables to be integer. 
B)  Round off all the non-integer arc flow decision variables. 
C)  Increase the supply until the solutions are all integer using a dummy supply node. 
D)  Increase the demand until the solutions are all integer using a dummy demand node. 
A)  Force all the arc flow decision variables to be integer. 
B)  Round off all the non-integer arc flow decision variables. 
C)  Increase the supply until the solutions are all integer using a dummy supply node. 
D)  Increase the demand until the solutions are all integer using a dummy demand node.

Question 11

A maximal flow problem differs from other network models in which way?

Accepted Answer

A)  arcs are two directional 
B)  multiple supply nodes are used 
C)  arcs have limited capacity 
D)  arcs have unlimited capacity 
A)  arcs are two directional 
B)  multiple supply nodes are used 
C)  arcs have limited capacity 
D)  arcs have unlimited capacity

Question 12

Which balance of flow rule should be applied at each node in a network flow problem when Total Supply > Total Demand?

Accepted Answer

A)  Inflow - Outflow $\le$Supply or Demand 
B)  Inflow- Outflow$\ge$ Supply or Demand 
C)  Inflow - Outflow = Supply or Demand 
D)  Inflow- Supply $\ge$ Outflow or Demand 
A)  Inflow - Outflow $\le$Supply or Demand 
B)  Inflow- Outflow$\ge$ Supply or Demand 
C)  Inflow - Outflow = Supply or Demand 
D)  Inflow- Supply $\ge$ Outflow or Demand

Question 13

How could a network be modified if demand exceeds supply?

Accepted Answer

A)  add extra supply arcs 
B)  remove the extra demand arcs 
C)  add a dummy supply 
D)  add a dummy demand 
A)  add extra supply arcs 
B)  remove the extra demand arcs 
C)  add a dummy supply 
D)  add a dummy demand

Question 14

What is the correct constraint for node 2 in the following diagram?

Accepted Answer

A)  X12 + X23 = 100 
B)  X12 -X23 $\le$100 
C)  -X12 + X23 $\ge$ -100 
D)  X12 -X23 $\ge$100 
A)  X12 + X23 = 100 
B)  X12 -X23 $\le$100 
C)  -X12 + X23 $\ge$ -100 
D)  X12 -X23 $\ge$100

Question 15

The right hand side value for the ending node in a shortest path problem has a value of

Accepted Answer

A)  -1 
B)  0 
C)  1 
D)  2 
A)  -1 
B)  0 
C)  1 
D)  2

Question 16

What is the objective function for the following shortest path problem?

Accepted Answer

A)  -X12 - X13 = 0 
B)  MIN -50 X12-200 X13 + 100 X24 + 35 X34 
C)  MIN 50 X12 + 200 X13 + 100 X24 + 35 X34 
D)  MAX -50 X12 - 200 X13 + 100 X24 + 35 X34 
A)  -X12 - X13 = 0 
B)  MIN -50 X12-200 X13 + 100 X24 + 35 X34 
C)  MIN 50 X12 + 200 X13 + 100 X24 + 35 X34 
D)  MAX -50 X12 - 200 X13 + 100 X24 + 35 X34

Question 17

Clifton Distributing has three plants and four distribution centers. The plants, their supply, the distribution centers, their demands, and the distance between each location is summarized in the following table:
 $$\begin{array} { l c c c c c } 
\text { Distance } & \text { Center 1 } & \text { Center 2 } & \text { Center 3 } & \text { Center 4 } & \text { Supply } \
\hline \text { Plant A } & 45 & 60 & 53 & 75 & 500 \
\text { Plant B } & 81 & 27 & 49 & 62 & 700 \
\text { Plant C } & 55 & 40 & 35 & 60 & 650 \
\hline \text { Demand } & 350 & 325 & 400 & 375 &
\end{array}$$ Draw the transportation network for Clifton's distribution problem.

Accepted Answer

The answer of Clifton Distributing has three plants and four...

Question 18

A company needs to ship 100 units from Seattle to Denver at the lowest possible cost. The costs associated with shipping between the cities are listed below. Also, the decision variable associated with each pair of cities is shown next to the cost.
 $$\begin{array}{l}
\text { Ta }\
\begin{array} { l c c c c } 
\text { From } & \text { Portland } & \text { Spokane } & \text { Salt Lake City } & \text { Denver } \
\hline \text { Seattle } & 100 \left( X _ { 12 } )\right. & 500 \left( X _ { 13 } \right) & 600 \left( X _ { 14 } \right) & - \
\text { Portland } & - & 350 \left( X _ { 23 } \right) & 300 \left( X _ { 24 } \right) & - \
\text { Spokane } & - & - & 250 \left( X _ { 34 } \right) & 200 \left( X _ { 35 } \right) \
\text { Salt Lake City } & - & - & - & 200 \left( X _ { 45 } \right)
\end{array}
\end{array}$$ Write out the LP formulation for this problem.

Accepted Answer

The answer of A company needs to ship 100 units...

Question 19

Solve the following minimal spanning tree problem starting at node 1.

Accepted Answer

The answer of Solve the following minimal spanning tree problem...

Question 20

What is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?

Accepted Answer

A)  Indicates unmet demand at demand nodes 
B)  Indicates unmet supply at demand nodes 
C)  Indicates unmet demand at supply nodes 
D)  Indicates unmet supply at supply nodes 
A)  Indicates unmet demand at demand nodes 
B)  Indicates unmet supply at demand nodes 
C)  Indicates unmet demand at supply nodes 
D)  Indicates unmet supply at supply nodes

A node which can both send to and receive from other nodes is a

A railroad needs to move the maximum amount of material through its rail network. Formulate the LP model to determine this maximum amount based on the following network diagram.

How many constraints are there in a transshipment problem which has n nodes and m arcs?

The following network depicts a transportation/distribution problem for Clifton Distributing. Formulate the LP for Clifton assuming they wish to minimize the total product-miles incurred.

Draw the network representation of this LP model. What type of problem is it? MAX $\quad$ $X_{41}$ Subject to: --=0 -=0 -=0 +-=0 0\leq\leq5 0\leq\leq4 0\leq\leq3 0\leq\leq2 0\leq\leq\infty

The minimal spanning tree solution algorithm works by defining a subnetwork and

In generalized network flow problems

A company wants to manage its distribution network which is depicted below. Identify the supply, demand and transshipment nodes in this problem.

If a side constraint for a network flow model cannot be avoided, and non-integer solutions result, how can the solution be expressed as an integer solution?

A maximal flow problem differs from other network models in which way?

Which balance of flow rule should be applied at each node in a network flow problem when Total Supply > Total Demand?

How could a network be modified if demand exceeds supply?

What is the correct constraint for node 2 in the following diagram?

The right hand side value for the ending node in a shortest path problem has a value of

What is the objective function for the following shortest path problem?

Solve the following minimal spanning tree problem starting at node 1.

What is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

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Exam 5: Network Modeling

A node which can both send to and receive from other nodes is a

A railroad needs to move the maximum amount of material through its rail network. Formulate the LP model to determine this maximum amount based on the following network diagram.

How many constraints are there in a transshipment problem which has n nodes and m arcs?

The following network depicts a transportation/distribution problem for Clifton Distributing. Formulate the LP for Clifton assuming they wish to minimize the total product-miles incurred.

Draw the network representation of this LP model. What type of problem is it? MAX \quad X41X_{41} X41​ Subject to: --=0 -=0 -=0 +-=0 0\leq\leq5 0\leq\leq4 0\leq\leq3 0\leq\leq2 0\leq\leq\infty

The minimal spanning tree solution algorithm works by defining a subnetwork and

In generalized network flow problems

A company wants to manage its distribution network which is depicted below. Identify the supply, demand and transshipment nodes in this problem.

If a side constraint for a network flow model cannot be avoided, and non-integer solutions result, how can the solution be expressed as an integer solution?

A maximal flow problem differs from other network models in which way?

Which balance of flow rule should be applied at each node in a network flow problem when Total Supply > Total Demand?

How could a network be modified if demand exceeds supply?

What is the correct constraint for node 2 in the following diagram?

The right hand side value for the ending node in a shortest path problem has a value of

What is the objective function for the following shortest path problem?

Solve the following minimal spanning tree problem starting at node 1.

What is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Draw the network representation of this LP model. What type of problem is it? MAX $\quad$ $X_{41}$ Subject to: --=0 -=0 -=0 +-=0 0\leq\leq5 0\leq\leq4 0\leq\leq3 0\leq\leq2 0\leq\leq\infty