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In a transshipment problem, which of the following statements is a correct representation of the balance-of-flow rule if Total Supply < Total Demand?


A) Inflow ≥\ge Outflow ≥\ge Supply or Demand
B) Inflow + Outflow ≥\ge Supply or Demand
C) Inflow ≤\le Outflow ≤\le Supply or Demand
D) Inflow + Outflow ≤\le Supply or Demand

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A company wants to determine the optimal replacement policy for its photocopier. The company does not keep photocopiers longer than 4 years. The company has estimated the annual costs for photocopiers during each of the 4 years and developed the following network representation of the problem. Write out the LP formulation for this problem. A company wants to determine the optimal replacement policy for its photocopier. The company does not keep photocopiers longer than 4 years. The company has estimated the annual costs for photocopiers during each of the 4 years and developed the following network representation of the problem. Write out the LP formulation for this problem.

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How many arcs are required to make a spanning tree in a network with n nodes and m arcs?


A) n
B) n -1
C) m
D) m - 1

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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: 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: What values should go into cells G6:L13 in the following Excel spreadsheet? What values should go into cells G6:L13 in the following Excel spreadsheet? 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: What values should go into cells G6:L13 in the following Excel spreadsheet?

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When might a network flow model for a transportation/assignment problem be preferable to a matrix form for the problem?


A) When an integer solution is required.
B) When the problem is large and not fully connected.
C) When the problem is large and fully connected.
D) When supply exceeds demand.

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

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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. 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.

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The following network depicts an assignment/transportation problem for Joe Fix's repair scheduling problem. Formulate the LP for Joe assuming he wishes to maximize the total repairperson to plane assignment preferences. The following network depicts an assignment/transportation problem for Joe Fix's repair scheduling problem. Formulate the LP for Joe assuming he wishes to maximize the total repairperson to plane assignment preferences.

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Draw the network representation of this LP model. What type of problem is it? Draw the network representation of this LP model. What type of problem is it?

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The constraint X13 + X23 -X34 ≥\ge 50 indicates that


A) 50 units are required at node 3.
B) 50 units will be shipped from node 3.
C) 50 units will be shipped in from node 1.
D) 50 units must pass through node 3.

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A company needs to ship 100 units from Roanoke to Washington at the lowest possible cost. The costs associated with shipping between the cities are: A company needs to ship 100 units from Roanoke to Washington at the lowest possible cost. The costs associated with shipping between the cities are: Draw the network representation of this problem. Draw the network representation of this problem.

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What is the constraint for node 2 in the following shortest path problem? What is the constraint for node 2 in the following shortest path problem? A) -X<sub>12</sub>-X<sub>13</sub> = 0 B) -X<sub>12</sub>-X<sub>24</sub> = 1 C) X<sub>12</sub> + X<sub>13</sub> = 0 D) -X<sub>12</sub> + X<sub>24</sub> = 0


A) -X12-X13 = 0
B) -X12-X24 = 1
C) X12 + X13 = 0
D) -X12 + X24 = 0

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Maximal flow problems are converted to transshipment problems by


A) connecting the supply and demand nodes with a return arc
B) adding extra supply nodes
C) adding supply limits on the supply nodes
D) requiring integer solutions

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What is the objective function in the following maximal flow problem? What is the objective function in the following maximal flow problem? A) MIN X<sub>41</sub> B) MAX X<sub>12</sub> + X<sub>13</sub> C) MAX X<sub>14</sub> D) MAX X<sub>41</sub>


A) MIN X41
B) MAX X12 + X13
C) MAX X14
D) MAX X41

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D

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


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

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Which property of network flow models guarantees integer solutions?


A) linear constraints and balance of flow equation format
B) linear objective function coefficients
C) integer objective function coefficients
D) integer constraint RHS values and balance of flow equation format

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D

Which formula should be used to determine the Net Flow values in cell K6 in the following spreadsheet model? Which formula should be used to determine the Net Flow values in cell K6 in the following spreadsheet model? A) SUMIF($C$6:$C$16,I6,$B$6:$B$16) -SUMIF($E$6:$E$16,I6,$B$6:$B$16) B) SUMIF($I$6:$I$12,B6,$B$6:$B$16) -SUMIF($I$6:$I$12,I6,$B$6:$B$16) C) SUMIF($E$6:$E$16,I6,$B$6:$B$16) -SUMIF($C$6:$C$16,I6,$B$6:$B$16) D) SUMPRODUCT(B6:B16,G6:G16)


A) SUMIF($C$6:$C$16,I6,$B$6:$B$16) -SUMIF($E$6:$E$16,I6,$B$6:$B$16)
B) SUMIF($I$6:$I$12,B6,$B$6:$B$16) -SUMIF($I$6:$I$12,I6,$B$6:$B$16)
C) SUMIF($E$6:$E$16,I6,$B$6:$B$16) -SUMIF($C$6:$C$16,I6,$B$6:$B$16)
D) SUMPRODUCT(B6:B16,G6:G16)

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


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

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


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

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Supply quantities for supply nodes in a transshipment problem are customarily indicated by


A) positive numbers.
B) negative numbers.
C) imaginary numbers.
D) either positive or negative numbers.

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