Mine
What is the constraint for node 2 in the following shortest path problem?
-X12 + X24 = 0
The right hand side value for the starting node in a shortest path problem has a value of
-1
An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3 (Refinery 1)?
.80 X 13 + .95 X 23 - X 35 - X 36 - X 37 = 0
Continue with question 22, What is the balance of flow constraint for node 7 (Diesel)?
.90 X 37 + .95 X 47 = 75
The right hand side value for the ending node in a shortest path problem has a value of
1
Consider the equipment replacement problem presented in the chapter. Recall that in the network model formulation of this problem a node represents a year when the equipment was purchased. An arc from node i to node j indicates that the equipment purchased in year i can be replaced at the beginning of year j. How could the network model below be modified to depict an equipment purchase in year 4 and operating costs only through the remainder of the planning window?
Add a dummy node, 6, so that arc 4-6 represents just the operating costs.
If a side constraint for a network flow model cannot be avoided, and non-integer solutions result, how can the solution be expressed as an integer solution?
Force all the arc flow decision variables to be integer.
What is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?
Indicates unmet demand at demand nodes
Which balance of flow rule should be applied at each node in a network flow problem when Total Supply > Total Demand?
Inflow - Outflow >= Supply or Demand
What is the objective function for the following shortest path problem?
MIN 50 X 12 + 200 X 13 + 100 X 24 + 35 X 34
Which formula should be used to determine the Net Flow values in cell K6 in the following spread- sheet model?
SUMIF($E$6:$E$16,I6,$B$6:$B$16) - SUMIF($C$6:$C$16,I6,$B$6:$B$16)
Consider modeling a warehouse with three inflow arcs and three outflow arcs. The warehouse node is a transshipment node but has a capacity of 100. How would one modify the network model to avoid adding a side constraint that limits either the sum of inflows or the sum of the outflows to 100?
Separate the warehouse node into two nodes, connected by a single arc, with capacity of 100.
What happens to the solution of a network flow model if side constraints are added that do not obey the balance of flow rules?
The model solution is not guaranteed to be integer.
When might a network flow model for a transportation/assignment problem be preferable to a matrix form for the problem?
When the problem is large and not fully connected.
In generalized network flow problems 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.
all of these
Decision variables in network flow problems are represented by
arcs
A maximal flow problem differs from other network models in which way?
arcs have limited capacity
Maximal flow problems are converted to transshipment problems by
connecting the supply and demand nodes with a return arc
The arcs in a network indicate all of the following except? routes paths constraints connections
constraints
A network flow problem that allows gains or losses along the arcs is called a
generalized network flow model.
Which property of network flow models guarantees integer solutions?
integer objective function coefficients
Which method is preferred for solving fully connected transportation problems?
linear programming
How many constraints are there in a transshipment problem which has n nodes and m arcs?
n
The number of constraints in network flow problems is determined by the number of
nodes
The street intersections in a city road network represent
nodes.
