Week 4 quiz

1.Decision variables in network flow problems are represented by:

a) arcs

b) nodes

c) demands

d) supplies

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

a) transshipment node

b) demand node

c) random node

d) supply node

3.The problem which deals with the distribution of goods from several sources to several destinations is the:

a) assignment problem

b) maximal flow problem

c) shortest-route problem

d) transportation problem

4. The assignment problem is a special case of the:

a) transportation problem

b) transshipment problem

c) maximal flow problem

d) shortest-route problem

5. The objective of the transportation problem is to:

a) Minimize the cost of shipping products from several origins to several destinations.

b) Minimize the total number of origins to satisfy total demand at the destinations.

c) Minimize the number of shipments necessary to satisfy total demand at destination.

d) Identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping costs.

6. The parts of a network that represent the origins are:

a) the capacities

b) the flows

c) the nodes

d) the arcs

7. Arcs in the transshipment problem:

a) must connect every node to the transshipment node

b) represent the cost of shipments

c) indicate the direction of flow

d) All of the alternatives are correct

8. If the transportation problem has 4 origins and 5 destinations, the LP formulation of the problem will have:

a) 18 constraints

b) 5 constraints

c) 20

d) 9

9. Maximal flow problem differs from the other network models in which way:

a) Arcs have unlimited capacity

b) Multiple supply nodes are usual

c) Arcs have limited capacity

d) Arcs are two directions

10. Maximal flow problem are converted to transshipment problems by:

a) Adding extra supply nodes

b) Adding supply limits on supply nodes

c) requiring integer solutions

d) Connecting the supply and demand nodes with the return arc

11. The objective value function for the ILP problem can never:

a) Be better than the optimal solution to its LP relaxation

b) Be as poor as the optimal solution to its LP relaxation

c) Be as good as theoptimal solution to its LP relaxation

d) Be as worse than the optimal solution to its LP relaxation

12. For minimization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem.

a) An additional constraint for the ILP

b) An upper bound

c) An alternative optimal solution

d) A lower bound

13. In the model X1 >= 0 and integer, X2 >= 0, and X3>= 0,1. (All the numbers in the question answers are small and in the lower right corner of the X)

a) X1=2, X2=3, X3=.578

b) X1= 5, X2=3 , X3= 0

c) .X1=0, X2= 8, X3= 0

d) X1=4, X2= 389, X3=1.

14. Rounding the solution of an LP relaxation integer to the nearest integer value provides:

a) An infeasible solution

b) An integer solution that might neither be feasible nor optimal

c) A feasible but not necessarily optimal integer

d) An integer solution that is optimal.

15. The solution the LP relaxation of a maximization integer linear programming involves:

a) An upper bound for the value of an objective function

b) A lower bound for the value of an objective function

c) An upper bound for the value of a decision variables

d) A lower bound for the value of a decision variable

16. Sensitivity analysis for the integer linear programming:

a) Can be provided only by computer

b) Does not have the same interpretation and should be disregarded

c) Has precisely the same interpretation as that from linear programming

d) Is most useful for 0-1 models

17. Let X1, X2, and X3 be 0-1 variables whose values indicates whether the projects are not done (0) or are done (1). Which answer below indicates that at least two of the projects? (All the numbers in the question answers are small and in the lower right corner of the X)

a) X1-X2=0

b) X1+X2+X3=2

c) X1+X2+X3<=2

d) X1+X2+X3>=2

18. In an all-integer linear program:

a) All objective functions coefficients must be integer

b) All objective functions coefficients and right hand side value must be integer

c) All variables must be integer

d) All right hand side values must be integer

19. How is an LP problem change into an ILP problem?

a) By adding constraints that the decision variables be non-negative

b) By adding integrality conditions

c) By making right hand side value integer

d) By adding discontinuity constraints

20. The constraint X1+X2+X3+X4<= 2 means that 2 two out of the first four projects must be selected: (all the numbers in the question answers are small and in the lower right corner of the X)

a) True

b) False

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