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