Deck 21: Dynamic Programming

Question 1

In solving a shortest route problem using dynamic programming the stages represent how many arcs you are from the terminal node.

Answer 1

True

Question 2

Dynamic programming is a general approach with stage decision problems differing substantially from application to application.

Answer 2

True

Question 3

If x₃ = t₄(x₄,d₄) = x₄ ? 2d₄ and r₄(x₄,d₄) = 16d₄, the stage transformation function is

A)t
B)x
C)r
D)d

Answer 3

A

Question 4

The solution of stage k of a dynamic programming problem is dependent upon the solution of stage k?1.

Question 5

A return function is a value such as profit or loss associated with making decision d_n at:

A)stage n for specific value of output variable x_n.
B)stage n for a specific value of input variable x_n.
C)stage n for a specific value of stage m.
D)input n for a specific value of output variable x_n.

Question 6

State variables in a shortest route problem represent

A)decisions.
B)locations in the network.
C)the minimum distance between nodes.
D)None of the alternatives is true.

Question 7

Dynamic programming is a general approach rather than a specific technique.

Question 8

The output of stage k is the input for stage k?1.

Question 9

Stages of a dynamic programming solution procedure

A)represent parts of a large mathematical model.
B)often represent a sequence of decisions made over time.
C)are usually not independent of each other.
D)All of the alternatives are true.

Question 10

Dynamic programming requires that its subproblems be independent of one another.

Question 11

State variables are a function of a state variable and a decision.

Question 12

The stage transformation function

A)transforms the input into the output.
B)transforms a stage into a state.
C)is a different function for each stage.
D)None of the alternatives is true.

Question 13

Stage transformation functions

A)are linear.
B)calculate the return.
C)determine the output of the stage.
D)All of the alternatives are true.

Question 14

Dynamic programming, when used for the shortest route problem, requires complete enumeration of paths from the beginning to ending node.

Question 15

Dynamic programming must only involve a finite number of decision alternatives and a finite number of stages.

Question 16

The return function for a shortest route problem refers to two directional arcs between nodes.

Question 17

The knapsack problem is to determine how many units of each item to place in the knapsack to:

A)minimize total value.
B)maximize total value.
C)minimize the number of items in the knapsack.
D)maximize the number of items in the knapsack.

Question 18

If x₃ = t₄(x₄,d₄) = x₄ ? 2d₄ and r₄(x₄,d₄) = 16d₄, the subscripts refer to

A)state.
B)stage.
C)transformation.
D)return.

Question 19

If x₃ = t₄ (x₄,d₄) = x₄ ? 2d₄ and r₄(x₄,d₄) = 16d₄ the state variable is

A)t
B)x
C)r
D)d