3. Operations Research

Dynamic Programming — Quiz

Test your understanding of dynamic programming with 5 practice questions.

Practice Questions

Question 1

In the context of dynamic programming, what is the primary distinction between a 'deterministic' and a 'stochastic' dynamic programming problem?

Question 2

Consider an inventory control problem where the objective is to minimize total costs over $N$ periods. The costs include ordering, holding, and shortage costs. If $f_t(I_t)$ is the minimum total cost from period $t$ to $N$ given an initial inventory $I_t$, and $x_t$ is the quantity ordered in period $t$, which of the following represents a valid recurrence relation for this problem?

Question 3

In a sequential decision-making problem, if the decision at each stage depends only on the current state and not on the sequence of decisions that led to that state, which property of dynamic programming is being satisfied?

Question 4

When applying dynamic programming to a resource allocation problem, if $f_n(x)$ represents the maximum return from allocating $x$ units of resource among $n$ stages, and $r_i(y)$ is the return from allocating $y$ units to stage $i$, which of the following recurrence relations is most appropriate for a backward recursion approach?

Question 5

In an inventory control problem, if $I_t$ is the inventory level at the beginning of period $t$, $d_t$ is the demand in period $t$, and $x_t$ is the quantity ordered in period $t$, which of the following expressions correctly represents the inventory level at the beginning of period $t+1$ after meeting demand and considering production $x_t$?