- Choose the correct alternative.
The first step in dynamic programming is to
(a)Define the nodes.
(b)Determine the optimal policy.
(c)Define the recursive relationship.
(d)Divide the given problem in to stages.
- Mark the correct statement:
(a)Dynamic programming is a technique that can be used to solve any complex problem.
(b)Dynamic programming uses a set of well-defined rules for solving all problems.
(c)Dynamic programming divides a problem into a number of decision stages.
(d)Dynamic programming deals only with deterministic decision-making problems.
- Mark the correct statement.
(a)Sub-problems of a given problem are called variables.
(b)In dynamic programming, solution to each sub-problem is obtained independently.
(c)Dynamic programming calls for standard mathematical formulation of a problem.
(d)Dynamic programming provides for a systematic procedure for determining optimal combination of decisions.
- Mark the incorrect statement.
(a)Dynamic programming cannot be used for solving problems that call for distributing scarce resources.
(b)Dynamic programming calls for dissecting a problem into a sequence of sub-problems.
(c)Dynamic programming provides a generalised approach to problem solving.
(d)Dynamic programming provides a multi-stage approach to solving problems.
- Mark the wrong statement.
(a)Dynamic programming problems require making a sequence of interrelated decisions.
(b)A state represents a decision point.
(c)Depending upon the variable of interest, the solution to a dynamic programming problem calls for maximisation or minimisation of the pay-off.
(d)Pay-off is also called the reward.
- Mark the wrong statement.
(a)The effect of a policy decision at each stage is to transform the current state to a state associated with the beginning of the previous stage.
(b)Determination of optimal policy at a given state requires calculation of immediate and total pay-offs.
(c)The best of all the (total) pay-offs in respect of different states of a stage is known as the optimal pay-off.
(d)Optimal policy for the entire problem consists of determining optimal policy at each stage for each state.
- Mark the wrong statement.
(a)Dynamic programming may be deterministic or probabilistic.
(b)In a dynamic programming problem, the state at the next stage is determined by the state and policy decision of the current stage.
(c)In a probabilistic dynamic programming problem, the next stage is not sure and there is a probability distribution of what the next stage would be.
(d)In probabilistic dynamic programming problems, the optimal policy at a given stage is based on expected the pay-offs.
- Mark the wrong statement.
(a)States of a given stage represent the possible conditions in which the system might be in that particular stage.
(b)A probabilistic dynamic programming problem is so called because states of various stages are not clearly defined.
(c)Given the current state, the optimal policy for the remaining stages does not depend on the policy decisions adopted in the previous stages.
(d)The optimal immediate decision depends only on the current state, and not how we got there.
- Mark the wrong statement.
(a)The recursive relationship establishes relationship between different states.
(b)Creation of a recursive relationship is an integral part of the formulation of a dynamic programming problem.
(c)A recursive relationship identifies the optimal policy for stage n, given that optimal policy for stage n+1 is available.
(d)In dynamic programming, it is possible to develop a recursive relationship for every problem.
- Mark the wrong statement.
(a)Moving forward from the first stage to the last is the final step in dynamic programming problem solution.
(b)In an investment problem, addition of a new investment proposal adds a new state.
(c)In dynamic programming, it is possible to get second-best solution as well as the best (optimal) solution.
(d)fn*(sn) represents the optimal pay-off at stage n, for state sn.