Dynamic Programming

This technique deals with the problems that arise in connection with multi period analysis and decisions. In contrast to Linear Programming there does not exist a standard mathematical formulation of Dynamic Programming rather it is a general type of approach to problem solving and a particular equation used in use  be developed to fit each individual situation. However the basic approach used in Dynamic Programming is to break down a problem into a series of problems in such a way that answer to the first sub problem can be used in deriving the solution to the next sub-problem and so forth finally giving solution to the whole  problem.

            This technique relies on the principle of optimality formulated by Richard Bellman. " An optimal policy (set of decisions) has the property that whatever the initial state and initial decisions are the remaining decisions must constitute an optimal policy with respect to the state resulting from the first decision"Dynamic Programming - An Operation Research Technique

Dynamic programming deals with the problems that arise in connection with multiperiod analysis and decision. In contrast to linear programming there does not exist a standard mathematical formulation of dynamic programming, rather it is general type of approach to problem solving and a particular equation used must be developed to fit each individual situation. However the basic approach used in dynamic programming is to break down into a series of problems in such a way that answers the first sub problem can be used in deriving the solution to the next sub problem and so forth finally giving solution to whole problem. This technique relies on the principle of optimality formulated by Richard Bellman. An optimal policy also called set of decisions has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with respect to the state resulting from the first decision.

Thus in computer science and mathematics, dynamic programming is a method to solve complex problems by breaking down them into simpler sub parts and problems. Dynamic programming is applicable to problems exhibiting the properties of overlapping sub problems which are only slightly smaller and optimal substructure.

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