Dynamic programming: It is a mathematical technique dealing with the optimization of multistage decision process. The word ‘programming’ has been used in the mathematical sense of selecting an optimum allocation of resources and ‘dynamic’ is particular useful for problems where decisions are taken at several distinct stages such as everyday or every weak. Dynamic programming is a technique for solving large complex problem (time varying variables) by splitting them into smaller problems, which are more easily solved.
Applications The following are a few of the large no of fields in which dynamics programming has been successfully applied:.
1. Production
2. Inventory control
3. Allocation of resources
4. Selection of advertising media
5. Spare part level determination
6. Equipment replacement policy.
PRINCIPLE OF OPTIMALITY:This principle implies that a wrong decision taken at one stage does not prevent from taking the optimum decision for the remaining stages.An optimal policy has the property that whatever the initial state and decision are,the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.
essential characteristics of dynamic programming
1. The problem can be divided into stages, with a policy decision required at eacfi stage.
2. Each stage has a number of states associated with it.
3. The effect of the policy decision at each stage is to transform the current state into a state associated with next stage.
4. Given the current stage, an optimal policy for remaining stages is independent of the policy adopted in the pervious stages.
5. The solution procedure begins by finding an optimum policy for each state of the last stage.
6. A functional equation is available which identifies the optimal policy for each state with (n —1) stages left.
7. Using this function4l equation, the solution procedure moves backward stage by stage, each time finding the policy when starting at initial stage.
Distinguish between linear programming and dynamic programming
Linear programming models assume that data do not change were the time It is one time decision process and assumes average values of the decision variables Other important limitation of linear programming is that it assumes that data to be known with certainty.
Dynamic programming can be used to determine optimal strategies, by taking into account the uncertainties and can analyze multiperiod and multistage problems. In other words the technique is free from the limitation of linear programming. But it can be used to tackle very simple situations involving a few variables. If the no. of variable is larger the computation took becomes quite complex and involved. Moreover linear programming has standard ways to formulate the problems and solve them; there is no standard approach in dynamic programming. It is on the other hand a general way of solving large, complex problem by splitting them into smaller problems, which are more easily solved.
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