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Dynamic Programming solved problem - Single multiplicative constraint additively Seprable

Dynamic programming solved example
Dynamic Programming solved problem -Single multiplicative constraint additively separable return
Dynamic Programming in Operation Research

In this video I have explained about MODEL III - Single Additive constraint additively separable , in continuous variable in OPERATION RESEARCH

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What is Dynamic Programming ?
What is Bellman's Principle Of Optimality?
Explanation about Bellman's Principle Of Optimality
What is Single multiplicative constraint additively separable return in dynamic programming?

* About Dynamic programming:
An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.

* Bellman’s principle of optimality: An optimal policy (set of decisions) has the property that whatever the initial state and decisions are, the remaining decisions must constitute and optimal policy with regard to the state resulting from the first decision.

* Mathematically, this can be written as:
fN(x)=max.[r(dn)+fN−1T(x,dn)]dn∈x
where fN(x)=the optimal return from an N-stage process when initial state is xr(dn)=immediate return due to decisiondnT(x,dn)=the transfer function which gives the resulting state{x}=set of admissible decisions
This equation is also known as a dynamic programming equation. It represents a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the value of a decision problem at a certain point in time in terms of the payoff from some initial choices and the value of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into simpler subproblems.

* About Single multiplicative constraint , additively separable return method:
Consider the problem: To minimize Z = f(y) subject to Y1 Y2 Y3 Y4 greater than P , (y , P , a all are greater than zero )
First , introduce state variable Sj= YnYn-1 = P , Sj-1 = Yn-1Yn-2
The general recursion formula becomes :
FjSj= min [ fjYj + Fj-1Sj-1 ]

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If you have any question related to this topic feel free to Whatsapp me on [phone]

[akshaybmenon]

Missed a multiplication by 7 in the last step. Optimal value would correspond to [0, 7.5].

[vallik]

Is there any specific reason to find out what kind of method needs to be done first?

[roshbarb]

Hi, since x1 ranges values from 0 to 3, solution is as follows Max [ (8*0+ 7*7.5), (8*3 + 7*0)] by putting values of x1 as 0 & 3 respectively by which we get Max [ 24, 52.5], which is 52.5 for x1=0 & x2= 7.5, which is also better value and satisfies both constraints, I confirmed this also by graphically.your calculation and solution for this problem seems to be incorrect, please recheck again

[zionboaron]

this method can work for more then 2 stages?

[deepaklodhirajput]

Useless vedio I did not get why I am doing this

[saqlainirshad]

Sir plz share the link of forward induction method

[jijireji]

Could you explain it in forward induction method

[georgechamilothoris]

I noticed that applying the forward method, one arrives at the solution x=[0.0, 7.5] which yields a value of z=52.5, while satisfying the constrains with slack s=[0.5, 0.0]. Could you please comment on this result?

[divyatiwadi]

Apne jb backwards method se kiya to answer maxz =24 aaya jbki hmari book me answer 105/2 aa rha h?? Please tell me

[nailu]

Sir kindly share Gmail I'd I have a question.