 Then, this is another technique which still not yet published, we are under processing of publishing. This is the first time we tried to do this conjunctive use modeling using stochastic dynamic programming, even though we have the soft computing techniques or whatever machine learning all these things, still we are unable to do this conventional stochastic dynamic programming which gives, which may give a better result than your soft computing techniques. The only problem here is the curse of dimensionality, when I increase the number of variables my matrix size goes on increasing. In soft computing techniques we are not solving any matrix, here we try to solve the matrix in optimization, when my matrix size is larger and larger my software or my computer may not be able to take care, 3 dimensional matrix, 4 dimensional matrix. In such cases we say that it is a curse of dimensionality, manually it is possible, but it that means small problems we can solve, large complex problems we cannot solve using these type of SDP models, right. So, in this SDP model we have considered the stochasticity of inflow as well as stochasticity of ground water level variations. As I have explained the same case study of Sri Ram Sagar project has been taken to find out what is the effect of considering the stochasticity in inflow as well as ground water level variations. I think this many people knows that what is stochastic dynamic programming, I have explained what is dynamic programming if I need a sequential decision and if I incorporate the stochasticity in the inflow into the dynamic programming I call this as stochastic dynamic programming. There are two ways of incorporating this stochasticity into the dynamic programming, one is called explicit stochastic dynamic programming, another one is implicit stochastic dynamic programming. Explicit stochastic dynamic programming is we never say that or we say that this is the chance of probability of occurrence with respect to time, then that probability is directly coupled with my model that means we are explicitly saying that this is the stochasticity of my inflow and such type of models are called stochastic explicit stochastic dynamic programming. Whereas implicit stochastic dynamic programming many people says that if I develop a deterministic dynamic programming that means develop only reservoir operation rules for only one set of inflow and then you use a simulation model to simulate the condition for longer length and derive the regression equation of relation between inflow and release that they call here we never say that this is the probability of occurrence this is the stochasticity of inflow, but we are trying to capture the stochasticity in terms of regression equations. Such types of models are called implicit stochastic dynamic programming, people have tried both and in some places it explicit works better in some places implicit works better. So many people have considered the surface water as the stochastic variable it is very easy to model the problem here is how to consider this stochastic model I have a reservoir I have an inflow then I have the release. So instead of carrying out for one inflow variable and one storage variable and one release variable I discretize my inflow into n number of stages that means if my inflow is this level and the storage is this much what will be the release then I start discretizing my inflow from minimum level to maximum level this may be 2 times 3 times 4 range 5 range or 6 range then I may have a 6 range of inflow then I may have a 6 range of storage then I may have 6 range of inflow. Suppose if my inflow is in first range and storage is in fifth range what is the release which is the optimum because my decision of next month depends upon previous month it is not just solving this matrix of 6 by 6 by 6 it is finding the optimal number of 6 by 6 by 6 so it is searching the solution within this that is why even if I consider only 6 discretization then the matrix to be solved is 6 by 6 6 times. So that means my computer you can find out how many times it has to do the iteration. So here we consider the objective function maximizing irrigation release and ground water pump page that means finding the deviation is lesser here the stages are time periods normally in stochastic dynamic programming we never start from the first that means for every reservoir operation there is a period that is called stabilization period after that only the releases becomes constant or independent of inflow that period as called as an steady state period I assume that the steady state period has occurred at longer period and I work backwards before that how to achieve this steady state how I have to modify the inflows in each and every month so that my release at end of this time period is steady state. So this is my recursive relationship that means when I am here my objective is to maximize the release for each and every month and also to maximize the ground water pump page since the study area is Sriramsagar project you know that is a waterlogged area my first priority is ground water this is deterministic but when I am at second period when I am at this period my objective function not only depends upon the best value of this one it also depends upon the stochasticity of inflow at this points right. So that is why when I am at t time period that is it is the seasonal time period you see this one this 12 it will go on reducing once we reach the first year then again it starts from next previous year 12 month. So this is the time period or time step in my model and this is the number of stages remaining to obtain my steady state policy this goes on increasing only. So there also my objective function is function of two state variable it is a two state problem most of the surface water are only one state variable states are release as well as ground water pump page it says that what happens at that current time period for surface release as well as for ground water release which is equal to maximization of this is that period t and this is the probable or best result during time period t plus 1 that is previous time period or previous stage multiplied with respect to its probability and this probability is called transition probability transition probability is nothing but it is the probability with respect to time what is the probability of inflow of this range in June month to July month. So you have to construct a transition probability matrix so for a monthly flow model if I consider 6 ranges in my inflow then I will have a 12 matrix of 6 by 6 I have to pick up a particular value to multiply it with the particular ranges all this thing has to be kept in the memory of my computer to solve this. So here transition probability of inflow is this one similarly the transition probability of ground water also we consider since we have three zones I have to that is ground water is three canals so I have to consider the probability of each and every canal separately. And here the stages ranges are considered as I have explained we have estimated what is the ground water available in each 1 meter cake so here our ranges are 5 if my ground water level this month is 1 what is the probability of my ground water level going to be in second meter next month what is the probability of my ground water going to be in 3 meters in next month that probability we have to work it out these transition probabilities are worked out from the historical data. So we model this in terms of lag 1 Markovian processes computational strategies the major set set back in the application of dynamic programming is curse of dimensionality as I said we have to work it out large number of three dimensional matrixes it is very difficult to pick up a particular values to the required manually it is very easy but for a computer it has to go through a range even if you start writing your program you can put a matrix of n i j i comma j comma k maximum 3 after that even for 3 matrix 3 by 3 matrix 3 by 3 by 3 by 3 by 3 matrix if you want to find out the inverse of this then our computers will say that it is very difficult so what happens to overcome this curse of dimensionality we suppose if I consider each and every well as a that is possible I have 688 wells in my command area I can consider the stochasticity of each and every well then I will have 688 matrix of 5 by 5 which is almost impossible so what we try to do is we try to consider this as a single matrix by 5 by 5 for that I cannot consider all the variables all the ground water all variation as a single well I cannot average it so to do this average there are many techniques are available one important technique is called cluster analysis that means we are clustering the spatial and temporal variation of ground water which are having common water level variations so the water levels which have the same range of variation are clubbed and taken together as a single well that means mathematically I am reducing 688 observation wells into 5 different zones which has same variations with a variation ranging within the deviations right so based upon that cluster analysis we discretized the initial storage storage in the reservoir as 7 ranges and releases as 7 ranges and ground water levels as 5 ranges so my matrix to be picked up is 7 by 7 by 5 so this cluster analysis is also called as grouping of wells we classified the wells which are having homogeneous ground water level variation within the standard deviation of their average many softwares are available in SSP softwares we can do this cluster analysis even people have tried applying fuzzy logic technique for this cluster analysis suppose if my range is within this how to club whether it has to be clubbed in one range or second range separate research is also going on because if I do not do this cluster analysis since I have 644 wells my matrix will be 644 by 644 none of the computer will find even the transfer of this matrix transpose of this matrix then as usual the termination criteria so what happens I go on finding out what is the best value considering all the stochasticity how to find out whether I have obtained my steady state or not that is called termination criteria I find the steady state if my releases of this 12th month and this 12th month are same then I call that as steady state policy for 12th month then I have to check for 11th month then I have to check for 10th month so if I find the difference between this value and this value and 11th month and 11th month not only the releases the difference between the objectives of this 12 month and this 12 month and for all the month should be same that means if I consider this one the net benefit of time period t and n plus 2 that is previous year all the best benefits minus of this current month everything should be constant for any type of range right so it is I know it is very difficult to visualize but when we do that we will come to know that so my objective function here is maximizing the surface water release and ground water pumpage subjected to the constraints first one is demand water constraint that means release should be less as the demand to be met from major surface water release or ground water pumpage we divided into five zones ground water also then surface water releases these are all general constraint which any DP program can also take these constraints will help us in removing the scenarios which are not possible so that I know need to work it out for 7 by 7 by 5 matrix many matrixes it may not be possible for example if my inflow is 7th range and the storage is also at the 7th range what is the release I do not need that much of release so I need no need to search my solution in that space or if my inflow is at the first range and storage is also in the first range and release is in the first range that is not possible because my demand has to be met that release may not be possible so this constraint will help us to cartil down our matrix size then ground water constraints all the ground water which you are pumping should be more than or equal to the ground water available within 3 meter so that all my area are free from water logging condition then storage constraint so considering the stochasticity if I go back so I can consider based upon these two stochastic if I do not consider this stochastic that will become a deterministic dynamic programming then I can consider the stochasticity of surface water alone or stochasticity of ground water alone or I can consider the stochasticity of both so depending upon that we had 6 different scenarios if I see that then for each and every scenarios we have to run the model and we have to get the optimal operating policy optimal operating policy is nothing but it will give you the which state where which state is the inflow and which state is the storage for that you will have release require release for each and every month it gives you a set of tabular solution as such we cannot implement it in the field what you have to do is we have to see how this solution optimal solution is working in the field that is what it is called optimization simulation model now we have finished the optimization now we have to simulate this condition in the real life in this real life in simulation what is this we have a set of operating rules derived from optimization model implement in the field to implement in the field the only input required is the inflow generate the inflow using various techniques that is where we can use our AN and GP or whatever it is here we used simple thermosphering model which can be very useful in generating inflow into a seasonal reverse right for seasonal inflow reverse we can still employ this summer thermosphering model very successfully so we try to see the scenario for 200 years we developed for 210 years first to 10 years is discarded to take care of the initial condition so this is the comparison of generated inflow and historical inflow the mean standard deviation skewness this should be same then only I can assume that generated inflow properties or generated inflow represent the historical inflow so this is the demand and if I consider various operational policies FID is frequency of irrigation deficit AID is average irrigation deficit PID is percentage irrigation deficit that means if I consider 2400 and 2400 months that means for 200 years 200 into 12 months that means I am running my system for 2400 months that means I have operated my reservoir for 200 years then for each and every month I can find out what is the release I know what is the demand find the difference this is the statistical properties so if I use only deterministic dynamic then my rule says that this many months I will have deficit in the system out of 2400 months the number is very less frequency but you see the percentage of deficit it is 100% out of 200 years one year will be we don't know in which year it has occur 15 months will be 100% deficit you cannot release if I consider my stochasticity in the inflow the number remains the same but the percentage reduces to its 50% I may not have 100% deficit but still I have 50 to 60% of deficit during these months not all the months very less periods if I considered deterministic model my scenario does not improve that means my stochastic model that's what in reality it happens in reality there is no 100% deficit it is only 50% 60% or 40% deficit that was well captured in this model so if I considered deterministic surface water and groundwater I have 100% deficit for very few months in this case the percentage of this has not increased since I have used conjunctives the number of months the deficit occurs reduced and this is considered in the stochasticity in surface water almost many months you are free from deficit this is the best scenario not this one this is the best scenario stochasticity in surface water as well as stochasticity in groundwater so even if I consider the stochasticity it is almost impossible to eliminate the deficit there will be some amount of deficit so that will be around 50 to 30% only for 2 or 4 months out of 200 years that will be a better scenario than having 100% deficit in 15 months so if I consider this stochasticity that will be a better one this is ranking that means if I consider stochasticity in surface water and groundwater that has average deficit is only 5% for 200 years so this is comparison between my because I have run a simple FLP model also it's very easy to run a FLP model single stroke you will get the result whereas stochastic dynamic programming it is not like that I have to model it I have to discretize I have to run the model for various scenarios I have to generate my inflow and then I have to find the scenarios on comparing this but still researchers consider SDP is the best way of modeling because it it says that is the reality but as a model or it is very difficult to do this modeling but when we compare the result of what we have received through our FLP model which I have explained in the first class and SDP model I think this FLP model gives fairly a better result or we can say not better result at least an equivalent result of this that of this complicated stochastic dynamic program that is where we say that soft computing techniques are better it is it is like that no I have to reach that place instead of going by steps I can go by an elevator also so my effort on this modeling is reduced the time required to do this modeling for if I apply this to achieve the same result it is very easy for me to do and soft computing technique of FLP rather than doing this stochastic dynamic programming this stochastic dynamic programming requires at least two years for a researchers to develop to get the data and to get the result for FLP model in three months or four months you can finish it so the time required to get the desired solution is faster in soft computing techniques that is why soft computing techniques are getting importance now everybody will requires better result in short time so rather than going in for SDP model we can go in for an FLP model even the complicated conjunct use studies that is the major output from this work so as a conclusion the study shows that stochasticity of groundwater availability needs to be accounted for conjunct use in previous cases I have not considered stochasticity it is only ranges considering ranges is something different from considering the stochasticity many people have accepted that if you do stochastic modeling that will give you a better result but curse of dimensionality restrict us if I consider my storages as hundred ranges I can run my system without any deficit but it is impossible to model with even with the advanced computing machines so the clustering approach to group the wells having homogeneous water levels has improved the modeling time of stochastic otherwise no I may not be able to do this stochastic dynamic program it is not possible to solve that 644 by 644 matrix it is not only 1644 by 644 it is 644 by 644 for 12 months and then I have to keep this result for at least 4 or 5 years until I receive my steady state policy so that much storage in the RAM it is not the storage see sdp model many people misunderstood we have 1gb 2gb 3gb 4gb that is not the storage required for my sdp model to run it is the RAM capacity it is not the storage capacity it is the area where my computer is working I have to keep this in a temporary memory so this temporary memory is not sufficient it is very difficult my either my system gets crashed or I have to stop it you know the number of combinations it works out to be 1 lakh or 2 lakhs so I have to search my solution within this space so the combined stochastic dynamic programming consider the stochasticity of inflows and groundwater as resulted in better performance and less irrigation deficit and also with less frequency the 10 percent result in a larger system of 400 kilometer square is a better scenario the stochastic consideration of surface water has also improved the result when stochastic variation in inflows is considered right only even if you consider only the stochasticity in the inflow also and consider the groundwater as the deterministic that also has improved the solutions right this is all the result this is the last result it was also found that simple fuzzy linear programming model can substitute the detailed stochastic dynamic programming model in deriving the optimal operational policies right so this will reduce the time effort and all these things.