Create a 3d plot, by changing a variable while using linear programming and system optimization.

IN MATLAB R2022b - academic use.

I need help creating a 3d plot.

I am using the function 'linprog' to find the least cost conservation plan for the Colorado River in Arizona, Nevada, and California. I have costs and conservation volums, as well as prepetual conservation (purchassing land from farmers, installing low-flow showers/toilets) and one year conservation (fallowing farm land/crop rotation).

As my time considered for conservation needs increases [line 2 variable 'yo'] the usefulness of the more expensive, propetual conservation, options become more ecconomical. My figure [line 45-51] plots the different conservation options and how much of each was sellected each year.

I want to turn this 2d plot into a 3d plot so the x and y become x and z (vertical height maintained) and the y axis shown the different amount of time considered

Then I want to do this again (seperatly) but with the change in Annual Budget [line 5] which also impacts the decision space.

I expect the function 'linprog' needs to be solved multiple times for each change in a variable. I dont know the best (or any) way to keep the data and display it in a 3d space.

Code Below:

For these varibles ['j' conservation and 'F' costs some are not never selected, that is fine]

clear,clc
    yo=20;                          %Number of Years considered
    gro=.01;                        %Growth of demand
    int=.05;                        %Interest rate of money
    ABudg=3E9;                      %Annual Budget
    
                                    %Legend for conservation options
    LegOpt={'Purchased', 'Toilets', 'Catchment', 'Fallowed','Rotated'};
    j=[-4.5,-.03, -.01,-4,-2];      %Conservation Savings (ac-ft/y)
    c=[1,1,1,0,0];                  %Which Options are propetual Conservation 1/0 y/n
F=[20000, 150, 100, 950,300];       %Conservation Cost ($)
    ub=repmat([inf,10000,10000,inf,inf],1,yo);
                                    %annual limits to purchase options

        c=j.*c;
        opt=length(j);
        o=zeros(1,opt);             %Counting and manipulation
                                   
for i=1:yo                          %Creating the 'A' Matrix
    A(i,:)=[repmat(c,1,i-1),j,repmat(o,1,yo-i)];
    
end

            f=zeros(yo,opt);
            b=zeros(1,yo);
            b(1)=1200000;
            f(1,:)=F;
    for i=2:yo                      %Compound Interest for Costs, Demand
        f(i,:)=f(i-1,:)*(1+int);
        b(i)=b(i-1)*(1+gro);
    end

f=reshape(f',1,[])';
    value=repelem(eye(yo),1,opt).*f';
    aBudg=repmat(ABudg,1,yo);
    lb=zeros(1,yo*opt);
    
[x of]=linprog(f,[A;value],[-b,aBudg],[],[],lb,ub);

    volum=reshape(x,opt,yo);    %How much of each option selected each year
    ACost=value*x;              %Annual Cost of options selected
    sum(ACost)                  %Total Outlay


figure(2)
    for i=1:opt
        plot(1:yo,volum(i,:)); hold on
    end

    legend(LegOpt)
    xlim([1,yo])

Answer 1

[Varun]

Hello William!

As per my understanding, you want to introduce new variables to your linear programming mechanism and expand its dimensionality to 3D. While I am not sure about exactly what results are expected from this analysis, I believe this sample plot (attached below) is similar to what you may be looking for:

Regarding the 3D plot, MATLAB has ready-to-go functions which you can use such as ‘plot3’. You may find the documentation for the same at https://www.mathworks.com/help/matlab/ref/plot3.html .

As for introducing the new variables, I think you’ll have to solve the system of equations for all existing variables repeatedly, each time the budget changes. You can store this new data generated as a cell array. Cell arrays are equipped to contain entire matrices in a single cell, so you don’t have to worry about merging/ appending your existing matrices with new data from the next iteration. You may find the relevant documentation here: https://www.mathworks.com/help/matlab/ref/cell.html.

Hope this helps!