FMINCON to schedule appliance usage to minimize total cost

Question

I would like to write a code to find the minimum cost of running a dishwasher. This is dependent on the power required, hourly tariff rate, and time used. I am using fmincon for this however the code provided below shows the following error message:

User supplied objective function must return a scalar value

My objective function is to minimize (Total Cost * Time) s.t total cost is equal to the summation of (hourly power)*(hourly cost) from hour 1 to 24 is equal to 0.8 kwh, also, the total cost must be greater than Ca and the total run time for the day is one hour.

% Array showing the hourly electricity rates (cents per kwh)
R=zeros(24,1);  
R(1:7,1)=6;
R(20:24,1)=6;
R(8:11,1)=9;
R(18:19,1)=9;
R(12:17,1)=13;

p_7 = transpose([0.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]); %This is the power pattern of appliance (operates at 0.8 kWh for 1 hour daily)

for k=1:23
P7(:, k+1) = circshift(p_7,k);     % This shows all the possible hours of operation
end

Total = P7*R;               % This is the total cost per hour at different hourly tariffs 

fun = @(x)Total.*(x);
x0 = [1];

A = Total;
%Ca = 0.5;
Ca = ones(1,24);
b = Ca;

Aeq = Total;
Daily_tot_7 = 2*ones(1,24);
beq = Daily_tot_7;

ub = 24;
lb = 1;

x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub)

I believe that my understanding on converting constraints to fmincon is not correct and that I may be missing vital constraints for this issue.

Answer 1

Your output is currently a vector of outputs. You stated that your cost function is the summation of hourly elements. Therefore, your function definition should be

fun = @(x)sum(Total.*(x));

However, if I'm reading into this right, you wish to solve for each hour individually. In that case, you need to set your x0 variable to be defined as a 24x1 input

x0 = ones(24,1);

If that is the case you need to adjust your A,b,Aeq, and beq variables accordingly. However, do you actually need these, you can just not use them by replacing them with []

Finally, your p7 variable is likely better redefined as

p7 = R*.8;

My apologies if I misunderstood what you are trying to accomplish here.