How to put this restriction using Gurobi in python

Question

I am doing an optimization problem for the filling and extraction of a warehouse. One of the constraints is that the filling volume cannot exceed a given limit for one day: For example, on the 3rd of April a maximum of 60 kg, on the 8th of May, 70 kg.

Using pandas I import the column with the maximum inventory profile for each day and impose the restriction as follows (For the lower limit I also have a profile that I impose for each day):

$$\sum_{i=0}^i X_i \le H_i$$ $$\sum_{i=0}^i X_i \ge L_i$$

m.addConstrs(sum(x[i] for i in dias)<=Hvol[i] for i in dias)

m.addConstrs(sum(x[i] for i in dias)>= Lvol[i] for i in dias)

Days is a list associated with the index $i$, representing each day. What python does is that the sum of 365 days is always less than $H_i$, instead of the sum up to day $i$ being less than $H_i$.

What python does: $$\min \sum_{i=0}^n X_i \le H_i$$ $$n=365$$ $$X_1+X_2+X_3+\ldots+X_{365} \le H_1$$

$$X_1+X_2+X_3+\ldots+X_{365} \le H_2$$

Instead of:

\begin{align}X_1&\le H_1\\X_1+X_2&\le H_2\\\cdots\end{align}

Answer 1

Firstly, your constraint should rather look this this: $$\sum_{j=0}^{i}X_j \leq H_i \quad \forall i \in I$$ $$\sum_{j=0}^{i}X_j \geq L_i \quad \forall i \in I$$

In your code this should translate to:

m.addConstrs(sum(x[j] for j in range(0,i))<=Hvol[i] for i in dias)

m.addConstrs(sum(x[j] for j in range(0, i))>= Lvol[i] for i in dias)

In case dias starts with index 1, then it should be range(1,i+1)