Actually the question below is not specific to Gurobi, but that's the tool I am using.
Consider a scheduling problem where a 2D array of binary variables $Z(i,v)$ is defined, where $i$ is index of time slot, and $v$ is index of operation, each $Z(i,v)$ is a 0-1 binary variable, $Z(i,v)=1$ means operation $v$ is allocated to time slot $i$.
Now consider adding the following constraint/penalty based on $Z(i,v)$:
- A certain operation $v_0$ can be scheduled multiple times, i.e., there are multiple $i$ values where $Z(i,v_0) = 1$. We want to add constraint to the "last $i$" where $Z(i,v_0)=1$, i.e., the last $v_0$ operation. For example, in the last $v_0$ operation the product volume $\operatorname{vol}(i, v_0)\ge100$. The problem is we must tell what is the last $i$ that satisfies $Z(i,v_0) = 1$, and only after that add $\operatorname{vol}(i,v_0)\ge100$, how to do that?
- This is an extension of the above problem. Here we consider multiple operations $v_0, v_1, \cdots, v_n$. In certain applications the "order" of those $n+1$ operations matter, meaning that certain order could incur extra cost, and that the objective should contain a penalty term that is a function of the order. To add penalty, we should know the order first, which in turns means that we should extract all those $i$ values where $Z(i, v_0)=1$, $Z(i,v_1)=1$, etc.
Comment: if $Z(i,v)$ is given, then I can just use a for loop to locate all those $i$ values where $Z(i,v)=1$, the problem is $Z(i,v)$ is part of the solution, and is unknown during the solution process. That's what gets me confused. But I expect that Gurobi has some built-in syntax/function to handle those scenarios because technically it should be possible.
