I am working on developing a MILP mathematical model which deals with cyclic tasks. I at a stage where I have to design constraints in this regard. here is the simplified version of the problem.
the are 4 tasks of A type: [A1, A2, A3, A4]. I need a constraint that
- first make sure the tasks are in order
- second, in the planning horizon, after task A4 is again A1. this cycle will go on till the planning horizon ends.
I have created constraints to verify the sequence of tasks:
X_A: = 1 if task A is being done
index a: tasks {1, 2, .... , A}
sum over planning horizon(X_a) >= sum over planning horizon(X_a+1) for all a in {1,2, ... A-1}
I am stuck on writing a constraint to make sure within the planning horizon after the last task it goes and start the first task and repeat the cycle.