the model student_coverage_optimization.py groups schools in a way that all schools qualify
This was harder before the CEP percentage was lowered to 25%. it still may help some districts.
The model reimbursement_optimization.py groups schools to optimize the CEP payments
The reimbursement rate formula is:
def grouped_cep_reimbursement(ISP_Count: list, enrollment: list, free_rate: float=4.5, paid_rate: float=0.5) -> float:
"""Take a list of ISP_counts and a list of enrollments and returns the enrollment weighted reimbursement
"""
itot = sum(ISP_count)
etot = sum(enrollment)
I = itot/etot
if I >= 0.625:
return etot * 4.5
elseif I >= 0.25:
return etot * ((free_rate * I * 1.6) + paid_rate * (1 - I))
else:
return etot * 0.5
This is modified to create a piece-wise linear optimization problem which can be more quickly solved. The solver takes user input on the number of groups. It's best to start with small er numbers first and see if they solve the problem
For some districts the optimization is trivial because they fall above or below thresholds. For example if every schools in a LAS has an ISP >62.5 any grouping or no grouping will be the same. For LAS ear the 25% and 62.5% cut points the optimization tools can improve coverage or reimbursement.
Both scripts currently use Gurobi, a commercial solver that requires a license. In the future I may modify the scripts to work with the Free solver from Google, ORTools
I started converting the Gurobi models to ortools so they could be distributed freely. The reimbursement model converted easily. The student model is very slow now. I need to test CP-SAT and some other approaches in ortools,