Partition non-overlapping item clusters

partition.py

from mip import *
import string, collections
a = string.ascii_uppercase
item_clusters, cluster_size = {}, collections.Counter()
for ci,c in enumerate([a[:6],a[:3],a[3:6],a[6:10],a[10:12]]):
    for i in c:
        name = 'c'+str(ci)
        cluster_size[name] += 1
        item_clusters.setdefault(i, set()).add( name )
print(item_clusters, cluster_size)


m = Model(sense=MAXIMIZE, solver_name=CBC)
cvars = {cname: m.add_var(var_type=INTEGER, name=cname) for cname in cluster_size}
coef_x = {}
m.objective = xsum(size * cvars[cname] for cname, size in cluster_size.items())
for i, clusters in item_clusters.items():
    m += xsum([cvars[cname]*int(cname in clusters) for cname in cluster_size]) == 1, "C"+i
status = m.optimize()

if status == OptimizationStatus.OPTIMAL:
    print('optimal solution cost {} found'.format(m.objective_value))
elif status == OptimizationStatus.FEASIBLE:
    print('sol.cost {} found, best possible: {}'.format(m.objective_value, m.objective_bound))
elif status == OptimizationStatus.NO_SOLUTION_FOUND:
    print('no feasible solution found, lower bound is: {}'.format(m.objective_bound))
if status == OptimizationStatus.OPTIMAL or status == OptimizationStatus.FEASIBLE:
    print('solution:')
    for v in m.vars:
        print('{} : {}'.format(v.name, v.x))