StackOverflow: https://stackoverflow.com/questions/48467666/ranking-optimization

so_min_cost_flow_course_assignment.py

    import itertools
    import networkx as nx

    """ DATA """
    S = ('S', [0, 1, 2])                                      # ranking: good to bad
    K = ('K', [1, 2, 0])
    L = ('L', [1, 2, 0])
    D = ('D', [0, 2, 1])
    A = ('A', [0, 2, 1])
    J = ('J', [2, 1, 0])
    P = [S, K, L, D, A, J]

    C = [('c0', 0, 1), ('c1', 1, 2), ('c2', 2, 3)]            # (name, index, limit)

    """ Helper """
    def get_cost(ranking, index):
        return ranking.index(index)**2                        # quadratic penalty

    """ Min-cost flow graph """
    G = nx.DiGraph()

    # Demands
    for p in P:
        G.add_node(p[0], demand=-1)
    G.add_node('sink', demand=len(P))

    # layer 1
    for p, c in itertools.product(P, C):
        G.add_edge(p[0], c[0], weight=get_cost(p[1], c[1]))

    # layer 2
    for c in C:
        G.add_edge(c[0], 'sink', capacity=c[2])

    flowCost, flowDict = nx.network_simplex(G)
    print('Cost: ', flowCost)

    """ SOLUTION """
    for p in P:
        for c in C:
            if flowDict[p[0]][c[0]]:
                print(p[0], '->', c[0])
# Output:
# -------
# Cost:  2
# S -> c0
# K -> c1
# L -> c1
# D -> c2
# A -> c2
# J -> c2