solve_vrp -- solve the vehicle routing problem.
       - start with assignment model (depot has a special status)
       - add cuts until all components of the graph are connected
    Parameters:
        - V: set/list of nodes in the graph
        - c[i,j]: cost for traversing edge (i,j)
        - m: number of vehicles available
        - q[i]: demand for customer i
        - Q: vehicle capacity
    Returns the optimum objective value and the list of edges used.

def vrp(V, c, m, q, Q):
    """solve_vrp -- solve the vehicle routing problem.
       - start with assignment model (depot has a special status)
       - add cuts until all components of the graph are connected
    Parameters:
        - V: set/list of nodes in the graph
        - c[i,j]: cost for traversing edge (i,j)
        - m: number of vehicles available
        - q[i]: demand for customer i
        - Q: vehicle capacity
    Returns the optimum objective value and the list of edges used.
    """

    model = Model("vrp")
    vrp_conshdlr = VRPconshdlr()

    x = {}
    for i in V:
        for j in V:
            if j > i and i == V[0]:       # depot
                x[i,j] = model.addVar(ub=2, vtype="I", name="x(%s,%s)"%(i,j))
            elif j > i:
                x[i,j] = model.addVar(ub=1, vtype="I", name="x(%s,%s)"%(i,j))

    model.addCons(quicksum(x[V[0],j] for j in V[1:]) == 2*m, "DegreeDepot")
    for i in V[1:]:
        model.addCons(quicksum(x[j,i] for j in V if j < i) +
                        quicksum(x[i,j] for j in V if j > i) == 2, "Degree(%s)"%i)

    model.setObjective(quicksum(c[i,j]*x[i,j] for i in V for j in V if j>i), "minimize")
    model.data = x

    return model, vrp_conshdlr