> So, what is the proper way to do it?  As I wrote, it's not really an 
>> option to solve the whole problem for each new constraint...
>>
>
> add a constraint, and solve again?
>
> Yes, and then?  I don't think I can remove it again, can I?  As I wrote, 
pseudo-code is as follows, and keep in mind that large_list really is a 
large list...

    p = MixedIntegerLinearProgram(constraint_generation=True, 
solver="CPLEX") # solver="GLPK") # twice as long # 
    assignment = p.new_variable(binary=True)

    p.add_constraint(... some relations in terms of assignment[box, colour] 
... )

    p.solve()

    for (box, colour) in large_list:
        p_new = copy(p)
        p_new.add_constraint(assignment[box, colour] == 0)
        try:
            p_new.solve()

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