'MILP: Formulating a sorted list for a constraint
For a MILP project planning problem I would like to formulate the constraint that activity i must be finished before activity j starts. The activities are to be ordered by duration p and the one of three modes m per activity is to be used which takes the shortest time.
So I created a dictionary with the minimum durations of activity i in mode m.
p_im_min = {i: np.min([p[i,m] for m in M_i[i]]) for i in V}
Then I sorted the durations by size:
p_sort = (sorted(p_im_min.items(), key = lambda kv: kv[1]))
Which gives (i,p) in the right order:
p_sort = [(0, 0),
(3, 1),
(4, 1),
(5, 1),
(7, 1),
(13, 1),
(14, 1),
(15, 1),
(19, 1),
(1, 2),
(2, 2),
(8, 2),
(16, 2),
(17, 2),
(18, 2),
(20, 2),
(6, 3),
(10, 3),
(9, 4),
(12, 4),
(11, 5)]
But now I want a list with (i,j), where i must always be finished before j starts. Since I could not find the function, I created this list manually, thus
order_act = [(0,3), (3,4), (4,5), (5,7), etc.
And finally (after formulating the parameters, variables and sets) added the following constraint:
mdl.addConstrs(y[i,j] == 1
for (i,j) in order_act)
My question:
Is there any way to use a formula/command in Python to create the list (i,j)? Because as it is now, it is not ideal and the solution is not satisfactory.
Sources
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