diff --git a/committees.org b/committees.org index ee32221..ba3dff1 100644 --- a/committees.org +++ b/committees.org @@ -25,12 +25,12 @@ administration: Mine mattekunnskaper er tydeligvis fraværende. Jeg klarer ikke finne en fornuftig løsning på dette: -| A: | 160 | -| B: | 150 | -| C: | 110 | -| D: | 60 | -| E: | 60 | -| F: | 30 | +| A | 160 | +| B | 150 | +| C | 110 | +| D | 60 | +| E | 60 | +| F | 30 | Det er snakk om sensur i inf1300 med 283 besvarelser. D og E kan ikke rette mot hverandre. De bør helst rette mot B eller C. @@ -499,15 +499,52 @@ cry for help. with correcting $40$ and /actually/ willing to correct $52$. Therefore, we can try to add some slack to the capacity. + In reality, the numbers from the original email were + + | A | 158 | + | B | 150 | + | C | 108 | + | D | 60 | + | E | 60 | + | F | 15 | + + But when we add them up, it turns out that they only have capacity to + correct $551$ exams (and we need $2*N = 566$). + + We create a new instance with the original values. + + #+BEGIN_SRC python :tangle committees.py + def original_instance(): + N = 283 + # A B C D E F + C = [158, 150, 108, 60, 60, 15] + S = {3 : {1, 2}, 4 : {1, 2}} + A = {frozenset([3, 4])} + return (N, C, S, A) + #+END_SRC + + Now we can compute a "badness"-score (or weight) for the examiners + capacities, rather than just stating we cannot surpass their capacity. + #+BEGIN_SRC python :tangle committees.py def capacity_slack(comms, i, C): a = sum(comms[c] for c in comms if i in c) return If(a > C[i], a - C[i], C[i] - a) + #+END_SRC + For the total weight of the capacities, we try to just sum the weights for + each examiner. + + #+BEGIN_SRC python :tangle committees.py def capacity_weight(comms, C): return sum(capacity_slack(comms, i, C) for i in range(len(C))) #+END_SRC + We can now add all of the optimization objectives, stating that it most + important to respect the capacities of the examiners, then prefer a small + number of committees, and lastly the /should/ requirement from the previous + section. + #+BEGIN_SRC python :tangle committees.py def optimize_instance(instance): N, C, S, A = instance @@ -527,6 +564,40 @@ cry for help. return o.model() #+END_SRC + We now get something like: + + #+BEGIN_EXAMPLE + 0: 158/158 + 1: 158/150 + 2: 110/108 + 3: 60/60 + 4: 65/60 + 5: 15/15 + + 0, 1: 158 + 2, 3: 45 + 2, 4: 65 + 3, 5: 15 + #+END_EXAMPLE + + If we were to prioritize the /should/ requirement over minimizing the number + of committees, then we would get something like: + + #+BEGIN_EXAMPLE + 0: 158/158 + 1: 151/150 + 2: 109/108 + 3: 64/60 + 4: 61/60 + 5: 23/15 + + 0, 1: 26 + 0, 2: 109 + 0, 5: 23 + 1, 3: 64 + 1, 4: 61 + #+END_EXAMPLE + * COMMENT Local variables # Local Variables: # eval: (add-hook 'after-save-hook 'org-html-export-to-html nil t)