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dekker.one
1% RUNS ON mzn20_fd
2% RUNS ON mzn-fzn_fd
3% RUNS ON mzn20_mip
4
5% mzn2fzn and minizinc aborted on this model with an error message about
6% being unable to compute set bounds. This was fixed in r8782.
7% (This is derived from the talent scheduling model in the MiniZinc
8% benchmarks.)
9
10include "all_different.mzn";
11
12int: numActors; % number of actors
13int: numScenes; % numer of scenes
14
15%-- Types ---------------------------------------------------------------------
16set of int: Actors = 1..numActors;
17set of int: Scenes = 1..numScenes;
18
19array[Actors,Scenes] of 0..1: ia; % 01 definition of actors in scenes
20array[Scenes] of set of Actors: a =
21 [ { j | j in Actors where ia[j,i] == 1} | i in Scenes] ; % actors for each scene
22array[Scenes] of int: d; % duration of each scene
23array[Actors] of int: c; % cost of each actor
24
25numScenes = 6;
26numActors = 4;
27ia = [|
281,0,0,0,1,1|
291,1,0,1,0,0|
300,1,1,0,1,0|
310,0,1,1,0,1|];
32c = [1,1,1,1];
33d = [1,2,3,4,5,6];
34
35%-- Decision variables --------------------------------------------------------
36
37array[Scenes] of var Scenes: s; % schedule of scenes
38
39%-- Auxilliary variables ------------------------------------------------------
40
41array[Scenes] of var set of Actors: bef; % actors appearing before time t
42array[Scenes] of var set of Actors: aft; % actors appearing after time t
43array[Scenes] of var set of Actors: dur; % actors on set at time t
44
45var int: cost;
46
47%-- Constraints ---------------------------------------------------------------
48
49constraint all_different(s); % each scene scheduled once
50
51constraint
52 bef[1] = {} /\ % no actors before time 1
53 aft[numScenes] = {} /\ % no actors after time numScenes
54 forall(t in 1..numScenes-1)(
55 bef[t+1] = a[s[t]] union bef[t] /\
56 aft[t] = a[s[t+1]] union aft[t+1] );
57
58constraint
59 dur[1] = a[s[1]] /\
60 forall(t in 2..numScenes-1)(
61 dur[t] = bef[t+1] intersect aft[t]
62 ) /\
63 dur[numScenes] = a[s[numScenes]];
64
65constraint cost = sum(i in Scenes)(
66 sum(j in Actors)(
67 c[j] * d[s[i]] * bool2int(j in dur[i])
68 )
69 );
70
71%-- symmetry breaking constraint
72constraint s[1] < s[numScenes];
73
74%-- Solving objective and solution output -------------------------------------
75
76solve :: int_search(s, first_fail, indomain, complete)
77 minimize cost;
78
79output ["cost = ", show(cost), ";\ns = ", show(s),
80 ";\ndur = ", show(dur),
81 ";\nbef = ", show(bef),
82 ";\naft = ", show(aft),
83 ";\na = ", show(a),
84 ";\n"];