subpack-glpk
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[9] | 1 | /* CPP, Critical Path Problem */ |
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| 2 | |
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| 3 | /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */ |
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| 4 | |
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| 5 | /* Note: Reduced costs of auxiliary variables phi[j,k] (see below) |
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| 6 | can be only zero or one. The critical path is defined by the |
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| 7 | constraints, whose reduced cost is one. */ |
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| 8 | |
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| 9 | set J; |
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| 10 | /* set of jobs (activities) */ |
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| 11 | |
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| 12 | set P{j in J}, in J, default {}; |
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| 13 | /* P[j] is a subset of jobs that immediately precede job j */ |
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| 14 | |
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| 15 | param t{j in J}, >= 0; |
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| 16 | /* duration required to perform job j */ |
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| 17 | |
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| 18 | var x{j in J}, >= 0; |
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| 19 | /* starting time of job j */ |
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| 20 | |
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| 21 | s.t. phi{j in J, k in P[j]}: x[j] >= x[k] + t[k]; |
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| 22 | /* job j can start only after all immediately preceding jobs have been |
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| 23 | completely performed */ |
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| 24 | |
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| 25 | var z; |
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| 26 | /* project makespan */ |
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| 27 | |
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| 28 | s.t. fin{j in J}: z >= x[j] + t[j]; |
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| 29 | /* which is the maximum of the completion times of all the jobs */ |
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| 30 | |
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| 31 | minimize obj: z; |
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| 32 | /* the objective is make z as small as possible */ |
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| 33 | |
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| 34 | data; |
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| 35 | |
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| 36 | /* The optimal solution is 46 */ |
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| 37 | |
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| 38 | param : J : t := |
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| 39 | A 3 /* Excavate */ |
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| 40 | B 4 /* Lay foundation */ |
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| 41 | C 3 /* Rough plumbing */ |
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| 42 | D 10 /* Frame */ |
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| 43 | E 8 /* Finish exterior */ |
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| 44 | F 4 /* Install HVAC */ |
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| 45 | G 6 /* Rough electric */ |
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| 46 | H 8 /* Sheet rock */ |
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| 47 | I 5 /* Install cabinets */ |
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| 48 | J 5 /* Paint */ |
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| 49 | K 4 /* Final plumbing */ |
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| 50 | L 2 /* Final electric */ |
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| 51 | M 4 /* Install flooring */ |
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| 52 | ; |
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| 53 | |
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| 54 | set P[B] := A; |
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| 55 | set P[C] := B; |
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| 56 | set P[D] := B; |
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| 57 | set P[E] := D; |
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| 58 | set P[F] := D; |
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| 59 | set P[G] := D; |
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| 60 | set P[H] := C E F G; |
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| 61 | set P[I] := H; |
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| 62 | set P[J] := H; |
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| 63 | set P[K] := I; |
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| 64 | set P[L] := J; |
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| 65 | set P[M] := K L; |
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| 66 | |
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| 67 | end; |
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