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/* CPP, Critical Path Problem */
/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
/* Note: Reduced costs of auxiliary variables phi[j,k] (see below) can be only zero or one. The critical path is defined by the constraints, whose reduced cost is one. */
set J;/* set of jobs (activities) */
set P{j in J}, in J, default {};/* P[j] is a subset of jobs that immediately precede job j */
param t{j in J}, >= 0;/* duration required to perform job j */
var x{j in J}, >= 0;/* starting time of job j */
s.t. phi{j in J, k in P[j]}: x[j] >= x[k] + t[k];/* job j can start only after all immediately preceding jobs have been completely performed */
var z;/* project makespan */
s.t. fin{j in J}: z >= x[j] + t[j];/* which is the maximum of the completion times of all the jobs */
minimize obj: z;/* the objective is make z as small as possible */
data;
/* The optimal solution is 46 */
param : J : t := A 3 /* Excavate */ B 4 /* Lay foundation */ C 3 /* Rough plumbing */ D 10 /* Frame */ E 8 /* Finish exterior */ F 4 /* Install HVAC */ G 6 /* Rough electric */ H 8 /* Sheet rock */ I 5 /* Install cabinets */ J 5 /* Paint */ K 4 /* Final plumbing */ L 2 /* Final electric */ M 4 /* Install flooring */;
set P[B] := A;set P[C] := B;set P[D] := B;set P[E] := D;set P[F] := D;set P[G] := D;set P[H] := C E F G;set P[I] := H;set P[J] := H;set P[K] := I;set P[L] := J;set P[M] := K L;
end;
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