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/* JSSP, Job-Shop Scheduling Problem */
/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
/* The Job-Shop Scheduling Problem (JSSP) is to schedule a set of jobs on a set of machines, subject to the constraint that each machine can handle at most one job at a time and the fact that each job has a specified processing order through the machines. The objective is to schedule the jobs so as to minimize the maximum of their completion times.
Reference: D. Applegate and W. Cook, "A Computational Study of the Job-Shop Scheduling Problem", ORSA J. On Comput., Vol. 3, No. 2, Spring 1991, pp. 149-156. */
param n, integer, > 0;/* number of jobs */
param m, integer, > 0;/* number of machines */
set J := 1..n;/* set of jobs */
set M := 1..m;/* set of machines */
param sigma{j in J, t in 1..m}, in M;/* permutation of the machines, which represents the processing order of j through the machines: j must be processed first on sigma[j,1], then on sigma[j,2], etc. */
check{j in J, t1 in 1..m, t2 in 1..m: t1 <> t2}: sigma[j,t1] != sigma[j,t2];/* sigma must be permutation */
param p{j in J, a in M}, >= 0;/* processing time of j on a */
var x{j in J, a in M}, >= 0;/* starting time of j on a */
s.t. ord{j in J, t in 2..m}: x[j, sigma[j,t]] >= x[j, sigma[j,t-1]] + p[j, sigma[j,t-1]];/* j can be processed on sigma[j,t] only after it has been completely processed on sigma[j,t-1] */
/* The disjunctive condition that each machine can handle at most one job at a time is the following:
x[i,a] >= x[j,a] + p[j,a] or x[j,a] >= x[i,a] + p[i,a]
for all i, j in J, a in M. This condition is modeled through binary variables Y as shown below. */
var Y{i in J, j in J, a in M}, binary;/* Y[i,j,a] is 1 if i scheduled before j on machine a, and 0 if j is scheduled before i */
param K := sum{j in J, a in M} p[j,a];/* some large constant */
display K;
s.t. phi{i in J, j in J, a in M: i <> j}: x[i,a] >= x[j,a] + p[j,a] - K * Y[i,j,a];/* x[i,a] >= x[j,a] + p[j,a] iff Y[i,j,a] is 0 */
s.t. psi{i in J, j in J, a in M: i <> j}: x[j,a] >= x[i,a] + p[i,a] - K * (1 - Y[i,j,a]);/* x[j,a] >= x[i,a] + p[i,a] iff Y[i,j,a] is 1 */
var z;/* so-called makespan */
s.t. fin{j in J}: z >= x[j, sigma[j,m]] + p[j, sigma[j,m]];/* which is the maximum of the completion times of all the jobs */
minimize obj: z;/* the objective is to make z as small as possible */
data;
/* These data correspond to the instance ft06 (mt06) from:
H. Fisher, G.L. Thompson (1963), Probabilistic learning combinations of local job-shop scheduling rules, J.F. Muth, G.L. Thompson (eds.), Industrial Scheduling, Prentice Hall, Englewood Cliffs, New Jersey, 225-251 */
/* The optimal solution is 55 */
param n := 6;
param m := 6;
param sigma : 1 2 3 4 5 6 := 1 3 1 2 4 6 5 2 2 3 5 6 1 4 3 3 4 6 1 2 5 4 2 1 3 4 5 6 5 3 2 5 6 1 4 6 2 4 6 1 5 3 ;
param p : 1 2 3 4 5 6 := 1 3 6 1 7 6 3 2 10 8 5 4 10 10 3 9 1 5 4 7 8 4 5 5 5 3 8 9 5 3 3 9 1 5 4 6 10 3 1 3 4 9 ;
end;
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