1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/examples/jssp.mod Mon Dec 06 13:09:21 2010 +0100
1.3 @@ -0,0 +1,114 @@
1.4 +/* JSSP, Job-Shop Scheduling Problem */
1.5 +
1.6 +/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
1.7 +
1.8 +/* The Job-Shop Scheduling Problem (JSSP) is to schedule a set of jobs
1.9 + on a set of machines, subject to the constraint that each machine can
1.10 + handle at most one job at a time and the fact that each job has a
1.11 + specified processing order through the machines. The objective is to
1.12 + schedule the jobs so as to minimize the maximum of their completion
1.13 + times.
1.14 +
1.15 + Reference:
1.16 + D. Applegate and W. Cook, "A Computational Study of the Job-Shop
1.17 + Scheduling Problem", ORSA J. On Comput., Vol. 3, No. 2, Spring 1991,
1.18 + pp. 149-156. */
1.19 +
1.20 +param n, integer, > 0;
1.21 +/* number of jobs */
1.22 +
1.23 +param m, integer, > 0;
1.24 +/* number of machines */
1.25 +
1.26 +set J := 1..n;
1.27 +/* set of jobs */
1.28 +
1.29 +set M := 1..m;
1.30 +/* set of machines */
1.31 +
1.32 +param sigma{j in J, t in 1..m}, in M;
1.33 +/* permutation of the machines, which represents the processing order
1.34 + of j through the machines: j must be processed first on sigma[j,1],
1.35 + then on sigma[j,2], etc. */
1.36 +
1.37 +check{j in J, t1 in 1..m, t2 in 1..m: t1 <> t2}:
1.38 + sigma[j,t1] != sigma[j,t2];
1.39 +/* sigma must be permutation */
1.40 +
1.41 +param p{j in J, a in M}, >= 0;
1.42 +/* processing time of j on a */
1.43 +
1.44 +var x{j in J, a in M}, >= 0;
1.45 +/* starting time of j on a */
1.46 +
1.47 +s.t. ord{j in J, t in 2..m}:
1.48 + x[j, sigma[j,t]] >= x[j, sigma[j,t-1]] + p[j, sigma[j,t-1]];
1.49 +/* j can be processed on sigma[j,t] only after it has been completely
1.50 + processed on sigma[j,t-1] */
1.51 +
1.52 +/* The disjunctive condition that each machine can handle at most one
1.53 + job at a time is the following:
1.54 +
1.55 + x[i,a] >= x[j,a] + p[j,a] or x[j,a] >= x[i,a] + p[i,a]
1.56 +
1.57 + for all i, j in J, a in M. This condition is modeled through binary
1.58 + variables Y as shown below. */
1.59 +
1.60 +var Y{i in J, j in J, a in M}, binary;
1.61 +/* Y[i,j,a] is 1 if i scheduled before j on machine a, and 0 if j is
1.62 + scheduled before i */
1.63 +
1.64 +param K := sum{j in J, a in M} p[j,a];
1.65 +/* some large constant */
1.66 +
1.67 +display K;
1.68 +
1.69 +s.t. phi{i in J, j in J, a in M: i <> j}:
1.70 + x[i,a] >= x[j,a] + p[j,a] - K * Y[i,j,a];
1.71 +/* x[i,a] >= x[j,a] + p[j,a] iff Y[i,j,a] is 0 */
1.72 +
1.73 +s.t. psi{i in J, j in J, a in M: i <> j}:
1.74 + x[j,a] >= x[i,a] + p[i,a] - K * (1 - Y[i,j,a]);
1.75 +/* x[j,a] >= x[i,a] + p[i,a] iff Y[i,j,a] is 1 */
1.76 +
1.77 +var z;
1.78 +/* so-called makespan */
1.79 +
1.80 +s.t. fin{j in J}: z >= x[j, sigma[j,m]] + p[j, sigma[j,m]];
1.81 +/* which is the maximum of the completion times of all the jobs */
1.82 +
1.83 +minimize obj: z;
1.84 +/* the objective is to make z as small as possible */
1.85 +
1.86 +data;
1.87 +
1.88 +/* These data correspond to the instance ft06 (mt06) from:
1.89 +
1.90 + H. Fisher, G.L. Thompson (1963), Probabilistic learning combinations
1.91 + of local job-shop scheduling rules, J.F. Muth, G.L. Thompson (eds.),
1.92 + Industrial Scheduling, Prentice Hall, Englewood Cliffs, New Jersey,
1.93 + 225-251 */
1.94 +
1.95 +/* The optimal solution is 55 */
1.96 +
1.97 +param n := 6;
1.98 +
1.99 +param m := 6;
1.100 +
1.101 +param sigma : 1 2 3 4 5 6 :=
1.102 + 1 3 1 2 4 6 5
1.103 + 2 2 3 5 6 1 4
1.104 + 3 3 4 6 1 2 5
1.105 + 4 2 1 3 4 5 6
1.106 + 5 3 2 5 6 1 4
1.107 + 6 2 4 6 1 5 3 ;
1.108 +
1.109 +param p : 1 2 3 4 5 6 :=
1.110 + 1 3 6 1 7 6 3
1.111 + 2 10 8 5 4 10 10
1.112 + 3 9 1 5 4 7 8
1.113 + 4 5 5 5 3 8 9
1.114 + 5 3 3 9 1 5 4
1.115 + 6 10 3 1 3 4 9 ;
1.116 +
1.117 +end;