/* JSSP, Job-Shop Scheduling Problem *//* Written in GNU MathProg by Andrew Makhorin <mao@mai2.rcnet.ru> *//* 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;