int: jobs; % no of jobs set of int: JOB = 1..jobs; int: tasks; % no of tasks per job set of int: TASK = 1..tasks; array [JOB,TASK] of int: d; % task durations int: total = sum(i in JOB, j in TASK)(d[i,j]);% total duration int: digs = ceil(log(10.0,total)); % digits for output array [JOB,TASK] of var 0..total: s; % start times var 0..total: end; % total end time % nooverlap predicate no_overlap(var int:s1, int:d1, var int:s2, int:d2) = s1 + d1 <= s2 \/ s2 + d2 <= s1; constraint %% ensure the tasks occur in sequence forall(i in JOB) ( forall(j in 1..tasks-1) (s[i,j] + d[i,j] <= s[i,j+1]) /\ s[i,tasks] + d[i,tasks] <= end ); constraint %% ensure no overlap of tasks forall(j in TASK) ( forall(i,k in JOB where i < k) ( no_overlap(s[i,j], d[i,j], s[k,j], d[k,j]) ) ); solve minimize end; output ["end = \(end)\n"] ++ [ show_int(digs,s[i,j]) ++ " " ++ if j == tasks then "\n" else "" endif | i in JOB, j in TASK ];