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tively. The entries in Table 1 are average values over
20 instances.
The results show that the presented heuristic per-
forms very well for the entire collection of instances.
We observe that δ decreases with the increase in the
number of jobs. On average δ = 1.79%, 0.52%,
0.45%, 0.29%, 0.15% and 0.15% for problems with
20, 40, 60, 80, 100, and 120 jobs, respectively. The
CPU time of the heuristic grows with the number of
jobs. This increase is more significant for the CG al-
gorithm than for the GA. The number of machines
does not seem to affect significantly the computation
time of the heuristic, however, we observe that in the
case of 2 machines the CG algorithm consumes less
CPU seconds than in the cases of 3 and 4 machines.
7 CONCLUSIONS
In this paper a heuristic combining the column gener-
ation algorithm with the genetic algorithm for solving
the two-stage flowshop preemptive scheduling prob-
lem with parallel unrelated machines and resource
constraints at the first stage, and a single machine at
the second stage has been developed. The heuristic
has been tested as to its effectiveness in finding a min-
imum makespan schedule and as to its computation
time. The obtained results indicate that for problems
with a large number of jobs the heuristic usually finds
schedules with makespan close to the optimal value
in reasonable computation time.
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PREEMPTIVE SCHEDULING IN A TWO-STAGE MULTIPROCESSOR FLOWSHOP WITH RESOURCE
CONSTRAINTS
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