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SS15 MINIMUM FLOW-SHOP
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Shop Scheduling
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Shop Scheduling
-
I
NSTANCE
:
Number
of processors, set
J
of jobs, each
consisting
of
m
operations
with
(with
to be
executed by processor
i
), and for each operation a length
.
-
S
OLUTION
:
An open-shop schedule for
J
, i.e., a collection of one-processor schedules
,
, such that
implies
, such that for each
the
intervals
are all disjoint.
-
M
EASURE
:
The completion time of the schedule, i.e.,
.
-
Good News:
Approximable within 2 [
250
].
-
Bad News:
Not approximable within 5/4
for any
[
345
].
-
Comment:
Approximable within 3/2 if
m=3
[
70
].
Variation in which
m=2
, but the two processors are replaced by
respectively
and
identical parallel processors, is
approximable within 3/2 if
, 5/3 if
and
otherwise [
71
].
-
Garey and Johnson:
SS14
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997