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Shop Scheduling
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SS16 MINIMUM TWO-PROCESSOR
-
I
NSTANCE
:
Number
of processors, set
J
of jobs, each
consisting
of a sequence of
operations
with
,
for each such operation a processor
and a length
.
-
S
OLUTION
:
A job shop schedule for
J
, i.e., a collection of one-processor schedules
such that
implies
and such
that
.
-
M
EASURE
:
The completion time of the schedule, i.e.,
.
-
Good News:
Approximable within
,
where
and
[
137
].
-
Bad News:
Not approximable within 5/4
for any
[
345
].
-
Comment:
Transformation from 3-P
ARTITION
.
Approximable within
if each job must be processed on each machine at most once
[
320
].
The variation in which the operations must be processed in an order
consistent to a particular partial order, and the variation in
which there are different types of machines, for each type, there are
a specified number of identical processors, and each operation may be
processed on any processor of the appropriate type,
are approximable within
[
320
].
-
Garey and Johnson:
SS18
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997