I
NSTANCE
:
Set
J
of activities, a directed acyclic graph defining precedence
constraints for the activities, a positive budget
B
, and for each activity
a non-increasing cost function
described as a step function
with
steps:
where
.
S
OLUTION
:
A one-processor schedule for
J
that obeys the precedence constraints and
activities durations
for each
that obeys the budget, i.e.
.
M
EASURE
:
The total duration of all activities, i.e.,
.
Good News:
Approximable within
, where
f
is the ratio of the maximum
allowed duration of any activity to the minimum allowed non-zero duration of
any activity [
325
].
Comment:
Variation in which
for all
i,j
is approximable within
3/2 but not approximable within
for any
[
325
].