7 research outputs found
Minimizing total completion time subject to job release dates and preemption penalties
2004-2005 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
Dynamic Windows Scheduling with Reallocation
We consider the Windows Scheduling problem. The problem is a restricted
version of Unit-Fractions Bin Packing, and it is also called Inventory
Replenishment in the context of Supply Chain. In brief, the problem is to
schedule the use of communication channels to clients. Each client ci is
characterized by an active cycle and a window wi. During the period of time
that any given client ci is active, there must be at least one transmission
from ci scheduled in any wi consecutive time slots, but at most one
transmission can be carried out in each channel per time slot. The goal is to
minimize the number of channels used. We extend previous online models, where
decisions are permanent, assuming that clients may be reallocated at some cost.
We assume that such cost is a constant amount paid per reallocation. That is,
we aim to minimize also the number of reallocations. We present three online
reallocation algorithms for Windows Scheduling. We evaluate experimentally
these protocols showing that, in practice, all three achieve constant amortized
reallocations with close to optimal channel usage. Our simulations also expose
interesting trade-offs between reallocations and channel usage. We introduce a
new objective function for WS with reallocations, that can be also applied to
models where reallocations are not possible. We analyze this metric for one of
the algorithms which, to the best of our knowledge, is the first online WS
protocol with theoretical guarantees that applies to scenarios where clients
may leave and the analysis is against current load rather than peak load. Using
previous results, we also observe bounds on channel usage for one of the
algorithms.Comment: 6 figure
Split Scheduling with Uniform Setup Times
We study a scheduling problem in which jobs may be split into parts, where
the parts of a split job may be processed simultaneously on more than one
machine. Each part of a job requires a setup time, however, on the machine
where the job part is processed. During setup a machine cannot process or set
up any other job. We concentrate on the basic case in which setup times are
job-, machine-, and sequence-independent. Problems of this kind were
encountered when modelling practical problems in planning disaster relief
operations. Our main algorithmic result is a polynomial-time algorithm for
minimising total completion time on two parallel identical machines. We argue
why the same problem with three machines is not an easy extension of the
two-machine case, leaving the complexity of this case as a tantalising open
problem. We give a constant-factor approximation algorithm for the general case
with any number of machines and a polynomial-time approximation scheme for a
fixed number of machines. For the version with objective minimising weighted
total completion time we prove NP-hardness. Finally, we conclude with an
overview of the state of the art for other split scheduling problems with job-,
machine-, and sequence-independent setup times
Split scheduling with uniform setup times
We study a scheduling problem in which jobs
may be split into parts, where the parts of a split job may be
processed simultaneously on more than one machine. Each
part of a job requires a setup time, however, on the machine
where the job part is processed. During setup, a machine
cannot process or set up any other job. We concentrate on
the basic case in which setup times are job-, machine- and
sequence-independent. Problems of this kind were encountered
when modelling practical problems in planning dis-
aster relief operations. Our main algorithmic result is a
polynomial-time algorithm for minimising total completion
time on two parallel identical machines. We argue, why the
same problem with threemachines is not an easy extension of
the two-machine case, leaving the complexity of this case as a
tantalising open problem. We give a constant-factor approximation
algorithm for the general case with any number of
machines and a polynomial-time approximation scheme for
a fixed number of machines. For the version with the objective
to minimise total weighted completion time, we prove
NP-hardness. Finally, we conclude with an overview of the
state of the art for other split scheduling problems with job-,
machine- and sequence-independent setup times
Strong LP formulations for scheduling splittable jobs on unrelated machines
International audienceA natural extension of the makespan minimization problem on unrelated machines is to allow jobs to be partially processed by different machines while incurring an arbitrary setup time. In this paper we present increasingly stronger LP-relaxations for this problem and their implications on the approximability of the problem. First we show that the straightforward LP, extending the approach for the original problem, has an integrality gap of 3 and yields an approximation algorithm of the same factor. By applying a lift-and-project procedure, we are able to improve both the integrality gap and the implied approximation factor to 1+Ï1+Ï , where ÏÏ is the golden ratio. Since this bound remains tight for the seemingly stronger machine configuration LP, we propose a new job configuration LP that is based on an infinite continuum of fractional assignments of each job to the machines. We prove that this LP has a finite representation and can be solved in polynomial time up to any accuracy. Interestingly, we show that our problem cannot be approximated within a factor better than eeâ1â1.582(unless =)eeâ1â1.582(unless P=NP) , which is larger than the inapproximability bound of 1.5 for the original problem
A survey of scheduling problems with setup times or costs
Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
Approximate feasibility in real-time scheduling: Speeding up in order to meet deadlines
Stougie, L. [Promotor]Marchetti-Spaccamela, A. [Promotor