22,949 research outputs found
A note on exact algorithms for the identical parallel machine scheduling problem
A recently published paper by Mokotoff presents an exact algorithm for the classical P//Cmax scheduling problem, evaluating its average performance through computational experiments on a series of randomly generated test problems. It is shown that, on the same types of instances, an exact algorithm proposed 10 years ago by the authors of the present note outperforms the new algorithm by some orders of magnitud
A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines
This paper presents a novel idea for the general case of the Common Due-Date
(CDD) scheduling problem. The problem is about scheduling a certain number of
jobs on a single or parallel machines where all the jobs possess different
processing times but a common due-date. The objective of the problem is to
minimize the total penalty incurred due to earliness or tardiness of the job
completions. This work presents exact polynomial algorithms for optimizing a
given job sequence for single and identical parallel machines with the run-time
complexities of for both cases, where is the number of jobs.
Besides, we show that our approach for the parallel machine case is also
suitable for non-identical parallel machines. We prove the optimality for the
single machine case and the runtime complexities of both. Henceforth, we extend
our approach to one particular dynamic case of the CDD and conclude the chapter
with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page
Stochastic scheduling on unrelated machines
Two important characteristics encountered in many real-world scheduling problems are heterogeneous machines/processors and a certain degree of uncertainty about the actual sizes of jobs. The first characteristic entails machine dependent processing times of jobs and is captured by the classical unrelated machine scheduling model.The second characteristic is adequately addressed by stochastic processing times of jobs as they are studied in classical stochastic scheduling models. While there is an extensive but separate literature for the two scheduling models, we study for the first time a combined model that takes both characteristics into account simultaneously. Here, the processing time of job on machine is governed by random variable , and its actual realization becomes known only upon job completion. With being the given weight of job , we study the classical objective to minimize the expected total weighted completion time , where is the completion time of job . By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee . Here, is arbitrarily small, and is an upper bound on the squared coefficient of variation of the processing times. We show that the dependence of the performance guarantee on is tight, as we obtain a lower bound for the type of policies that we use. When jobs also have individual release dates , our bound is . Via , currently best known bounds for deterministic scheduling are contained as a special case
Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model
We consider online scheduling on multiple machines for jobs arriving
one-by-one with the objective of minimizing the makespan. For any number of
identical parallel or uniformly related machines, we provide a
competitive-ratio approximation scheme that computes an online algorithm whose
competitive ratio is arbitrarily close to the best possible competitive ratio.
We also determine this value up to any desired accuracy. This is the first
application of competitive-ratio approximation schemes in the online-list
model. The result proves the applicability of the concept in different online
models. We expect that it fosters further research on other online problems
Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling
This paper establishes performance guarantees for online algorithms that
schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the
expected total weighted completion time. Prior work on unrelated machine
scheduling with stochastic jobs was restricted to the offline case, and
required linear or convex programming relaxations for the assignment of jobs to
machines. The algorithms introduced in this paper are purely combinatorial. The
performance bounds are of the same order of magnitude as those of earlier work,
and depend linearly on an upper bound on the squared coefficient of variation
of the jobs' processing times. Specifically for deterministic processing times,
without and with release times, the competitive ratios are 4 and 7.216,
respectively. As to the technical contribution, the paper shows how dual
fitting techniques can be used for stochastic and nonpreemptive scheduling
problems.Comment: Preliminary version appeared in IPCO 201
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
Throughput Maximization in Multiprocessor Speed-Scaling
We are given a set of jobs that have to be executed on a set of
speed-scalable machines that can vary their speeds dynamically using the energy
model introduced in [Yao et al., FOCS'95]. Every job is characterized by
its release date , its deadline , its processing volume if
is executed on machine and its weight . We are also given a budget
of energy and our objective is to maximize the weighted throughput, i.e.
the total weight of jobs that are completed between their respective release
dates and deadlines. We propose a polynomial-time approximation algorithm where
the preemption of the jobs is allowed but not their migration. Our algorithm
uses a primal-dual approach on a linearized version of a convex program with
linear constraints. Furthermore, we present two optimal algorithms for the
non-preemptive case where the number of machines is bounded by a fixed
constant. More specifically, we consider: {\em (a)} the case of identical
processing volumes, i.e. for every and , for which we
present a polynomial-time algorithm for the unweighted version, which becomes a
pseudopolynomial-time algorithm for the weighted throughput version, and {\em
(b)} the case of agreeable instances, i.e. for which if and only
if , for which we present a pseudopolynomial-time algorithm. Both
algorithms are based on a discretization of the problem and the use of dynamic
programming
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