187 research outputs found
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Single machine scheduling with a generalized job-dependent cumulative effect
We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time
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Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance
We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants
An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint
In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS)
Parallel-machine scheduling with simple linear deterioration to minimize total completion time
2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
Order Acceptance and Scheduling: A Taxonomy and Review
Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area
Scheduling linear deteriorating jobs with an availability constraint on a single machine
2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
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
FPTAS for half-products minimization with scheduling applications
Cataloged from PDF version of article.A special class of quadratic pseudo-boolean functions called “half-products” (HP) has recently been introduced. It has been
shown that HP minimization, while NP-hard, admits a fully polynomial time approximation scheme (FPTAS). In this note, we
provide a more efficient FPTAS. We further show how an FPTAS can also be derived for the general case where the HP function is
augmented by a problem-dependent constant and can justifiably be assumed to be nonnegative. This leads to an FPTAS for certain
partitioning type problems, including many from the field of scheduling.
c 2008 Elsevier B.V. All rights reserved
An FPTAS for scheduling with piecewise linear decreasing processing times to minimize makespan
Author name used in this publication: T. C. E. Cheng2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe
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