463 research outputs found
A fast FPTAS for single machine scheduling problem of minimizing total weighted earliness and tardiness about a large common due date
We address the single machine scheduling problem to minimize the total weighted earliness and tardiness about a nonrestrictive common due date. This is a basic problem with applications to the just-in-time manufacturing. The problem is linked to a Boolean programming problem with a quadratic objective function, known as the half-product. An approach to developing a fast fully polynomial-time approximation scheme (FPTAS) for the problem is identified and implemented. The running time matches the best known running time for an FPTAS for minimizing a half-product with no additive constan
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
Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments
In the current work we introduce a novel estimation of distribution algorithm
to tackle a hard combinatorial optimization problem, namely the single-machine
scheduling problem, with uncertain delivery times. The majority of the existing
research coping with optimization problems in uncertain environment aims at
finding a single sufficiently robust solution so that random noise and
unpredictable circumstances would have the least possible detrimental effect on
the quality of the solution. The measures of robustness are usually based on
various kinds of empirically designed averaging techniques. In contrast to the
previous work, our algorithm aims at finding a collection of robust schedules
that allow for a more informative decision making. The notion of robustness is
measured quantitatively in terms of the classical mathematical notion of a norm
on a vector space. We provide a theoretical insight into the relationship
between the properties of the probability distribution over the uncertain
delivery times and the robustness quality of the schedules produced by the
algorithm after a polynomial runtime in terms of approximation ratios
Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product
We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizing the total weighted flow time with controllable processing times, minimizing the makespan with controllable release dates, minimizing the total weighted flow time for two models of scheduling with rejection
04231 Abstracts Collection -- Scheduling in Computer and Manufacturing Systems
During 31.05.-04.06.04, the Dagstuhl Seminar 04231 "Scheduling in Computer and Manufacturing Systems" was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
Minimizing weighted mean absolute deviation of job completion times from their weighted mean
Cataloged from PDF version of article.We address a single-machine scheduling problem where the objective is to minimize the
weighted mean absolute deviation of job completion times from their weighted mean. This
problem and its precursors aim to achieve the maximum admissible level of service equity.
It has been shown earlier that the unweighted version of this problem is NP-hard in the
ordinary sense. For that version, a pseudo-polynomial time dynamic program and a 2-
approximate algorithm are available. However, not much (except for an important solution
property) exists for the weighted version. In this paper, we establish the relationship
between the optimal solution to the weighted problem and a related one in which the deviations
are measured from the weighted median (rather than the mean) of the job completion
times; this generalizes the 2-approximation result mentioned above. We proceed to
give a pseudo-polynomial time dynamic program, establishing the ordinary NP-hardness
of the problem in general. We then present a fully-polynomial time approximation scheme
as well. Finally, we report the findings from a limited computational study on the heuristic
solution of the general problem. Our results specialize easily to the unweighted case; they
also lead to an approximation of the set of schedules that are efficient with respect to both
the weighted mean absolute deviation and the weighted mean completion time.
2011 Elsevier Inc. All rights reserved
Approximation Algorithms and an FPTAS for the Single Machine Problem with Biased Tardiness Penalty
This paper addresses a new performance measure for scheduling problems, entitled “biased tardiness penalty.” We study the approximability of minimum biased tardiness on a single machine, provided that all the due dates are equal. Two heuristic algorithms are developed for this problem, and it is shown that one of them has a worst-case ratio bound of 2. Then, we propose a dynamic programming algorithm and use it to design an FPTAS. The FPTAS is generated by cleaning up some states in the dynamic programming algorithm, and it requires On3/ε time
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