370 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
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
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
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
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
Single machine scheduling with exponential time-dependent learning effect and past-sequence-dependent setup times
AbstractIn this paper we consider the single machine scheduling problem with exponential time-dependent learning effect and past-sequence-dependent (p-s-d) setup times. By the exponential time-dependent learning effect, we mean that the processing time of a job is defined by an exponent function of the total normal processing time of the already processed jobs. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions
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
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
From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
The next few years will be exciting as prototype universal quantum processors
emerge, enabling implementation of a wider variety of algorithms. Of particular
interest are quantum heuristics, which require experimentation on quantum
hardware for their evaluation, and which have the potential to significantly
expand the breadth of quantum computing applications. A leading candidate is
Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates
between applying a cost-function-based Hamiltonian and a mixing Hamiltonian.
Here, we extend this framework to allow alternation between more general
families of operators. The essence of this extension, the Quantum Alternating
Operator Ansatz, is the consideration of general parametrized families of
unitaries rather than only those corresponding to the time-evolution under a
fixed local Hamiltonian for a time specified by the parameter. This ansatz
supports the representation of a larger, and potentially more useful, set of
states than the original formulation, with potential long-term impact on a
broad array of application areas. For cases that call for mixing only within a
desired subspace, refocusing on unitaries rather than Hamiltonians enables more
efficiently implementable mixers than was possible in the original framework.
Such mixers are particularly useful for optimization problems with hard
constraints that must always be satisfied, defining a feasible subspace, and
soft constraints whose violation we wish to minimize. More efficient
implementation enables earlier experimental exploration of an alternating
operator approach to a wide variety of approximate optimization, exact
optimization, and sampling problems. Here, we introduce the Quantum Alternating
Operator Ansatz, lay out design criteria for mixing operators, detail mappings
for eight problems, and provide brief descriptions of mappings for diverse
problems.Comment: 51 pages, 2 figures. Revised to match journal pape
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