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

ПОСТРОЕНИЕ РАСПИСАНИЙ ДЛЯ ОДНОСТАДИЙНЫХ СИСТЕМ ОБСЛУЖИВАНИЯ

Приведен обзор результатов, полученных в лаборатории математической кибернетики ОИПИ НАН наук Беларуси по решению задач теории расписаний для одностадийных детерминированных систем обслуживания

Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems

NP-hard cases of the single-item capacitated lot-sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist, by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave backlogging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models

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

A faster fully polynomial approximation scheme for the single-machine total tardiness problem

Lawler [E.L. Lawler, A fully polynomial approximation scheme for the total tardiness problem, Operations Research Letters 1 (1982) 207-208] proposed a fully polynomial approximation scheme for the single-machine total tardiness problem which runs in time (where n is the number of jobs and [epsilon] is the desired level of approximation). A faster fully polynomial approximation scheme running in time is presented in this note by applying an alternative rounding scheme in conjunction with implementing Kovalyov's [M.Y. Kovalyov, Improving the complexities of approximation algorithms for optimization problems, Operations Research Letters 17 (1995) 85-87] bound improvement procedure.Single-machine sequencing Total tardiness Fully polynomial approximation