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Single-machine scheduling

About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.


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Journal ArticleDOI
TL;DR: An O(n2 log n) time algorithm is proposed to solve the single-machine common due-window assignment scheduling problem with deteriorating jobs to minimize the weighted sum of earliness, tardiness and due- window location penalties.
Abstract: In this paper, we consider a single-machine common due-window assignment scheduling problem with deteriorating jobs. Jobs’ processing times are defined by function of their starting times and job-dependent deterioration rates that are related to jobs and are not all equal. The objective is to determine an optimal combination of sequence and common due-window location so as to minimize the weighted sum of earliness, tardiness and due-window location penalties. We propose an O(n2 log n) time algorithm to solve the problem and discuss several instances to illustrate it.

17 citations

Book ChapterDOI
05 Apr 2011
TL;DR: This paper addresses the problem of single machine scheduling in which due to some constraints like capacity, rejection of a set of jobs is accepted, and suggests the application of Lorenz-dominance to an adapted bi-objective simulated annealing algorithm.
Abstract: Scheduling problems have been studied from many years ago. Most of the papers which were published in this domain are different in one or many of issues as following: objective functions, machine environment, constraints and methodology for solving the problems. In this paper we address the problem of single machine scheduling in which due to some constraints like capacity, rejection of a set of jobs is accepted. The problem is considered as bi-objective one: minimization of the sum of weighted completion times for the accepted jobs and minimization of the sum of penalties for the rejected jobs. We find that in this problem, the solutions are not handled in a satisfactory way by general Paretodominance rule, so we suggest the application of Lorenz-dominance to an adapted bi-objective simulated annealing algorithm. Finally we justify the use of Lorenz-dominance as a useful refinement of Pareto-dominance by comparing the results.

17 citations

Book
01 Jan 1998
TL;DR: Efficient approximation algorithms for some NP-Hard deterministic machine scheduling and related problems are described and several approximability and inapproximability results are obtained that include a PTAS for vector scheduling when the dimension is fixed.
Abstract: This thesis describes efficient approximation algorithms for some NP-Hard deterministic machine scheduling and related problems. An approximation algorithm for an NP-Hard optimization problem is a polynomial time algorithm which, given any instance of the problem, returns a solution whose value is within some guaranteed multiplicative factor of the optimal solution value for that instance. The factor is called the approximation ratio of the algorithm. A typical problem in machine scheduling consists of a set of jobs that are to be executed on a set of available machines subject to a variety of constraints. Two common objectives are minimizing makespan (the time to complete all jobs) and minimizing average completion time. Constraints that we study include precedence constraints and release dates. Brief descriptions of the problems we study and highlights of our results follow. (1) Minimizing average completion time and its weighted generalization for single and parallel machine problems. We introduce new techniques that either improve earlier results and/or result in simple and efficient approximation algorithms. For single machine scheduling we obtain an e/$(e - 1)$ approximation with release dates only and a 2 approximation with precedence constraints only. We give an algorithm that converts an x approximate single machine schedule into a $(2x + 2)$ approximate parallel machine schedule. The conversion algorithm is simple and yields efficient algorithms for several variants. (2) Minimizing makespan on machines with different speeds when jobs have precedence constraints. We obtain an $O(\log m)$ approximation (m is the number of machines) in $O(n\sp3)$ time. (3) Scheduling pipelined operator trees. This belongs to a class of new scheduling problems that arise from query optimization in parallel databases. The novel aspect consists of modeling communication costs between operators in a task system representing a query execution plan. We obtain a PTAS for this problem. We also obtain simpler $O(n \log n)$ time algorithms that have ratios of 3.56 and 2.58 respectively. (4) Multi-dimensional generalizations of three well known problems in combinatorial optimization: multi-processor scheduling, bin packing, and the knapsack problems. We obtain several approximability and inapproximability results that include a PTAS for vector scheduling when the dimension is fixed.

17 citations

Journal ArticleDOI
TL;DR: The unrestricted case is shown to be equivalent to a polynomial time solvable problem, whereas the restricted case is shows to be NP-hard, and suggestions are made for further research.
Abstract: The purpose of this paper is to analyse a special case of the non-pre-emptive single machine scheduling problem where the distinct due dates for each job are related to processing times according to the Equal–Slack rule. The scheduling objective is to minimize the sum of earliness and tardiness penalties. After determining some properties of the problem, the unrestricted case is shown to be equivalent to a polynomial time solvable problem, whereas the restricted case is shown to be NP-hard, and suggestions are made for further research.

17 citations

Journal ArticleDOI
TL;DR: An approach to developing a fast fully polynomial-time approximation scheme (FPTAS) for the single machine scheduling problem to minimize the total weighted earliness and tardiness about a nonrestrictive common due date.
Abstract: 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 constant.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202333
202270
202188
202083
201972
201889