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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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TL;DR: A one-machine scheduling model wheren different jobs are classified intoK groups depending on which additional resource they require is analyzed and a polynomial time solution algorithm is given that runs in O(n logn) time.
Abstract: In this paper a one-machine scheduling model is analyzed wheren different jobs are classified intoK groups depending on which additional resource they require. The change-over time from one job to another consists of the removal time or of the set-up time of the two jobs. It is sequence-dependent in the sense that the change-over time is determined by whether or not the two jobs belong to the same group. The objective is to minimize the makespan. This problem can be modeled as an asymmetric Traveling Salesman Problem (TSP) with a specially structured distance matrix. For this problem we give a polynomial time solution algorithm that runs in O(n logn) time. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

26 citations

Journal ArticleDOI
TL;DR: This result generalizes the well-known "ratio rule" of W. E. Smith for minimizing total weighted completion time and is applicable to problems involving discounted linear delay costs, discounted linear processing Costs, discounted resetting and processing costs and linear combinations of these costs.
Abstract: Suppose n jobs are to be processed consecutively by a single machine, without interruption and without idle time. Each job j has a known processing time pj and has associated with it a time-varying cost density function cj. The cost of processing job j in the time interval [t-pj, t] is Cjt = ∫t-pjtcjudu. We show that if the cost density functions of the jobs satisfy certain simple conditions, a sequence minimizing total cost is easily obtained. This result generalizes the well-known "ratio rule" of W. E. Smith for minimizing total weighted completion time and is applicable to problems involving discounted linear delay costs, discounted linear processing costs, discounted resetting and processing costs, and linear combinations of these costs. Moreover, we show that for such costs, sequences that are optimal subject to series parallel precedence constraints can be found in 0n log n time.

26 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide optimal algorithms to solve a new scheduling problem in which there is a possibility that a disruption will happen at a particular time and last for a period of time with a certain probability.

26 citations

Journal ArticleDOI
TL;DR: This work investigates a single-machine problem with two-scenario-based processing times, where the goal is to minimize the maximum total completion times over two scenarios, and proposes seven low level heuristics to solve this problem.
Abstract: Many practical productions are full of significant uncertainties. For example, the working environment may change, machines may breakdown, workers may become unstable, etc. In such an environment, job processing times should not be fixed numbers. In light of this situation, we investigate a single-machine problem with two-scenario-based processing times, where the goal is to minimize the maximum total completion times over two scenarios. When the uncertainty of the job processing times is confronted, the robust version of this problem is NP-hard, even for very restricted cases. To solve this problem, we derive some dominance rules and a lower bound for developing branch-and-bound algorithms to find optimal solutions. As for determining approximate solutions, we propose five heuristics, adopting combined two-scenario-based dependent processing times, to produce initial solutions and then improve each with a pairwise interchange. Further, we propose a simulated annealing hyper-heuristic incorporating the proposed seven low level heuristics to solve this problem as well. Finally, the performances of all proposed algorithms are tested and reported.

26 citations

Journal ArticleDOI
TL;DR: In this article, the authors use interval number theory for renewable energy in uncertainty modelling and propose two interval single-machine scheduling problems, and derive Pareto-optimal solutions of the bi-objective optimisation problem,, using the lexicographic-weighted Tchebycheff method.
Abstract: Carbon dioxide (CO2) in particular is by far the primary driver of global warming. One of the most effective ways to reduce CO2 emissions is to increase the amount of power from renewable energy. A key challenge in utilising renewable energies, such as wind and solar, is their uncertainty in terms of when and to what degree and force renewable energies will become available next time. This study uses interval number theory for renewable energy in uncertainty modelling and proposes two novel interval single-machine scheduling problems, and . A solution procedure is formulated to optimise these problems with interval numbers using interval arithmetic. Additionally, this study derives Pareto-optimal solutions of the bi-objective optimisation problem, , using the lexicographic-weighted Tchebycheff method. Some managerial implications are obtained by parameter analysis. Analytical results offer decision-makers an intuitive view of how these factors impact scheduling results and provide practical guidelines for...

26 citations


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