Online heuristic for the preemptive single machine scheduling problem of minimizing the total weighted completion time

Batsyn, Mikhail; Goldengorin, Boris; Pardalos, Pãnos M.; Sukhov, Pavel

doi:10.1080/10556788.2013.854360

Cited by 16 publications

(21 citation statements)

References 18 publications

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“…Meanwhile, the batch processing time P k of each batch is equal to the sum processing time of jobs which are assigned to this batch. Constraint set (5) guarantees that at most one part of each batch can be performed in each time slot. Constraint set (6) specifies the last P k th part of each batch is processed after its previous parts.…”

Section: Problem Formationmentioning

confidence: 99%

“…Brucker et al [6] gave an overview of new results on preemptive single-machine and parallel-machine scheduling problems in recent years. Recently, Batsyn et al [5] studied a preemptive single machine scheduling problem with arbitrary processing times and release dates, and their objective was to minimize the total weighted completion time. An efficient heuristic based on the Weighted Shortest Remaining Processing Time rule was proposed to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

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Preemptive scheduling in a two-stage supply chain to minimize the makespan

Pei

Fan

Pardalos

et al. 2014

Optimization Methods and Software

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This paper deals with the problem of preemptive scheduling in a two-stage supply chain framework. The supply chain environment contains two stages: production and transportation. In the production stage n jobs are processed on a manufacturer's bounded serial batching machine, preemptions are allowed, and set-up time is required before a new batch is processed. In the transportation stage each batch is delivered to a customer by a single vehicle. The objective is to minimize the makespan by making decisions for both mutually coordinated stages. Specifically, two versions are studied. The first one is that all jobs are available to be processed at time zero, and the second one is that jobs have different release times. An O(n log n) time algorithm is developed for the first version, and we show that it can produce the optimal schedule for the entire problem. For the second version, based on some useful properties we have designed an O(n log n) time heuristic and a novel lower bound. The worst-case performance ratio of our algorithm is bounded by 2. Our computational study with random instances of different scales shows high-quality solutions for either small-scale or large-scale instances returned in a reasonable PC times.

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Section: Problem Formationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Preemptive scheduling in a two-stage supply chain to minimize the makespan

Pei

Fan

Pardalos

et al. 2014

Optimization Methods and Software

Self Cite

View full text Add to dashboard Cite

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“…Total tardiness minimization is commonly reduced to solving a combinatorial problem. In particular, the well-known Boolean linear programming model [5,6] is used for that. Nevertheless, struggling to compute a schedule with the exactly minimal total tardiness may become very resource-consuming (implying processor clock speed, memory space, and time of computations) even for a few jobs divided into more than 10 processing periods [6].…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, struggling to compute a schedule with the exactly minimal total tardiness may become very resource-consuming (implying processor clock speed, memory space, and time of computations) even for a few jobs divided into more than 10 processing periods [6]. Thus, as the number of jobs and the numbers of their processing periods increase, the exact solution of the total tardiness minimization problem may become practically intractable [5,7,8]. The problem of tractability can be slightly stretched and strengthened by using an optimal substitute for infinity in the Boolean linear programming model [9] and re-arranging jobs for either job ascending order input or job descending order input [6,10,11].…”

Section: Introductionmentioning

confidence: 99%

“…Along with obtaining an exact solution, there are a lot of heuristics allowing to find an approximate solution, which often coincides with the exact one and ensures thus the minimal total tardiness also [3,8,11,12]. In general, the heuristics operate with the remaining available period [8,12], remaining slack [3,8,11], and remaining processing period [5,8,11,12]. A heuristic, in which the decisive ratio is the reciprocal of the maximum of a pair of the remaining processing period (RPP) and remaining available period (RAP) [8], is closely the best one [12,13].…”

Section: Introductionmentioning

confidence: 99%

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A Sorting Improvement in the Heuristic Based on Remaining Available and Processing Periods to Minimize Total Tardiness in Progressive Idling-Free 1-Machine Preemptive Scheduling

Romanuke

2021

KPI SN

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Background. In preemptive job scheduling, which is a part of the flow-shop sequencing tasks, one of the most crucial goals is to obtain a schedule whose total tardiness would be minimal. Total tardiness minimization is commonly reduced to solving a combinatorial problem which becomes practically intractable as the number of jobs and the numbers of their processing periods increase. To cope with this challenge, heuristics are used. A heuristic, in which the decisive ratio is the reciprocal of the maximum of a pair of the remaining processing period and remaining available period, is closely the best one. However, the heuristic may produce schedules of a few jobs whose total tardiness is 25 % greater than the minimum or even worse. Therefore, this heuristic needs a corrective branch which would further try to minimize total tardiness under certain conditions. Objective. The goal is to ascertain what is to be corrected in the heuristic so that the total tardiness value could be obtained lesser. The heuristic will be applied to tight-tardy progressive idling-free 1-machine preemptive scheduling, where the release dates are given in ascending order starting from 1 to the number of jobs, and the due dates are tightly set after the release dates. In this scheduling problem, the inaccuracy of finding the minimal total tardiness has the strongest negative impact, so this is almost the worst case, which defines the accuracy limit of the heuristic and positively serves just as the principle of minimax guaranteeing decreasing losses in the worst conditions. Methods. The heuristic sorts maximal decisive ratios by release dates, where the scheduling preference is given to the earliest job. To achieve the said goal, three other sorting approaches are presented and a computational study is carried out with applying each of the four heuristic approaches to minimize total tardiness. For this, two series of 266000 and 1064000 scheduling problems are generated. Results. The earliest-job sorting ensures a heuristically minimal total tardiness value in more than 97.6 % of scheduling problems, but it fails to minimize total tardiness in no less than 2.2 % of the cases. Nevertheless, a sorting approach with minimizing remaining processing periods produces a heuristically minimal total tardiness for almost any scheduling problem. If an exception occurs, this sorting approach “loses” to the other sorting approaches very little. Moreover, the exceptions are quite rare as it has been registered just a one scheduling problem (out of 31914 cases followed by a sole “win” of a heuristic version) whose minimal total tardiness is achieved by the earliest-job sorting. Conclusions. The best heuristic version is that one which uses the sorting approach with minimizing remaining processing periods. This, however, is confirmed only for the case where jobs do not have any priorities. The case when jobs have their priority weights is to be yet analyzed.

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Analysis of Optimal Solutions to the Problem of a Single Machine with Preemption

Chernykh

Servakh

2021

Communications in Computer and Information Science

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Online heuristic for the preemptive single machine scheduling problem of minimizing the total weighted completion time

Cited by 16 publications

References 18 publications

Preemptive scheduling in a two-stage supply chain to minimize the makespan

Preemptive scheduling in a two-stage supply chain to minimize the makespan

A Sorting Improvement in the Heuristic Based on Remaining Available and Processing Periods to Minimize Total Tardiness in Progressive Idling-Free 1-Machine Preemptive Scheduling

Analysis of Optimal Solutions to the Problem of a Single Machine with Preemption

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