Tropical optimization problems in time-constrained project scheduling

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Tropical optimization problems in time-constrained project scheduling. / Krivulin, N.

In: Optimization, Vol. 66, No. 2, 2017, p. 205-224.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{2de8ae45b8c54a0a95d4d6d62f7021f4,

title = "Tropical optimization problems in time-constrained project scheduling",

abstract = "We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and finish-start precedence relationships, release times, deadlines and due dates. Scheduling problems are formulated to find optimal schedules for the project with respect to different objective functions to be minimized, such as the project makespan, the maximum deviation from the due dates, the maximum flow-time and the maximum deviation of finish times. We represent these problems as optimization problems in terms of tropical mathematics, and then solve them by applying direct solution methods of tropical optimization. As a result, new direct solutions of the scheduling problems are obtained in a compact vector form, which is ready for further analysis and practical implementation. The solutions are illustrated by simple numerical examples.",

keywords = "idempotent semifield, optimization problem, project scheduling, precedence relationship, scheduling objective",

author = "N. Krivulin",

year = "2017",

doi = "10.1080/02331934.2016.1264946",

language = "English",

volume = "66",

pages = "205--224",

journal = "Optimization",

issn = "0233-1934",

publisher = "Taylor & Francis",

number = "2",

}

RIS

TY - JOUR

T1 - Tropical optimization problems in time-constrained project scheduling

AU - Krivulin, N.

PY - 2017

Y1 - 2017

N2 - We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and finish-start precedence relationships, release times, deadlines and due dates. Scheduling problems are formulated to find optimal schedules for the project with respect to different objective functions to be minimized, such as the project makespan, the maximum deviation from the due dates, the maximum flow-time and the maximum deviation of finish times. We represent these problems as optimization problems in terms of tropical mathematics, and then solve them by applying direct solution methods of tropical optimization. As a result, new direct solutions of the scheduling problems are obtained in a compact vector form, which is ready for further analysis and practical implementation. The solutions are illustrated by simple numerical examples.

AB - We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and finish-start precedence relationships, release times, deadlines and due dates. Scheduling problems are formulated to find optimal schedules for the project with respect to different objective functions to be minimized, such as the project makespan, the maximum deviation from the due dates, the maximum flow-time and the maximum deviation of finish times. We represent these problems as optimization problems in terms of tropical mathematics, and then solve them by applying direct solution methods of tropical optimization. As a result, new direct solutions of the scheduling problems are obtained in a compact vector form, which is ready for further analysis and practical implementation. The solutions are illustrated by simple numerical examples.

KW - idempotent semifield

KW - optimization problem

KW - project scheduling

KW - precedence relationship

KW - scheduling objective

UR - https://arxiv.org/abs/1502.06222

U2 - 10.1080/02331934.2016.1264946

DO - 10.1080/02331934.2016.1264946

M3 - Article

VL - 66

SP - 205

EP - 224

JO - Optimization

JF - Optimization

SN - 0233-1934

IS - 2

ER -

ID: 7733254