Minimizing the maximum lateness on a single machine with raw material constraints by branch-and-cut

Györgyi, Péter; Kis, Tamás

doi:10.1016/j.cie.2017.11.016

Cited by 12 publications

(10 citation statements)

References 20 publications

(21 reference statements)

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“…The first problem that we consider is 1|rm = 1, a j = 1| C j . The complexity of this problem was posed as an open question in [11]. We show that the problem is NP-hard in the strong sense.…”

Section: Our Resultsmentioning

confidence: 95%

“…, n, and M = j∈J a j /n is an integer, was considered in [2]. Recently, Györgyi and Kis [11] gave polynomial time algorithms for several special cases, and also showed that the problem remains weakly NP-hard even under the very strong assumption that the processing time, the resource requirement and the weight are the same for each job. They also provided a 2-approximation algorithm for this variant, and a polynomial-time approximation scheme (PTAS) when the number of resource arrival times is a constant and the processing time equals the weight for each job, while the resource requirements are arbitrary.…”

Section: Introductionmentioning

confidence: 99%

“…In a series of papers [6,7,8,9,10], Györgyi and Kis presented approximation schemes and inapproximability results both for single and parallel machine problems with the makespan and the maximum lateness objectives. In [11], they proposed a bracnh-and-cut algorithm for minimizing the maximum lateness.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scheduling with Non-Renewable Resources: Minimizing the Sum of Completion Times

Bérczi¹,

Király²,

Omlor³

2019

Preprint

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The paper considers single-machine scheduling problems with a non-renewable resource. In this setting, we are given a set jobs, each of which is characterized by a processing time, a weight, and the job also has some resource requirement. At fixed points in time, a certain amount of the resource is made available to be consumed by the jobs. The goal is to assign the jobs non-preemptively to time slots on the machine, so that at any time their resource requirement does not exceed the available amounts of resources. The objective that we consider here is the minimization of the sum of weighted completion times.We give polynomial approximation algorithms and complexity results for single scheduling machine problems. In particular, we show strong NP-hardness of the case of unit resource requirements and weights (1|rm = 1, a j = 1| C j ), thus answering an open question of Györgyi and Kis. We also prove that the schedule corresponding to the Shortest Processing Time First ordering provides a 3/2-approximation for the same problem. We give simple constant factor approximations and a more complicated PTAS for the case of 0 processing times (1|rm = 1, p j = 0| w j C j ). We close the paper by proposing a new variant of the problem in which the resource arrival times are unknown. A 4-approximation is presented for this variant, together with an (4 − ε)-inapproximability result.

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Section: Our Resultsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Scheduling with Non-Renewable Resources: Minimizing the Sum of Completion Times

Bérczi¹,

Király²,

Omlor³

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…The first problem that we consider is 1|rm = 1, a j = 1| C j . The complexity of this problem was posed as an open question in [12]. We show that the problem is NP-hard in the strong sense.…”

Section: Introductionmentioning

confidence: 95%

“…In a series of papers [7][8][9][10][11], Györgyi and Kis presented approximation schemes and inapproximability results both for single and parallel machine problems with the makespan and the maximum lateness objectives. In [12], they proposed a branch-and-cut algorithm for minimizing the maximum lateness.…”

Section: Introductionmentioning

confidence: 99%

Scheduling with Non-renewable Resources: Minimizing the Sum of Completion Times

Bérczi

Király

Omlor

2020

Lecture Notes in Computer Science

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We consider single-machine scheduling problems with a nonrenewable resource. In this setting, there are n jobs, each characterized by a processing time, a weight, and a resource requirement. At given points in time, certain amounts of the resource are made available to be consumed by the jobs. The goal is to assign the jobs non-preemptively to time slots on the machine, so that each job has the required resource amount available at the start of its processing. We consider the objective of minimizing the weighted sum of completion times.The main contribution of the paper is a PTAS for the case of 0 processing times (1|rm = 1, pj = 0| wjCj). In addition, we show strong NP-hardness of the case of unit resource requirements and weights (1|rm = 1, aj = 1| Cj), thus answering an open question of Györgyi and Kis. We also prove that the schedule corresponding to the Shortest Processing Time First ordering provides a 3/2-approximation for the latter problem.

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An agent-based heuristics optimisation model for production scheduling of make-to-stock connector plates manufacturing systems

Madi,

Al-Bazi,

Buckley

et al. 2023

Soft Comput

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The manufacturing systems’ success directly relates to their accurate, reliable and flexible schedules, including how production is planned and scheduled and which constraints are considered in generating the schedules. The study's objective arises from the need to generate an optimal production scheduling system in a connecting plates manufacturing company that works on a Make-To-Stock basis. This research investigates the impact of demand and operational constraints on production schedules, including the facility capacity, operators and machines availability, raw materials availability, inventory level and warehouse capacity. A multi-agent-based optimisation model is developed to face the complexity of considering demand and operational constraints and reflects their impact on generating a reliable production schedule. This model involves a proposed heuristic algorithm that considers demand and operations constraints in such a manufacturing environment and optimises the production schedule based on these restrictions/requirements. A real-life case study based on a connecting plates manufacturer company is used as a test bench of the proposed agent-based heuristic optimisation model. The proposed algorithm is compared with other related approaches to check its superiority based on key criteria, including inventory levels, missed/unsatisfied orders and total production time. Results show that the proposed heuristics algorithm reduced the number of missed orders by 34% compared with similar approaches.

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Minimizing the maximum lateness on a single machine with raw material constraints by branch-and-cut

Cited by 12 publications

References 20 publications

Scheduling with Non-Renewable Resources: Minimizing the Sum of Completion Times

Scheduling with Non-Renewable Resources: Minimizing the Sum of Completion Times

Scheduling with Non-renewable Resources: Minimizing the Sum of Completion Times

An agent-based heuristics optimisation model for production scheduling of make-to-stock connector plates manufacturing systems

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