Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost

Wang, Yichun; Wang, Sihan; Wang, Ji-Bo

doi:10.3390/math11010222

Cited by 9 publications

(3 citation statements)

References 23 publications

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“…Other recently related studies can be found in Zhang et al [12], Masadeh et al [13], Zhang et al [14], Kim and Kim [15], Valouxis et al [16], and Wang et al [17] among many others.…”

Section: Notation Terminology P Jmentioning

confidence: 91%

Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs

2023

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We consider the scheduling of jobs with multiple weights on a single machine for minimizing the total weighted number of tardy jobs. In this setting, each job has m weights (or equivalently, the jobs have m weighting vectors), and thus we have m criteria, each of which is to minimize the total weighted number of tardy jobs under a corresponding weighting vector of the jobs. For this scheduling model, the feasibility problem aims to find a feasible schedule such that each criterion is upper bounded by its threshold value, and the Pareto scheduling problem aims to find all the Pareto-optimal points and for each one a corresponding Pareto-optimal schedule. Although the two problems have not been studied before, it is implied in the literature that both of them are unary NP-hard when m is an arbitrary number. We show in this paper that, in the case where m is a fixed number, the two problems are solvable in pseudo-polynomial time, the feasibility problem admits a dual-fully polynomial-time approximation scheme, and the Pareto-scheduling problem admits a fully polynomial-time approximation scheme.

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“…Other recently related studies can be found in Zhang et al [12], Masadeh et al [13], Zhang et al [14], Kim and Kim [15], Valouxis et al [16], and Wang et al [17] among many others.…”

Section: Notation Terminology P Jmentioning

confidence: 91%

Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs

2023

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“…32 Although our lives are fundamental as compared to the myriad things, we should not solely cultivate ourselves (dushan qishen 独善其身) to the neglect of the myriad things. 33 Instead, his reasoning is that we cultivate and help ourselves so that we can do the same for others. 34 It is within this context of cultivation that Wang Gen suggests we should exercise agency and let the myriad things depend on us and not the other way round.…”

Section: Primacy Of Selfmentioning

confidence: 99%

Which is More Important? Moral Virtue or Life itself?: An Exploration of a Confucian Theme

Chew

2024

Philosophy Compass

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This paper examines a dilemma within the Confucian tradition wherein one is forced to choose between upholding moral virtue and preserving one's own life. The mainstream view valorises and exalts the act of sacrificing one's life in order to uphold moral virtue. There are many supporters of this view, spanning across different periods, including but not limited to Confucius, Mencius, the Cheng brothers, Zhu Xi, and so on. There is, however, an opposing voice within the Confucian tradition. Wang Gen, a Neo‐Confucian thinker and founder of the Taizhou School of thought, opposes the mainstream position by arguing for the primacy of life and against the glorification of these acts of sacrifice. This paper has two aims. The first aim is to trace the development of the mainstream view within the Confucian tradition. The second aim investigates how Wang Gen argues against the mainstream position whilst situating himself within the Confucian tradition.

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“…Learning effects appear in, for example, the way that workers' repeated processing of similar jobs improves their skills (see Azzouz et al [1], Sun et al [2], Zhao [3], Wang et al [4], Chen et al [5], Ren et al [6], Wang et al [7]). The processing times of jobs can be controlled by allocating a common limited resource, such as fuel, the financial budget, energy, or manpower (see Guan et al [8], Wang and Cheng [9], Shabtay and Steiner [10], Zhang et al [11], Wang et al [12], Wang et al [13], Liu and Wang [14]).…”

Section: Introductionmentioning

confidence: 99%

Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect

Wang

2023

Mathematics

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In classical schedule problems, the actual processing time of a job is a fixed constant, but in the actual production process, the processing time of a job is affected by a variety of factors, two of which are the learning effect and resource allocation. In this paper, single-machine scheduling problems with resource allocation and a time-dependent learning effect are investigated. The actual processing time of a job depends on the sum of normal processing times of previous jobs and the allocation of non-renewable resources. With the convex resource consumption function, the goal is to determine the optimal schedule and optimal resource allocation. Three problems arising from two criteria (i.e., the total resource consumption cost and the scheduling cost) are studied. For some special cases of the problems, we prove that they can be solved in polynomial time. More generally, we propose some accurate and intelligent algorithms to solve these problems.

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Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost

Cited by 9 publications

References 23 publications

Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs

Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs

Which is More Important? Moral Virtue or Life itself?: An Exploration of a Confucian Theme

Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect

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