A faster algorithm for the maximum weighted tardiness problem

Fields, Morgan; Frederickson, Greg N.

doi:10.1016/0020-0190(90)90184-y

Cited by 6 publications

(2 citation statements)

References 4 publications

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“…For the maximum tardiness problem, the addition of weights does not change the complexity of the problem, that is, the weighted problem, 1|| max j w j T j , is solvable in polynomial time [12], [7]. Moreover, the problem remains tractable even in the addition of arbitrary precedence constraints [15].…”

Section: Definition 22mentioning

confidence: 99%

Minimizing Tardiness in a Scheduling Environment with Jobs' Hierarchy

Sinai¹,

Tamir²

2021

Annals of Computer Science and Information Systems

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In many scheduling environments, some jobs have higher priority than others. Such scenarios are theoretically modelled by associating jobs with weights, or by having precedence constraints that limit jobs' processing order. In this paper we define and consider a new model, motivated by real-life behaviour, in which the priority among jobs is defined by a dominance hierarchy. Specifically, the jobs are arranged in hierarchy levels, and high ranking jobs are ready to accept only outcomes in which the service they receive is better than the service of subordinate jobs. We first define the model and the set of feasible schedules formally. We then consider two classical problems: minimizing the maximal tardiness and minimizing the number of tardy jobs. We provide optimal algorithms or hardness proofs for these problems, distinguishing between a global objective function and a multi-criteria objective.

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Section: Definition 22mentioning

confidence: 99%

Minimizing Tardiness in a Scheduling Environment with Jobs' Hierarchy

Sinai¹,

Tamir²

2021

Annals of Computer Science and Information Systems

View full text Add to dashboard Cite

show abstract

“…Due to the precedence constraints, in that schedule the associated main job  is completed before job  + , so it is before its deadline  00  , as needed. For problem 1jdue dates d 0  precj max f    g we can apply the ( +  log )-time algorithm proposed in [4] for problem 1jprecj max f    g, where  is the number of precedence constraints. Since in our case  = , we can …nd a solution to problem 1jdue dates d 0  precj max f    g with auxiliary jobs in ( log ) time and use it as a solution for problem 1jdue dates d 0  deadlines d 00 j max f    g. Finally, (6) provides the optimal adjusted due dates b d for the reverse problem.…”

Section: Theorem 1 Depending On the Type Of The Normmentioning

confidence: 99%