Non-approximability Results for Scheduling Problems with Minsum Criteria

Hoogeveen, Han; Schuurman, Petra; Woeginger, Gerhard J.

doi:10.1007/3-540-69346-7_27

Cited by 55 publications

(38 citation statements)

References 12 publications

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“…In this section, we will show that there is no polynomial-time algorithm for the problem {P, star}| pr ec; c i j = d(π * , π l ) = 1; p i = 1| j C j with a performance bound smaller than (1 + 1 13 ) unless P = N P. This result is obtained by the polynomial transformation used for proof of Theorem 3.5 and the gap technique (see Hoogeveen et al (1998)). …”

Section: Total Job Completion Time Minimizationmentioning

confidence: 95%

Scheduling UET-tasks on a star network: complexity and approximation

2010

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In this article we investigate complexity and approximation on a processor network where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no polynomial-time heuristic with a performance guarantee smaller than 6 5 (respectively 14 13 ) for minimization of the makespan (respectively the total job completion time) on a processor network represented by a star. Moreover, we design an efficient polynomial-time approximation algorithm with a worst-case ratio of four. We also prove that a polynomial-time algorithm exists for a schedule with a length of at most four. Lastly, we generalize all previous results on complexity and approximation.

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Section: Total Job Completion Time Minimizationmentioning

confidence: 95%

Scheduling UET-tasks on a star network: complexity and approximation

2010

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“…Our patient scheduling problem therefore corresponds to an open shop problem with processing times including values of zero: O| p i j = {0, sat m i j }| C i (standard scheduling notation), with p i j the processing time of activity a i j , and sat m i j is the standard activity time of resource m i j . The general open shop problem is NP-hard [25]. Different to most OR approaches, we do not consider performance guarantees, but average performances, given the stochastic parameters and for large number of patients.…”

Section: Discussionmentioning

confidence: 98%

Multi-agent Pareto appointment exchanging in hospital patient scheduling

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Somefun

et al. 2007

SOCA

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We present a dynamic and distributed approach to the hospital patient scheduling problem, in which patients can have multiple appointments that have to be scheduled to different resources. To efficiently solve this problem we develop a multi-agent Pareto-improvement appointment exchanging algorithm: MPAEX. It respects the decentralization of scheduling authorities and continuously improves patient schedules in response to the dynamic environment. We present models of the hospital patient scheduling problem in terms of the health care cycle where a doctor repeatedly orders sets of activities to diagnose and/or treat a patient. We introduce the Theil index to the health care domain to characterize different hospital patient scheduling problems in terms of the degree of relative workload inequality between required resources. In experiments that simulate a broad range of hospital patient scheduling problems, we extensively compare the performance of MPAEX to a set of scheduling benchmarks. The distributed and dynamic MPAEX performs almost as good as the best centralized and static scheduling heuristic, and is robust for variations in the model settings.Keywords Health care · Patient scheduling · Multi-agent systems A preliminary version of this work has appeared as [1].

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“…This result is obtained by the polynomial-time transformation used for the proof of Theorem 3 and the gap technique (see [18]). …”

Section: Total Job Completion Time Minimizationmentioning

confidence: 96%

“…We also extend the non-approximability result in the case of the completion time, denoted in what follows by P j C j with C j = t j + 1. In order to obtain this result, the polynomial-time transformation using in the NP-completeness proof for makespan minimization, and the gap technique proposed by Hoogeveen et al [18] are used.…”

Section: Introductionmentioning

confidence: 99%