An exact algorithm for single-machine scheduling without machine idle time

Tanaka, Shotaro; Fujikuma, Shuji; Araki, Mikiya

doi:10.1007/s10951-008-0093-5

Cited by 75 publications

(111 citation statements)

References 18 publications

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“…In this section, we also put this claim to test in the context of our risk-averse scheduling problem. For the analyses in this section, the deterministic model is solved to optimality by the SiPS solver provided by Tanaka et al (2009). SD-SMS is invoked with a time limit of 1800 seconds, and CPLEX is allotted the same period of time for solving the risk-neutral model.…”

Section: Value Of the Risk-averse Modelmentioning

confidence: 99%

Minimizing value-at-risk in single-machine scheduling

2016

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The vast majority of the machine scheduling literature focuses on deterministic problems in which all data is known with certainty a priori. In practice, this assumption implies that the random parameters in the problem are represented by their point estimates in the scheduling model. The resulting schedules may perform well if the variability in the problem parameters is low. However, as variability increases accounting for this randomness explicitly in the model becomes crucial in order to counteract the ill effects of the variability on the system performance. In this paper, we consider single-machine scheduling problems in the presence of uncertain parameters. We impose a probabilistic constraint on the random performance measure of interest, such as the total weighted completion time or the total weighted tardiness, and introduce a generic risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) of the random performance measure at a specified confidence level. We propose a Lagrangian relaxation-based scenario decomposition method to obtain lower bounds on the optimal VaR and provide a stabilized cut generation algorithm to solve the Lagrangian dual problem. Furthermore, we identify promising schedules for the original problem by a simple primal heuristic. An extensive computational study on two selected performance measures is presented to demonstrate the value of the proposed model and the effectiveness of our solution method.

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Section: Value Of the Risk-averse Modelmentioning

confidence: 99%

Minimizing value-at-risk in single-machine scheduling

2016

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“…Unlike the problem in Tanaka et al (2009), machine idle time should be considered in our problem. Fortunately, the extension is not difficult: Our problem can be converted into a problem without machine idle time by introducing zero cost dummy jobs with a unit processing time that correspond to unit idle times.…”

Section: Network Representationmentioning

confidence: 99%

“…The objective is to minimize the total job completion cost i∈N f i (C i ). For a special class of this problem, the single-machine scheduling problem without machine idle time (and with equal release dates), the authors (Tanaka et al 2009) already proposed an efficient exact algorithm. This algorithm is an improvement of the algorithm proposed by Ibaraki and Nakamura (1994) that is based on the SSDP (Successive Sublimation Dynamic Programming) method (Ibaraki 1987).…”

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confidence: 99%

“…This state elimination is also effective for reduction of computational efforts. In our previous study (Tanaka et al 2009), it is shown that the algorithm can handle 300 jobs instances when it is applied to the total weighted tardiness problem (1|| w i T i , according to the standard classification of scheduling problems in Graham et al (1979)) and the total weighted earliness-tardiness problem (1|| (α i E i + β i T i )) without machine idle time. In this study we will extend this algorithm to a more general singlemachine problem where machine idle time is permitted.…”

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confidence: 99%

“…Furthermore, he has already proposed to utilize the constraint propagation technique in their algorithm, which we will also introduce in this paper. As pointed out in Tanaka et al (2009), one of the primary differences is that our algorithm is based fully on dynamic programming, while his one is a branch-and-bound algorithm. This difference makes our algorithm much faster than the Sourd's algorithm, which will be shown by numerical results for benchmark instances of 1|| (α i E i + β i T i ) and 1|r i | (α i E i + β i T i ).…”

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confidence: 99%

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A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

Tanaka

Fujikuma

2011

J Sched

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This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors' previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of singlemachine scheduling problems: the total weighted earlinesstardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.

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