Stability of Johnson's schedule with respect to limited machine availability

Braun, Oliver; Lai, Tsung-Chyan; Schmidt, Günter; Sotskov, Yuri N.

doi:10.1080/00207540210159527

Cited by 29 publications

(10 citation statements)

References 10 publications

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“…Figure 6 shows plots for the average proportion of the variance covered by the stability radii at each scheduling method. This analysis departs from the two-station analysis proposed by Braun et al (2002) as it has been extended to multiple stations. In brief, the processing times were randomly generated 200 times for each Taillard problem, a sequence was generated by each scheduling method and the bottleneck station was identified.…”

Section: Resultsmentioning

confidence: 91%

“…In the stability radii approach, for a given sequence, a range of variation within the processing times is identified that does not affect the original solution (Braun et al 2002;Lai and Sotskov 1999;Sotskov, Tanaev, and Werner 1998). Stability radii has been explored for n-job, 2-machine flow-shop problems when minimising makespan, but has not been extended to a multiple machine flow line.…”

Section: Introductionmentioning

confidence: 99%

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The effect of work content imbalance and its interaction with scheduling method on sequential flow line performance

Freiheit

2016

International Journal of Production Research

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Uneven workflow in serial flow lines is common when job work content varies. Unfortunately, work content imbalance between stations or between jobs degrades system performance. The effect of this imbalance can be mitigated by proper job sequencing. In this paper, we uncouple the influence of station-to-station and job-to-job imbalance within a set of jobs, introducing metrics to quantify the degree of imbalance, and determine their impact on line performance. We then examine the sensitivity of several scheduling methods at different problem scales and processing time variance levels, and compare the sensitivity to process time stability radii. Within the case studies explored, we determine that greater station imbalance can degrade solution quality regardless of problem scale and variance level. Greater job imbalance can either improve or diminish solution quality (i.e. relative performance from a given scheduling method), but less than station imbalance. Scheduling methods that sequence jobs based on the sums of processing times, e.g. SPT, can benefit from greater station imbalance. Scheduling methods that sequence jobs based on idle time between stations, e.g. the state-space heuristic, are more sensitive to station imbalance, but can also benefit from job imbalance. Finally, we conclude that job sequence has a greater impact on solution quality than stability radii.

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Section: Resultsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

The effect of work content imbalance and its interaction with scheduling method on sequential flow line performance

Freiheit

2016

International Journal of Production Research

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“…Kubzin, Potts, and Strusevich (2009) improve the R 6 1 error bound to R 6 1/2 by a fast heuristic for the problem when several holes occur on M 1 . Braun, Lai, Schmidt, and Sotskov (2002) study the question of whether Johnson's permutation remains optimal if there are w P 1 unavailability intervals on M 1 and M 2 in the two-machine flow shop problem (F2, h jw |r À a|C max , note that, in this place w is a fixed positive integer, so this notation F2, h jw |r À a|C max here is different from F2, h jk |r À a|C max ). It is well known that JA is optimal when all machines are continuously available (w = 0).…”

Section: Two-machine Flow Shop Without Storage Constraintsmentioning

confidence: 98%

A survey of scheduling with deterministic machine availability constraints

Chu

Zuo

2010

Computers & Industrial Engineering

362

119

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“…Later, Lee (1999) extended the previous work to the semi-resumable case and the case where availability constraints are imposed on both machines. Braun, Lai, Schmidt, and Sotskov (2002) studied the scheduling problem of minimising the makespan in the two-machine flow shop with w unavailability intervals on each of the two machines. Blazewicz, Breit, Formanowicz, Kubiak, and Schmidt (2001) and Kubiak, Blazewicz, Formanowicz, Breit, and Schmidt (2002) studied twomachine flow shop problem with limited machine availability and resumable job processing to minimise the makespan.…”

Section: Introductionmentioning

confidence: 99%

Two-machine flow shop scheduling integrated with preventive maintenance planning

Wang

Liu

2014

International Journal of Systems Science

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This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.

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Stability of Johnson's schedule with respect to limited machine availability

Cited by 29 publications

References 10 publications

The effect of work content imbalance and its interaction with scheduling method on sequential flow line performance

The effect of work content imbalance and its interaction with scheduling method on sequential flow line performance

A survey of scheduling with deterministic machine availability constraints

Two-machine flow shop scheduling integrated with preventive maintenance planning

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