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Standard Mathematical Models
Published in William S. Levine, The Control Handbook: Control System Fundamentals, 2017
William S. Levine, James T. Gillis, Graham C. Goodwin, Juan C. Agüero, Juan I. Yuz, Harry L. Trentelman, Richard. Hill
In [22], a complete solution to this problem was given. Again, for this we would have to introduce the behavioral theory of dissipative systems and two-variable polynomial matrices, which goes beyond the scope of this study. It turns out that the optimal stability radius γ* can be computed in terms of certain two-variable polynomial matrices obtained after polynomial spectral factorization.
Distributionally robust and risk-averse optimisation for the stochastic multi-product disassembly line balancing problem with workforce assignment
Published in International Journal of Production Research, 2022
Xin Liu, Feng Chu, Feifeng Zheng, Chengbin Chu, Ming Liu
Some researches focus on stochastic ALBPs with task processing times within given intervals. Gurevsky, Battaïa, and Dolgui (2012) restrict the maximal working time of workstations no larger than the cycle time, to minimise the maximum working time of workstations. They discuss the stability radius for feasible solutions and propose a polynomial time algorithm computing the stability radius. Gurevsky et al. (2013) also restrict the maximal working time of workstations no larger than the cycle time. They propose a branch-and-bound algorithm, to minimise the number of workstations. HazıR and Dolgui (2013) consider the cycle time minimisation and propose a tight upper bound for the problem. A decomposition-based solution approach is developed. Moreira et al. (2015) restrict the maximal working time of workstations no larger than the cycle time. They propose two mixed-integer programming formulations and a construction heuristic, to minimise the number of workstations. Pereira and Alvarez-Miranda (2018) restrict the maximal working time of workstations no larger than the cycle time, to minimise the number of workstations. For the problem, several lower bounds, a heuristic and an exact branch-and-bound method are developed. Pereira (2018) minimises the maximal regret of the cycle time.
Two parallel identical machines scheduling to minimise the maximum inter-completion time
Published in International Journal of Production Research, 2020
Feifeng Zheng, Yang Sui, E Zhang, Yinfeng Xu, Ming Liu
Another related area is job scheduling such that the total absolute deviation of completion times of jobs is mainly involved in the objective function (Jos and Kim 2003; Mosheiov 2004; Ganesan and Sivakumar 2006; Oron 2008; Li et al. 2009; Kuo, Hsu, and Yang 2011; Zhao, Hsu, and Yang 2011; Mor and Mosheiov 2011; Hsu and Yang 2014; Ben-Yehoshua, Hariri, and Mosheiov 2015; Su and Wang 2017; Mor and Mosheiov 2018; Kovalev et al. 2019). Some authors also took interest on robust scheduling problems with uncertainty on the processing times or arrival times of jobs (Rahmani and Heydari 2014; Liu et al. 2017). Che, Kats, and Levner (2017) considered a stable robotic flow shop scheduling problem where the robot transportation times may have small perturbations. For the bi-criteria objective of minimising the cycle time and maximising the stability radius, they proposed a strongly polynomial algorithm. Yan et al. (2018) investigated a real-time dynamic job-shop scheduling problem in a robotic cell, where multiple jobs enter the cell with unexpected arriving rates. They formulated the problem as a sophisticated mixed-integer programming model, and proposed an exact iterative algorithm to solve it.
Stability of a schedule minimising the makespan for processing jobs on identical machines
Published in International Journal of Production Research, 2023
It is worthwhile to mention that Algorithm Stability-Radius may be used for finding the most stable optimal schedule for the problem . To this end, it is sufficient to repeat steps 4–16 for all optimal semi-active schedules S(t), which are constructed at step 1 and ordered at step 3. Then, it is needed to choose a schedule from the set S(t) with the largest value of the stability radius .