A note on “Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan”

Production, maintenance and resource scheduling: A review

“…The SA by Rudek & Rudek (2012) cannot be compared to the ACO and CPSO developed by Huang & Yu (2016) , since Huang & Yu (2016) considers deteriorating maintenance duration while Rudek & Rudek (2012) focuses on deterioration of job processing times. Seif et al (2018) propose a GA-inspired algorithm which they name ALG and show that the ALG outperforms a standard GA. Aggoune (2003) , Kaabi, Varnier, & Zerhouni (2004) , Allaoui, Lamouri, Artiba, & E.Aghezzaf (2008) , Gara-Ali & Espinouse (2014 , Hadda (2015) , Mosheiov et al (2018) , Besbes, Teghem, & Loukil (2010) , Luo, Huang, Zhang, & Dai (2011) , Benbouzid-Si Tayeb, Guebli, Bessadi, Varnier, & Zerhouni (2011) , Nouri, Fattahi, & Ramezanian (2013 , Benbouzid-Si Tayeb & Belkaaloul (2014) , Boudjelida (2019) and Chansombat, Pongcharoen, & Hicks (2019) consider scheduling PM in a flexible window. Most studies use strict flexible windows, but in the studies by Kaabi et al (2004) , Benbouzid-Si Tayeb et al (2011) , Nouri et al (2013) , Benbouzid-Si Tayeb & Belkaaloul (2014 and Boudjelida (2019) , maintenance may be delayed or advanced beyond the time window, imposing earliness and tardiness penalties on the objective function.…”

A Bi-Objective Approach to Minimize Makespan and Energy Consumption in Flow Shops with Peak Demand Constraint

“…In the first assumption, some researchers considered one maintenance period in the horizon, for example the authors of [15][16][17] focused on scheduling resumable jobs in two-machine flow shops and the authors of [18,19] focused on the non-resumable jobs. Some researchers considered that the intervals are periodically fixed, for example the authors of [20][21][22] investigated the two-machine flow shops and the authors of [23,24] studied the multi-machine flow shops. In the second assumption, some researchers considered that the continuous working time of machine must be smaller than a threshold, for example the authors of [25] compared the difference between fixed constraint and flexible constraint.…”

“…The purpose of our paper is to establish an integrated model to minimize the bi-objective of makespan and energy consumption in flow shops with PM constraint and peak demand constraint. Compared with the methods in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], this paper belongs to the energy-efficient scheduling problem. Compared with the methods in , the main difference of this paper is considering the impact of PM constraint and peak demand constraint.…”

“…are binaries; others are continuous variables (22) The objectives in Equations ( 1) and ( 2) are two kinds of considerations, which show the tradeoff between two conflict aspects. The constraint in Equation ( 3) ensures that one job must be located in one position of each machine and can only be processed with one speed.…”

“…The constraint in Equation ( 21) is the peak demand constraint, which requires the average energy consumption in each interval below the threshold. The constraint in Equation (22) shows the features of decision variables.…”