Robust single machine makespan scheduling with release date uncertainty

Sequencing mixed-model assembly lines with risk-averse stochastic mixed-integer programming

“…Robust optimization has been investigated in single-machine scheduling (Daniels and Kouvelis 1995, Yang and Yu 2002, de Farias et al 2010, Kasperski 2005, Lu et al 2012, Atakan et al 2017, Bachtler et al 2020, two-machine flow shop scheduling (Kouvelis et al 2000, Kasperski et al 2012) and manufacturing environments in general (Sabuncuoglu & Goren 2009) to determine the schedule with the best worst-case performance. Recently, it has drawn increasing attention in assembly line balancing problems (Xu and Xiao 2009, Dolgui and Kovalev 2012, Gurevsky et al 2013, Moreira et al 2015, Pereira et al 2018, Chica et al 2019, Samouei and Ashayeri 2019, Yilmaz 2020 where schedulers are more concerned with the worst realizations of uncertainties.…”

“…Predictive-reactive scheduling develops an initial predictive schedule and updates it later in response to disruptions (Akturk and Gorgulu 1999). Proactive scheduling, also known as robust scheduling, anticipates possible disruptions when generating schedules and optimizes either the expected realized performance to achieve the best performance on average (Wu et al 1999) or the performance in the worst scenario (Bachtler et al 2020). The scheduling approach adopted in this work is based on the proactive strategy, in which uncertainty factors are incorporated to the decision-making model.…”

Robust unrelated parallel machine scheduling problem with interval release dates

“…Even though a large body of literature refers to robust optimization, relatively few papers include only release dates as an imprecise parameter. The paper [17] addresses the profound analysis of the robust scheduling problem 1|r j |C max with uncertain release dates. Absolute robustness and robust deviation criteria are considered and the authors proved that both problems could be solved in polynomial time.…”

“…The latter is proven to be polynomially solvable. Both [17] and [18] use the concept of gamma-robustness to model uncertainty. On the contrary, the authors of [19] investigate the robust (minimax regret) version of 1|r j |W T max , which is NP-hard.…”

“…To obtain a solution, they propose the modified Gusfield's algorithm and constructive heuristic. Despite different criteria in [17] and [19], it is showed that the number of feasible scenarios equals the number of given jobs.…”