This special issue of the Journal of Scheduling contains selected papers submitted in response to an open call for papers announced after the Third International Workshop on Dynamic Scheduling Problems (IWDSP 2021), held in June 2021 at the Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland. The workshop, originally planned to be held in June 2020, in view of the COVID-19 pandemic was postponed for a year and organized as a hybrid event, with on-site and online attendance.

The IWDSP 2021 was the third workshop in the IWDSP series. Its predecessors, the IWDSP 2016 and IWDSP 2018 workshops, were held at the same faculty five and three years earlier, respectively. Books of extended abstracts of the papers, plenary lectures and a tutorial presented at the three workshops, written by the authors from Australia, Belarus, Belgium, Canada, Egypt, France, Germany, India, Israel, Italy, the Netherlands, Poland, P. R. China, Russian Federation, Taiwan, the UK and the USA, were published by the Polish Mathematical Society (https://iwdsp2016.wmi.amu.edu.pl/wp-content/uploads/2015/12/iwdsp2016.pdf, https://iwdsp2018.wmi.amu.edu.pl/wp-content/uploads/2018/09/iwdsp2018.pdf, https://iwdsp2021.wmi.amu.edu.pl/wp-content/uploads/2021/07/iwdsp2021.pdf). Selected papers presented at the IWDSP 2018 workshop were published in an earlier special issue of the Journal of Scheduling (https://link.springer.com/journal/10951/volumes-and-issues/23-6/).

The aim of the IWDSP 2021 workshop was to present new results related to the theory and practice of dynamic scheduling problems, in which job processing times, machine speeds or other parameters of the considered problems are variable and dynamically change in time. Therefore, the scope of this workshop, similar to its predecessors, included scheduling with time-, position- or resource-dependent job processing times, scheduling with factors affecting job execution, scheduling on variable speed machines, scheduling with rate-modifying activities, scheduling with constraints on machine availability, scheduling under uncertainty, and online scheduling, among others. These topics have already gained a significant place in the literature, confirmed by the publication of relevant monographs (Agnetis et al., 2014; Gawiejnowicz, 2020b; Strusevich & Rustogi, 2017) and reviews (Azzouz et al., 2018; Gawiejnowicz, 2020a; Shabtay & Steiner, 2007).

In response to the open call announced after the IWDSP 2021 workshop, we received eleven submissions. After a meticulous reviewing process, four papers were selected for publication.

The papers included in this special issue concern scheduling with a learning effect, scheduling with deteriorating jobs, modeling the work at an assembly line and scheduling with periodic availability constraints. The results presented in the papers concern both theoretical and practical aspects of dynamic scheduling problems. The content of these papers is as follows.

In the paper ‘Single machine scheduling with step-learning’, Atsmony, Mor and Mosheiov study a single-machine minimum-makespan scheduling problem with step-learning, in which the processing times of the jobs started after their job-dependent learning dates are reduced. They prove \({\mathcal{N}\mathcal{P}}\)-hardness of the case when idle times between consecutive jobs are not allowed, and propose for it a pseudo-polynomial-time dynamic programming algorithm. For the cases when all jobs have a common learning date or when idle times are allowed, the authors propose two other dynamic programming algorithms.

In the paper ‘Exact algorithms and approximation schemes for proportionate flow shop scheduling with step-deteriorating processing times’, Mor and Shabtay consider two proportionate flow shop scheduling problems with the maximum completion time criterion and step-deteriorating job processing times. They show that the problems can be represented in a unified form, provide for this form a pseudo-polynomial-time algorithm and explain how to convert this algorithm into a fully polynomial-time approximation scheme. The authors also analyze the parametrized complexity of the problem with respect to the number of different deterioration dates.

In the paper ‘Mixed-model moving assembly line material placement optimization for a shorter time-dependent worker walking time’, Sedding studies the problem of minimizing the walking distance of a worker along an assembly line. Modeling the distance with a time-dependent V-shaped function, he formulates the problem as an \({\mathcal{N}\mathcal{P}}\)-hard sequencing problem with a recursive and non-linear objective function. He also gives a lower bound on the criterion function value of partial solutions, established by a Lagrangian relaxation that can be solved in quadratic time, and presents branch-and-bound-based algorithms for solving real-world size instances.

Finally, in the paper ‘Scheduling with periodic availability constraints to minimize makespan’, Yu and Tan conduct the worst-case analysis of two algorithms, SFFD and DFFD, for non-preemptive minimum-makespan scheduling on a single machine or two parallel machines with periodic availability constraints, provided that the periods of the availability and unavailability of the machines, each period of the same type of equal length, appear alternately on each machine. For the single-machine problem, they give the worst-case ratio of the SFFD algorithm, tight for \(\beta > 0.1022\), and propose an algorithm with the worst-case ratio arbitrarily close to \(\frac{2\beta +2}{\beta +2}\), where parameter \(\beta \) is the ratio between the length of the unavailability period and the length of the availability period. For the two-machine problem, the authors show a tight worst-case ratio of the DFFD algorithm.

We express our sincere thanks to Edmund Burke, Editor-in-Chief of the Journal of Scheduling, who accepted our proposal and trusted our recommendations. We thank the referees who, despite tight deadlines and numerous duties, have provided insightful, high-quality reviews.

Research on dynamic scheduling problems is in progress, and many of them still await a solution. We hope that this special issue will encourage the reader to learn more about these interesting and challenging problems.