Optimal scheduling is an important area of operations research, as it has both theoretical and practical aspects.It is clear that efficient algorithms are most desirable for practical applications, since most real-world scheduling problems have large sizes but require fast decisions.Due to this, practitioners often prefer to use rather simple algorithms which provide schedules that may be far from optimal with respect to their quality.This book is based on a Special Issue entitled "Algorithms for Scheduling Problems".In the Call for Papers, we invited prospective authors to submit their latest research in the area of the development of scheduling algorithms.We were looking for new and innovative approaches to solving scheduling problems exactly or approximately.High-quality papers were solicited to address both theoretical and practical issues of scheduling algorithms.Submissions were welcome both for traditional scheduling problems, as well as for new applications.We mentioned that potential topics included, but were not limited to, sequencing in single-stage systems and multi-stage systems with additional constraints such as setup times or costs, precedence constraints, batching, lot sizing, resource constraints, etc., also including single-or multi-criteria objectives and a broad range of scheduling problems in emerging applications such as sports, healthcare, and energy management.In response to the Call for Papers, we selected eleven submissions, all of which are of high quality, reflecting the stable and growing interest in the area of effective and efficient algorithms to solve problems for real-world production planning and scheduling.All submissions have been reviewed by at least three experts in the operations research area.Each chapter of this book contains one of these selected papers.We hope that practical schedulers will find some interesting theoretical ideas in this Special Issue, while researchers will find new practical directions for implementing their scheduling algorithms.In the following, we give some short comments on the particular chapters.The first three chapters deal with single-machine problems.Chapter 1 presents a new greedy insertion heuristic with a multi-stage filtering mechanism for energy-efficient single-machine scheduling.The authors wrote that in order to improve energy efficiency and maintain the stability of the power grid, time-of-use (TOU) electricity tariffs have been widely used around the world, which bring both opportunities and challenges to energy-efficient scheduling problems.Although methods based on discrete-time or continuous-time models have been suggested for addressing these problems, they are deficient in solution quality or time complexity, especially when dealing with large-size instances.For such problems, a new greedy insertion heuristic algorithm with a multi-stage filtering mechanism including coarse granularity and fine granularity filtering is developed in this paper.To show the effectiveness of the proposed algorithm, a real case study is provided, and detailed computational results are given.Chapter 2 is devoted to a stability approach to scheduling problems with uncertain parameters.The stability approach combines a stability analysis of the optimal schedules with respect to possible variations of the job processing times, a multi-stage decision framework, and the solution concept of a minimal dominant set of schedules, which optimally covers all possible scenarios (i.e., for any fixed scenario, this minimal dominant set contains at least one optimal schedule).In contrast to fuzzy, stochastic, and robust approaches, the aim of the stability approach is to construct a schedule which remains optimal for the most possible scenarios.If there exists a schedule dominating the other ones for all possible scenarios, then this schedule remains optimal for each scenario, which may be realized.This may be possible if the level of uncertainty is not high.Otherwise, a decision-maker must look ix for a schedule which provides optimal-or close to optimal-objective function values for the most possible scenarios among other schedules.To this end, the desired schedule must dominate a larger number of the schedules.This may be possible if the schedule has the largest optimality (stability) box.The authors address a single-machine scheduling problem with uncertain durations of the given jobs.The objective function is the minimization of the sum of the job completion times.The stability approach is applied to the considered uncertain scheduling problem using the relative perimeter of the optimality box as a stability measure of the optimal job permutation.The properties of the optimality box are investigated and used to develop algorithms for constructing job permutations that have the largest relative perimeters of the optimality box.Chapter 3 addresses a scheduling problem where jobs with given release times and due dates must be processed on a single machine.The primary criterion of minimizing the maximum lateness of the given jobs makes this problem strongly NP-hard.The author proposes a general algorithmic scheme to minimize the maximum lateness of the given jobs, with the secondary criterion of minimizing the maximum completion time of the given jobs.The problem of finding a Pareto optimal set of solutions with the above two criteria is also strongly NP-hard.The author states the properties of the dominance relation along with conditions when a Pareto optimal set of solutions can be found in polynomial time.The proven properties of the dominance relation and the proposed general algorithmic scheme provide a theoretical background for constructing an implicit enumeration algorithm that requires an exponential running time and a polynomial approximation algorithm.The latter allows for the generation of a Pareto sub-optimal frontier with a fair balance between the above two criteria.The next three chapters deal with flow shop and job shop scheduling problems as well as their hybrid (flexible) variants, often inspired by real-life applications.In Chapter 4, the maximization of the number of just-in-time jobs in a permutation flow shop scheduling problem is considered.A mixed integer linear programming model to represent the problem as well as solution approaches based on enumerative and constructive heuristics are proposed and computationally implemented.The ten constructive heuristics proposed produce good-quality results, especially for large-scale instances in reasonable time.The two best heuristics obtain near-optimal solutions, and they are better than adaptations of the classic NEH heuristic.Chapter 5 addresses a scheduling problem in an actual environment of the tortilla industry.A tortilla is a Mexican flat round bread made of maize or wheat often served with a filling or topping.It is the most consumed food product in Mexico, so efficient algorithms for their production are of great importance.Since the underlying hybrid flow-shop problem is NP-hard, the authors focus on suboptimal scheduling solutions.They concentrate on a complex multi-stage, multi-product, multi-machine, and batch production environment considering completion time and energy consumption optimization criteria.The proposed bi-objective algorithm is based on the non-dominated sorting genetic algorithm II (NSGA-II).To tune it, the authors apply a statistical analysis of multi-factorial variance.A branch-and-bound algorithm is used to evaluate the heuristic algorithm.To demonstrate the practical relevance of the results, the authors examined their solution on real data.Chapter 6 is devoted to the effectiveness in managing disturbances and disruptions in railway traffic networks, when they inevitably do occur.The authors propose a heuristic approach for solving the real-time train traffic re-scheduling problem.This problem is interpreted as a blocking job-shop scheduling problem, and a hybridization of the mixed graph and alternative graph is used for modeling the infrastructure and traffic dynamics on a mesoscopic level.A heuristic algorithm is x