# Special Issue on Algorithms for Scheduling Problems
## 2 Special Issue
To formulate this problem, a newsvendor modeling-based approach is considered. The developed model is solved using a Frank-Wolfe linearization technique along with Benders' decomposition method. The paper [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 developed and applied to resolve the conflicts by re-timing, re-ordering, and locally re-routing the trains. A part of the Southern Swedish railway network from the center of Karlskrona to Malmo city is considered for an experimental performance assessment of the approach. A comparison with the corresponding mixed-integer program formulation, solved by the commercial state-of-the-art solver Gurobi, is also made to assess the optimality of the generated solutions. In the paper [7], it is written that the current literature presents optimal control computational algorithms with regard to state, control, and conjunctive variable spaces. The authors of this paper first analyze the advantages and limitations of different optimal control computational methods and algorithms which can be used for short-term scheduling. Second, they develop an optimal control computational algorithm that allows the solution of short-term scheduling in an optimal manner. Moreover, a qualitative and quantitative analysis of the scheduling problem arising in the manufacturing system is presented. The paper [8] 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 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. The paper [9] 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 alimentation 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.