# Special Issue on Exact and Heuristic Scheduling Algorithms
## 2 Main Results of the Special Issue  
In response to the call for papers, we selected eight submissions for this special issue, all of which are of high quality, reflecting the interest in the area of developing exact and heuristic algorithms to solve real-world production planning and scheduling problems. As a rule, all submissions have been reviewed by three experts in the Discrete Optimization and Scheduling area. Subsequently, we survey the published papers in increasing order of their publication dates for this special issue. The paper [1] was the first one accepted for this special issue. It deals with a real-world distribution problem arising in the vehicle production industry in Mexico. This problem includes both the loading and optimal routing of each auto-carrier, where both the capacity constraints and the time windowshave to be taken into account. The authors suggest a two-stage heuristic algorithm. First, a route is constructed by an optimal insertion heuristic. Then a feasible loading is determined. For the computational experiments, two scenarios were generated with 11 different instances of the demand. Here one instance describes a real problem of a logistics company in Mexico. The algorithm allowed to obtain the routes and the loading of the vehicles for problems with 4400 vehicles and 44 dealerships considered. The results showed that the developed algorithm was successful in minimizing total traveling distance, loading/unloading operations and transportation costs. The paper [2] is devoted to the heuristic solution of job shop scheduling problems with blocking constraints and minimization of total tardiness. This problem has many applications in manufacturing, but also in railway scheduling. Due to the hardness of the problem, the development of heuristics is of high relevance. In particular, a permutation-based heuristic is derived. The authors use three interchange- and shift-based transition schemes. However, typical neighborhoods applied to job shop problems often generate blocking infeasible solutions. Therefore, the core of this paper is to present two repair mechanisms that always generate blocking feasible neighbors. Characteristics for the complex neighborhoods such as the average distance of a neighbor are analyzed. The suggested neighborhoods are embedded into a simulated annealing algorithm. Detailed computational results have been given for the modified Lawrance instances with up to 30 jobs and 15 machines as well as for hard train inspired instances with up to 20 jobs and 11 machines. A computational comparison was made with the MIP formulation given in the paper [3]. It turned out that for small instances, the heuristic often obtained an optimal or near-optimal solution, while for larger instances several of the best known solutions by the MIP solver have been improved. The paper [4] deals with scheduling jobs on a set of uniform parallel machines subject to given unavailability intervals with the objective to minimize the makespan. For this \(NP\)-hard problem, a new quadratic model is developed. In addition, the authors present a two-stage heuristic procedure. In the first phase, a modified Longest-Processing-Time rule is used to construct a schedule, which is then improved by pairwise interchanges of jobs between the machines. Computational results have been presented for instances with up to 2001 jobs and 1000 machines. The experiments showed that the quadratic model can solve small- and medium-size instances with roughly up to 140 jobs and 70 machines within a time limit of one hour. The heuristic algorithm presented in this paper was very fast and outperformed also an earlier heuristic from [5]. In the paper [6], some special cases of flow and job shop problems with so-called \(s\)-precedence constraints are addressed. This means that a task of a job cannot start before the task which precedes it has started.