## 2 State-of-the-Art  
### Problem Definition: RCMPSP  
The basic model of resource-constrained multi-project scheduling problem (RCMPSP) was developed by [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14], among others. Based on the work by [PERSON] et al. [14], [PERSON] [15] (pp. 556-567) formulated some extensions with regard to decentralized control and developed a benchmark library [16] based on this model. The so-called Multi-Project Scheduling Problem Library (MPSPLIB) is a library with 140 different models differing in number of resources, projects, jobs, and network character. Solutions can be uploaded and checked for feasibility. The MPSPLIB is based on models of the Project Scheduling Problem Library (PSPLIB, [17]) which considers the RCPSP. The models differ mainly in terms of the number of projects (\(|I|=2,\ldots,20\)) and the number of jobs (\(|I_{i}|=30,\ldots,120\)). Furthermore, there are differences regarding the number of different instances of the individual projects (\(iz=1\): all projects have the same instances; \(iz=2\): each project has an individual instance). For mathematical modelling of the basic problem of the decentral resource constrained multi-project scheduling problem (DRCMPSP) [15] (pp. 556-557), the problem is briefly described as follows: A set of projects with individual objective functions has to be controlled in parallel in a production system. The production system consists of local (only used by project \(i\)) and global renewable resources (used by all projects \(|I|\)). Each project consists of a set of jobs with precedence constraints. The processing times of the jobs on the resources are stochastic. At the time of sequencing, only the expected value of the distribution and the coefficient of variation are known. The projects use both local and global renewable resources. Other project properties concern the earliest start time and due date. As [PERSON] et al. [18] proved, the resource-constrained project scheduling problem as a generalization of the job shop problem is one of the NP-hard (non-deterministic polynomial-time hardness) optimization problems. As a generalization of the resource-constrained project scheduling problem, the resource-constrained multi-project scheduling problem with specific extensions of the process time variations considered in this paper thus belongs to the NP-hard optimization problems [19] (p. 153). Exact procedures that lead to optimal results are largely suitable for generating benchmark solutions [20] (p. 149). The number of calculation steps and thus the calculation time increase with the problem size [21] (p. 38). Already from 60 jobs on, most problems cannot be solved with exact methods [22]. For practical problems, which usually involve considerably more jobs, heuristics are therefore indispensable in order to achieve good results in a shorter computation time. The application of the theory of simulation-based optimization, coupled with heuristics, is also more appropriate for complex models if complex relationships cannot be described simply with the help of mathematical formulas. Furthermore, the advantage is the clarity of simulation models (step-by-step event handling by discrete event simulation), which leads to a higher acceptance than with mathematical optimization models [21] (p. 30). For this reason, we use discrete event simulation as a simulation method. There are many software frameworks. With many of these software frameworks, the job-shop problem can be mapped. For modelling project scheduling problems, however, a high effort of customization is necessary.