## 2 State-of-the-Art
### Approaches for Decentralized Control of RCMPSP  
In contrast to deterministic optimization, at least one parameter in stochastic optimization is subject to random events [23] (p. 45). Solutions, e.g., schedules or PRs, generated under deterministic conditions may be invalid in the stochastic environment [24] (p. 2); [10] (p. 111); [25] (pp. 21-23). The suitable methods for solving the stochastic optimization problem depend mainly on the dimension of the stochastic influences [19] (p. 249). If stochastic influencing variables can only be described by random variables, methods of stochastic optimization are suitable for scheduling [26] (p. 160). With a static approach, the PRs do not change during the observation period. In contrast, in a dynamic approach, the PRs are adapted during the production process. Thus, we focus on stochastic optimization with a static approach of PR since in the case study of the customized assembly of complex large products the job processing times are characterized by random variables of a logarithmic normal distribution and there are no possibilities for adaption of the PR during production. PRs such as CPRs are suitable for the considered problem domain with similar functionality and application as SPRs. Simply stated, CPRs are attributes calculated according to a rule from the information on the product, process, resource, and system. The result of the calculation determines the job priority in the queue. A comprehensive review about CPRs and hyper-heuristics is given by [PERSON] et al. [10]. Their paper proposes a taxonomy and guidelines for designing CPRs. As a hyper-heuristic, GAs or neuronal networks are mostly used. Multi-objective algorithms, such as the NSGA-III [27], are not used in the literature. There are a lot of PPC approaches using CPRs for production control. The majority of existing approaches using CPRs focus on job-shop problems [10] (pp. 110-111), which are in general less complex (e.g., less complex precedence constraints and disjoint resources) compared to resource-constrained project scheduling problems (RCPSP). [PERSON] et al. [28] developed a method based on real-time data to adapt the control model based on CPRs. For this purpose, a simulation is permanently carried out at the same time as actual production. If changes or disturbances occur, the simulation model and consequently the control model are adapted. Permanent data availability is necessary for concept implementation. [PERSON] et al. [29] presented an approach to maintain planning reliability while simultaneously taking advantage of the benefits of autonomous control. Central planning provides information such as start and end times. Sequential decision trees determine job release, sequencing, and resource allocation. In addition to the information provided by central planning, these decision trees depend on extensive information on system status in production. Moreover, this concept requires an extensive database which is not available yet. Decentralized approaches for solving the project scheduling problem focus mainly on agent-based auction and negotiation approaches [30] (pp. 695-704). Only [PERSON] et al. [31] solves the control problem of project manufacturing with CPRs in a stochastic environment. [PERSON] et al. [31] considers the stochastic RCPSP. Project-specific objectives are not considered. [PERSON] et al. [32] also points out that a Pareto optimization (multi-criteria) is hardly considered. Strategies that are mainly used in shop-floor production can also be implemented in project-oriented production and vice versa. In contrast with shop floor manufacturing with machines as the main resource, project controlled environments with human resources have less sophisticated data. Thus, it should not be assumed in such environments.