## 4 Description of the Approach
### Prioritization of the Risk Treatment Paths with a Hybrid MCDM Approach
#### 4.1.1 Normalization of the Decision Matrix  
The model developed by [PERSON] et al. [6] evaluates each path according to the trilemma of cost, energy flexibility, and a risk priority number. In this research paper, the trilemma is modified to fulfill the requirements of criteria selection in MCDM problems, as stated by [PERSON] et al. [42]. The authors define five principles to be obeyed when identifying suitable criteria: (1) the systemic principle, (2) the consistency principle, (3) the independency principle, (4) the measurability principle, and (5) the comparability principle. The systemic principle demands a holistic assessment of the regarded problem. In every PPC system, costs are one of the key decision factors [12] and therefore need to be considered in the decision problem, hereinafter referred to as cost. [PERSON] and [PERSON] [43] propose energy flexibility as a key indicator in the energy-oriented PPC, as it incorporates several energy-related variables in one indicator, hereinafter referred to as energy flexibility. Furthermore, this research is positioned in risk and fault management, and thus a risk-related dimension needs to be added to the problem to describe it holistically. The risk-related indicator is hereinafter referred to as risk reduction. The expert weighting of the three criteria additionally ensures that the criteria of the decision problem are in line with the decision-maker's goals; thus, criteria (1) and (2) are considered fulfilled. To demonstrate that principles (3) to (5) are fulfilled, a closer look at how the criteria are calculated is necessary. The costs are calculated according to the cost model introduced by [PERSON] et al. [6], which distinguishes between, e.g., production costs, logistic costs, and delay costs, and it divides these in turn into respective sub-categories, such as material or personnel costs. Costs are defined as the change in costs in the modified production schedule in relation to the unmodified production schedule. The deviation is the sum of deviations in the above-mentioned cost categories. For every cost component, only measure-induced costs are regarded, resulting in the measure-induced change in costs \(\Delta C_{tot}{}^{M}\), where \(\Delta C_{tot}{}^{M}\) is negative for cost savings, positive for increased costs, and \"0\" for unchanged costs [6]. Thus, for \(\Delta C_{tot}{}^{M}\), the lower the better. The cost thus indicates the costs incurred through the integration of the measures on the path. In practice, they therefore often correspond to the deviation from cost-optimal scheduling, which does not consider any risk effects. The energy flexibility indicates the remaining flexibility available in the system to react to disruptions influencing the production system's energy consumption. The regarded dimensions of energy flexibility are the potential to change loads or so-called energy flexibility states \(EF_{states}\), the potential to shift the time of consumption \(EF_{t}\), and the potential of energy-flexibility technologies, e.g., the use of storage facilities and flexible on-site generation \(EF_{tch}\). The overall energy flexibility EF is then calculated by multiplying the three dimensionless components:  
\[EF=EF_{t}\Delta EF_{states}\Delta EF_{tch} \tag{1}\]  
A value higher than one indicates the desired high energy flexibility, whereas a value lower than one indicates undesired low energy flexibility. Risk reduction indicates how much the risk is reduced by the integration of the measures into the production schedule, such as a change in production sequence or a shift of production starts.