## 4 Description of the Approach
### Integration of Preventive and Reactive Measures in the Production Schedule  
Once measures have been successfully divided into reactive and preventive, implementation of the measures into the production schedule needs to be planned. The rescheduling of reactive measures is considered to be segment-based rescheduling, similar to Toba [54]. This means that for reactive measures, only the segments after the potential risk occurrence are affected and rescheduled, whereas for preventive measures, the measure execution must be prior to the expected time of disruption to be effective. Therefore, the implementation of preventive measures may affect the entire production schedule. The production schedule needs to be modified so that the previously selected measures are integrated as well as they can be, taking into account the logistical goals of the production system and the boundary conditions for the planned energy consumption. Due to the differentiation into preventive and reactive measures, new production schedules must be generated. These are the modified production schedule with all preventive measures, which replaces the original plan. Furthermore, a backup plan is drawn up for each reactive measure implemented, as the reactive measures only come into effect when a disruption occurs. The integration of measures is formalized as a MILP, which can be solved through branch-bound-and-cut optimization, e.g., in MATLAB(r)[54, 55]. For the present problem, it is important to aim for short computation times to ensure the applicability of the approach in operational practice. This can be achieved by reducing complexity wherever the problem setting allows it. The goal of this optimization is to integrate the measures energy optimally and thereby create a risk-treated, energy-optimal production schedule by the addition of preventive and reactive measures. In the course of this section, the term _production_ schedule refers to a plan that aggregates all relevant jobs on all workstations for the respective production period under consideration of resources and sequence restrictions, whereby one _job_ contains a product's production steps, i.e., the necessary workstations including durations, sequence restrictions, and resource consumptions. The workstations come with capacity restrictions, and not every job is necessarily processed on every workstation. The initial production schedule prior to risk treatment is assumed to be available and energy-optimal, hereinafter referred to as energy-oriented PPC. Measures are thus either treated as jobs and are fixed in their allocation to one workstation or modify the load and time dimensions of jobs scheduled by the energy-oriented PPC. When scheduling the measures, the risk-treated energy-oriented PPC must still comply with logistical and energy-consumption target values. Consequently, two options remain for the risk treatment:  
1. An extension of the original energy-oriented PPC by risk-specific target values and constraints leading to a detailed and comprehensive optimization problem. 2. Setting the results of the initial energy-oriented PPC as an input variable for an optimization problem that is limited to the implementation of measures. Option (1) results in correspondingly higher computing times due to increased complexity. This also leads to more difficulties in understanding the solution process and thus lowers the acceptance of the approach for the end users. Option (2), on the other hand, results in a non-optimal solution, but with expected significantly shorter calculation times, thus increasing flexibility in the application of the approach. It is also advantageous that the energy-oriented PPC is not redesigned but expanded. This increases understanding and acceptance if the generated solution fulfills the end user's standards. Due to the predominant advantages of option (2), this will be pursued further below.