Clear strategies that address all energy sectors, not just electricity, are required to achieve a sustainable and reliable energy system. Integrating multiple energy carriers (in this research electricity, heating and gas) in a so-called multi-energy system (MES) can represent a great opportunity for system improvements. This research builds upon an existing model for designing MES, coupling both temporal and geographical constraints for the investment planning of three energy networks. Large problem instances and complicating substructures of the model result in excessive computing times. This research therefore focuses on improving computation times of finding (near) optimal solutions. First, within a theoretical framework, the computational complexity of the model is investigated for insight into the worst-case performance of algorithms and interesting substructures. Second, in a practical setting, an empirical research with different problem instances will be performed, to investigate the efficiency of different methods within the branch-and-cut algorithm, such as parameter adjustments for the solver, the consideration of an existing network and the implementation of valid inequalities. Third, decomposition methods are compared. It appears that, overall, the MIP solver with the additional valid inequalities performs best.

Background
Scheduling is a form of decision-making that plays a very important role in manufacturing industries. It is the method by which work gets assigned to resources that compute it. In this thesis we want to assign jobs (cycles of a lithography process) to different machines in such a way that the machines are running for as little time as possible. The difficulty lies in the fact that some jobs require the same resource, and thus cannot be processed simultaneously.

Results
It appears that the following scheduling problems are NP-hard:
• P2kCmax and R2kCmax
• P3|res · 11, pj = 1|Cmax and R3|res · 11, pj = 1|Cmax
• P3|res · 11, pj = 1|
P Cj and R3|res · 11, pj = 1|
P Cj
We try to approximate an optimal solution for the scheduling problem Rm|res · 11| P Cj by calculating a ratio with a lower bound, where we ignore resource constraints, and an upper bound, that is found by a Greedy algorithm (w.r.t. resource constraints).

Conclusions
It appears that Greedy is not a very good approximation algorithm for this problem, since the ratio in which the optimal Total Completion Time should lie is about 8,33% of the average calculated Total Completion Time