Motivated by the challenges emerging in the energy sector, this brief presents a comprehensive framework for the optimal operation of large-scale Mixed Logical Dynamical (MLD) systems modeling engineering systems characterized by interleaved physical, logical, and digital components and subject to operational constraints. When the performance index is linear, the problem translates into a Mixed Integer Linear Program (MILP) that is NP-hard and becomes prohibitive as the size of the system increases. In the case of multi-agent systems that are constraint-coupled, decentralized schemes with provable feasibility guarantees are introduced to recover computational tractability by reducing the global MILP to multiple smaller ones that are iteratively solved in parallel. If the matrix modeling the MILP constraints is sparse, a method is proposed to possibly recover a hidden constraint-coupled multi-agent structure to which the decentralized resolution schemes can then be applied. Finally, multi-agent constraint-coupled MILPs with uncertain local constraints are considered and probabilistic feasibility guarantees are derived for their data-based decentralized solution. The framework is tested on an application in the energy sector concerning the provision of ancillary services to the power distribution grid.