Abstarct: This monograph deals with the issue of safe allocation of resources in discrete event systems. Most of computer systems around us is a DES or can be abstracted as it. Employing parallel processes and shared resources, these systems are highly complex. Therefore, safe resource allocation of shared resources to parallel processes is a critical task to avoid deadlock and buffer overflow. For this reason, formal models, e.g. Petri nets, have been used for control and monitoring of resource allocation systems. These models can both simulate system and provide verification methods for modeled system. There are three important criteria to assess supervisory control policies: optimality of behavio, structural efficiency, and computational efficiency. Several researches, e.g. Language-baxsed approaches, reachability graph-baxsed approaches, Psiphon-baxsed and similarity-baxsed approaches have been completed to improve some or all of these three criteria. These algorithems face with high time and space complexity in large-scale systems. Reduction of number of controlled Psiphons, introducing concepts of over state and vector covering include the work done dealing with this problem. This monograph provides Petri nets-baxsed Supervisory Control in two related approaches. In the first approach, investigate and prove the feasibility of the calculation of modular supervision using synthesis operators of Petri nets. Utilization of modular design in calculation of a maximum supervisory control reduces the computational complexity of supervisor calculations. The furetheremore, utilizing place-merging operators reduce the number of uncotrolled siphones that must be handeled In addition, we prove liveness preservation of transition-merging operator in certain well-specified conditions. This approach can independently be used to prove the liveness preservation in synthesis operators. The second approach solves Supervisory Control problem by introducing a linear programming methods. The use of specification/ generalization vectors leads to a maximally permissive supervisory control with minimal structure and low computational time. The second approach can be used modularly to further reduce the computational time of supervisor calculation in large-scale systems.