To find feasible paths that satisfy multiple independent quality-of-service (QoS) constraints, the methodology of optimal supervisory control is applied. The network is modelled as a discrete event system (DES) and the penalties of the states and the disabling costs of the events of the DES are assigned considering the given metrics. After introducing the DES and assigning the penalties and the disabling costs, the feasible paths are found using the modified optimal supervisor design algorithm.