A generic well-defined methodology for the construction and operation of dynamic process models of discrete industrial systems following a number of well-defined steps is introduced. The sequence of steps for the application of the method as well as the necessary inputs, conditions, constraints and the results obtained are defined. The proposed methodology covers the classical offline modelling and simulation applications as well as their online counterpart, which use the physical system in the context of digital twins, with extensive data exchange and interaction with sensors, actuators and tools from other scientific fields as analytics and optimisation. The implemented process models can be used for what-if analysis, comparative evaluation of alternative scenarios and for the calculation of key performance indicators describing the behaviour of the physical systems under given conditions as well as for online monitoring, management and adjustment of the physical industrial system operations with respect to given rules and targets. An application of the proposed methodology in a discrete industrial system is presented, and interesting conclusions arise and are discussed. Finally, the open issues, limitations and future extensions of the research are considered.