Petri nets are widely used as an underlying framework for formalizing and verifying IT system models. Based on their easy-to-understand graphical representation, rich mathematical background, and precise semantics, they are appropriate to model IT systems, e.g., production systems with quantitative properties. The production of desired materials can be formulated as a reachability problem of its Petri net model, which can be analyzed by linear algebraic techniques (solving linear inequality systems). However, traditional reachability analysis techniques can result in a state space explosion, while the much more efficient numerical methods (often with polinomial runtime) for invariant computations give either sufficient or necessary conditions only. Process Network Synthesis algorithms, developed by a research group of the University of Veszprém, are widely used in chemical engineering to estimate optimal resource allocation and scheduling in order to produce desired products from given raw materials. By means of PNS algorithms, sufficient and necessary conditions for solution structures are determined defining the entirely solution space, and the search of optimal solutions (with respect to functions interpreted over the state space) is provided. The aim of the ongoing research is to adapt PNS algorithms to Petri nets in order to give more efficient mathematical methods for their analysis, and to elaborate a unified treatment for Petri nets and production nets.