The talk is focused on presenting the role of stochastic numerical models for sustainable innovation. The key aspect of sustainability in production systems is the core topic of various scientific contributions regarding mathematical modeling and stochasticity appears a central and unavoidable tool. In fact, as highlighted by the vast literature existing on stochastic modeling in multiple declinations, stochasticity allows us to effectively include terms of environmental capacity in the model. Under a more strict numerical point of view, geometric numerical integration of stochastic differential equations (SDEs) for sustainability is useful to describe the effects of virtuous processes in waste management, which also include the reuse and recycling of materials, policies at the basis of the so-called green supply chains. Techniques and results of geometric numerical integration of SDEs are presented in the framework of sustainable innovation. A selection of numerical experiments is also presented. This talk falls within the activities of PRIN-MUR 2022 project 20229P2HEA ``Stochastic numerical modelling for sustainable innovation", CUP: E53D23017940001, granted by the Italian Ministry of University and Research within the framework of the Call relating to the scrolling of the final rankings of the PRIN 2022 call.