The talk is focused on presenting the role of stochastic numerical models for sustainability. The key aspect of sustainability in production systems is the subject, on the modeling front, of various scientific contributions. The use of stochastic modeling appears central and inevitable. 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. Furthermore, numerical modeling for reverse supply chains may provide the mathematical study of waste recycling and its re-entry into the production system. In this regard, geometric numerical integration of stochastic differential equations (SDEs) for sustainability is central to numerically 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. A selection of numerical experiments is also presented.