One way to achieve energy efficiency in manufacturing is to equip plants with on-site renewable energy generation systems to partially power industrial processes. However, renewable energy sources are highly intermittent and their availability is difficult to predict accurately. Therefore, we study an integrated industrial production and energy supply planning problem under uncertain renewable energy availability. We propose a multi-stage stochastic programming model for this problem. The intermittency of renewable energy generation and the uncertainty of the demand are represented by a scenario tree. The resulting production and energy supply planning can be seen as a multi-stage decision process where some decisions are made at the beginning of the planning horizon whereas the others are postponed to later decision stages when more information on the uncertain parameters are revealed. At the beginning of the planning horizon, we build a setup and startup plan for a proportional lot-sizing and scheduling problem in a single-machine multi-item setting. Then based on the available information on renewable energy generation and demand, an energy supply and adjusted production plan is constructed for the upcoming stage, which has to satisfy the startup plan of the system previously determined at the beginning of the planning horizon. Computational experiments will be presented to show the practical efficiency of the proposed approach.