Industrial production sites are nowadays faced with two major concerns: the need to reduce the environmental impact of their processes and the economic difficulties caused by the rising energy prices. Both challenges may be partially tackled by powering industrial processes with electricity generated on-site from renewable sources. However, the volatility of the electricity prices and the intermittence of the locally generated renewable energy sources result in the need to solve an integrated industrial production and energy supply planning problem. This work investigates a single-machine multi-product lot-sizing problem for an industrial process powered by both grid electricity and on-site renewable energy. We propose a new extension of the Proportional Lot-sizing and Scheduling Problem relying on a two-level structure for time discretization. The first level is related to the product demand satisfaction, the second one is used for both production and energy supply planning. The proposed extension is compared to a previously published extension of the General Lot-sizing and Scheduling Problem dealing with a similar problem. Our preliminary numerical results show that in most cases, our model provides a production plan of the same cost, but with a significantly reduced computational effort.