In e-commerce, the order orchestration is the process that decides which stock source to use to fulfil each online order. This initial choice has an impact on the logistics flows, and performing an optimised orchestration may lead to a significant costs reduction. A previous work has introduced the GTP-ED, a model of green order orchestration with a comprehensive environmental function, which confirmed that mathematical optimisation provides significant savings. However, the GTP-ED presents two main issues that complicates the rolling out to retailers : the computation time was not matching operational requirements and the comprehensive objective function requires a lot of parameters that retailers may not possess. In our work, we want to tackle those issues and offer a green order orchestration that can be operationnaly used in a short term. We first show that an online version of the GTP-ED provides good quality solutions, and then we propose several optimisation criteria relying on more accessible data to approximate the comprehensive objective function.