Lignocellulosic biorefineries consist of multiple processing steps that can be carried out by a single or by different actors. In the latter case, biorefineries can be decomposed into suppliers of intermediates and consumers of them. Following this decomposition, a multi-actor multi-objective optimization problem can be formulated and a two-level Lagrangian approach used to find the solution that optimizes the profit of the biorefinery. This methodology is applied here to a date palm waste biorefinery in which an organosolv process is used to produce a sugar stream; and fermentation to ethanol and succinic acid are considered to compete for the utilization of it. Results shows that at selling price of $400/t ethanol and $1500/t succinic acid, it is feasible to produce these products with an organosolv-sugar stream selling at $510/t.