Process flowsheet optimization of a lignocellulosic biorefinery coproducing levulinic acid, succinic acid, and ethanol was performed to maximize an economic objective function (either the net present value, NPV, or the internal rate of return, IRR, alternatively) by means of mathematical programming methods. Most promising alternative industrial processes were selected to build the superstructure of the biorefinery. A discretization method was applied to obtain a MILP approximation of the resulting MINLP master problem. NPV maximization for a biorefinery with hardwood feedstock provided with an optimal flowsheet with all three products. Larger biomass allocation values resulted for levulinic acid and succinic acid (more than 40% each). A sensitivity analysis highlighted that the optimal flowsheet was significantly dependent on the economic scenario (chemical products selling price, discount rate) and on the plant scale. Finally, alternative maximization of NPV and of IRR provided different optimal flowsheets and biomass allocation to chemical products.