It could be that the current method (i.e. human solves it by making a decision for each item) could be proved to give an optimal solution. However, if that is n

It could be that the current method (i.e. human solves it by making a decision for each item) could be proved to give an optimal solution. However, if that is not the case, the hardest part will be to get the right model. There are very competitive open source solvers for LP with 10ˆ5 or even 10ˆ6 variables/constraints (https://projects.coin-or.org/Clp https://projects.coin-or.org/Clp), so the true limit here is formulating the model correctly. There are various optimization modeling languages out there, also in the open-source arena. As for getting the model right, some trial-and-error approach should work: 1) if the solution violates a constraint you hadn't thought of, just add it to the formulation and re-solve; 2) if the solution is too conservative, then there might be a constraint that's too restrictive (you can check which constraints are active, i.e. restricting, at the optimal solution you found), so just eliminate it or relax it.