Weighted interval scheduling with variable weights

Weighted interval scheduling with variable weights

In the traditional weighted interval scheduling problem, we have a list
{i_1, ..., i_n} of intervals with weights w_j. An algorithm to solve the
weighted interval scheduling problem is given here and is a basic dynamic
programming problem. However, what happens when if in a schedule, the
weight of a selected interval depends on the weight of the interval before
it (and in turn, so that the weight depends on the order)? An example
would be w_j' = w_j'*(w_(j-1)' + 1) where primed variables are the
intrinsic weights and unprimed weights are the "actual" weights taking the
order into account, i.e. the ones you actually use for the objective
function. Is this problem NP-hard? It sure sounds like it.