I have the following shortest path problem.
Consider a directed graph with $n$ levels. Each level has $m$ nodes. Each node at level $i$ is connected to all nodes at level $i+1$. Let us also make a starting node that is connected to all nodes at level $1$ (the first level).
Each edge is labelled by a pair of non-negative integer weights. Each level $i$ has a single non-negative integer label which we call $L_i$.
The goal is to minimize the shortest path with respect to the first weight in each edge weight pair from the starting node to the last level while ensuring that the weight of the path from the starting node with respect to the second weight in each edge weight pair is no more than $L_i$ at each level $i$.
Has this problem been studied? Is it known to be NP-hard?