  Our study aims to maximize the total reward in a transportation system with
$M$ buses that serve specific Origin-Destination (OD) pairs. Each bus can
operate on at most one line from a set of candidate lines. Operating a line
incurs different types of resource costs. The goal is to efficiently assign the
buses to the lines to serve integral portions of given OD demands while
respecting bus capacity, resource limits, and demand constraints.
  We propose a series of algorithms that address various facets of the problem.
For a scenario where all lines costs are zero, we achieve an optimal
approximation ratio of $1-\frac{1}{e}$. For instances with sufficiently small
line costs, our algorithm reaches an approximation ratio of
$1-\frac{1}{e}-\eta$. For the most general case, we obtain an approximation
ratio of $\frac{1}{2} - \frac{1}{2e} - \eta$. Lastly, we offer an approach that
ensures an approximation ratio of $1-\frac{1}{e}-\eta$ while limiting resource
usage to at most $1+\tau$ units for each type of resource. Here $\eta$ and
$\tau$ are arbitrary fixed constants.
  Our results also extend current methods and provide new avenues for
addressing a broad class of assignment problems involving multiple resource
constraints.
