# Help formulating/finding the general class of this problem

Imagine a bus serving a line with N stations. Each station, $i, i=1,…N$, has $s_{ij}$ passengers that want to board the bus to go to $j$, $\forall j \neq i$. (one direction). So there are $\sum_j s_{ij}$ passengers waiting at station $i$ to board the bus. Now, suppose that station $m$, is a strategically important station and we want to make sure there will be enough room on the bus to board waiting passengers. Assume the bus can choose how many people to board at each station, regardless of their destination. We now want to determine how many passengers at each of the stations (prior to station m) should board the train to ensure everyone at station $m$ can board the bus.

What type of optimization problem is this? Typical network optimization problems involve maximizing flow or capacity, but not this sort of problem. How would one go about modeling this? Are there any examples of problems similar to this?

• I would think that this is a variation of the "packing problem" and "assignment problem". It may also be related to the "scheduling problem". Nov 17 '16 at 2:56
• The important question is: What do you want to optimize? Transport as much passengers as possible? Maximize some monetary profit? Jan 19 '17 at 14:14