  In this research, we examine the minsum flow problem in dynamic path networks
where flows are represented as discrete and weighted sets. The minsum flow
problem has been widely studied for its relevance in finding evacuation routes
during emergencies such as earthquakes. However, previous approaches often
assume that individuals are separable and identical, which does not adequately
account for the fact that some groups of people, such as families, need to move
together and that some groups may be more important than others. To address
these limitations, we modify the minsum flow problem to support flows
represented as discrete and weighted sets. We also propose a 2-approximation
pseudo-polynomial time algorithm to solve this modified problem for path
networks with uniform capacity.
