The quickest path problem with batch constraints

The quickest path problem has been proposed to cope with flow problems through networks whose arcs are characterized by both travel times and flowrate constraints. Basically, it consists in finding a path in a network to transmit a given amount of items from a source node to a sink in as little time as possible, when the transmission time depends on both the traversal times of the arcs and the rates of flow along arcs. The paper is focused on the solution procedure when the items transmission must be partitioned into batches with size limits. For this problem we determine how many batches must be made and what the sizes should be.