(Dynamic Network Flows) The arcs (i, j) of a graph carry flow xij (t) in time period t, where t = 1,...,T. Each arc requires one time unit for traversal; that is, flow xij (t) sent from node i to node j along arc (i, j) at time t arrives at node j at time t + 1. The difference between the total flow departing and arriving at node i at time t = 2,...,T is a given scalar si(t). The total flows departing from each node i at time 1 and arriving at each node i at time T + 1 are also given
and X(t) is a given set for each t, as a network optimization problem involving a suitable graph that consists of multiple copies of the given graph.
(b) Repeat part l case where traversal of an arc (i, j) requires a given integer number of periods τij