dates. We use a directed graph G with n nodes, where arcs represent pipes and nodes
represent locations. We also define a set L of r transportation orders and a subset F⊂ L of
further orders. A feasible solution to our model is a pumping sequence that delivers the
products corresponding to all orders in LF We prove that the problem of finding such a
solution is NP-hard, even if G is acyclic. For the special case where the products …