Pipeline transportation of petroleum products with no due dates

We introduce a new model for pipeline transportation of petroleum products with no due 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 c L of further orders. A feasible solution to our model is a pumping sequence that delivers the products corresponding to all orders in L - F. 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 corresponding to orders in F are initially stored at nodes, we propose the BPA algorithm. This algorithm finds a feasible solution in O(r(2) log r + s(2) (rn + log s)) time, where s is the total volume in the arcs of G. We point out that the input size is Omega(s). If G is acyclic, then BPA finds a minimum cost solution.