The complexity of makespan minimization for pipeline transportation

Abstract

AbstractSPTP is a model for the pipeline transportation of petroleum products. It uses a directed graph G, where arcs represent pipes and nodes represent locations. In this paper, we analyze the complexity of finding a minimum makespan solution to SPTP. This problem is called SPTMP. We prove that, for any fixed ε>0, there is no η1−ε-approximate algorithm for the SPTMP unless P=NP, where η is the input size. This result also holds if G is both planar and acyclic. If G is acyclic, then we give a m-approximate algorithm to SPTMP, where m is the number of arcs in G