Eleyat M., Haugland D., Hetland M.L., Natvig L. (2012) Parallel algorithms for the maximum flow problem with minimum lot sizes. In: Klatte D., Lüthi HJ., Schmedders K. (eds) Operations Research Proceedings 2011. Operations Research Proceedings (GOR (Gesellschaft für Operations Research e.V.)). Springer, Berlin, Heidelberg
In many transportation systems, the shipment quantities are subject to minimum lot sizes in addition to regular capacity constraints. This means that either the quantity must be zero, or it must be between the two bounds. In this work, we prove that the maximum flow problem with minimum lot-size constraints on the arcs is strongly NP-hard, and we enhance the performance of a previously suggested heuristic. Profiling the serial implementation shows that most of the execution time is spent on solving a series of regular max flow problems. Therefore, we develop a parallel augmenting path algorithm that accelerates the heuristic by an average factor of 1.25.