Level of Repair Analysis (LORA) is a prescribed procedure for defence logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize overall life-cycle costs. We consider the LORA optimization problem (LORAP) introduced by Barros (1998) and Barros and Riley (2001) who solved LORAP using branch-and-bound heuristics. The surprising result of this paper is that LORAP is, in fact, polynomial-time solvable. We prove it by reducing LORAP to the maximum weight independent set problem on a bipartite graph.