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Level of Repair Analysis
and Minimum Cost Homomorphisms of Graphs
Gregory Gutin, Arash Rafiey-Hafshejani, Anders Yeo and Michael Tso
Discrete Applied Mathematics
Volume to appear,
2005.
AbstractLevel 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. For a LORA problem with two
levels of indenture with three possible repair decisions, which is
of interest in UK and US military and which we call LORA-BR, Barros
(1998) and Barros and Riley (2001) developed certain
branch-and-bound heuristics. The surprising result of this paper is
that LORA-BR is, in fact, polynomial-time solvable. To obtain this
result, we formulate the general LORA problem as an optimization
homomorphism problem on bipartite graphs, and reduce a
generalization of LORA-BR, LORA-M, to the maximum weight independent
set problem on a bipartite graph. We prove that the general LORA
problem is NP-hard by using an important result on list
homomorphisms of graphs. We introduce the minimum cost graph
homomorphism problem, provide partial results and pose an open
problem. Finally, we show that our result for LORA-BR can be applied
to prove that an extension of the maximum weight independent set
problem on bipartite graphs is polynomial time solvable. [Edit]
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