Hierarchical Approaches to Solution of Modes

Abstract : PDRC Report 86-09 discussed an averaging algorithm to solve the aggregate-disaggregate reformulation of MRMATE. The procedure was presented as an alternative to Benders' decomposition for solving the LIFTCAP/MRMATE linking problems in MODES in PDRC Report 87-06. This report presents two approaches for solving MODES. The first approach formulates MODES as a hierarchy of decisions to be generated. The hierarchy consists of an aggregated version of LIFTCAP that generates allocation of assets to aggregate channels. An aggregate MRMATE model allocates MRs to these aggregated channels generated by aggregate LIFTCAP. An aggregate LIFTCAP model and an aggregate MRMATE model constitute the aggregate MODES model. A solution to the aggregate MODES model is then disaggregated by disaggregate LIFTCAP and disaggregate MRMATE model. The disaggregate problems generate solutions at the required level of detail consistent with aggregate MODES solutions. Consistency implies that detailed channel capabilities and MR allocations added across an aggregate bundle is bounded by the aggregate channel capabilities and MR allocations generated by the aggregate MODES model. The second approach considers the MODES problem from a different perspective. In some situations, the dominant objective is to move all MRs to their destination within their desired time window using the minimum number of assets. The driving problem in this version of modes is the MRMATE problem. MRMATE generates allocations of MRs to their best (minimum penalty) channels. This defines channel capabilities.