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001158 21 Representation of the Transfer in the Basin Model As the final mechanism for accomplishing the transfer-of Juniper rights ",0 in stream flow use is not yet defined, the basin model has been configured to simulate two mechanisms, the subordination of the Juniper right to future depletions and the transfer of Juniper rights to existing and proposed reservoirs. The alternative of transferring pieces of the Juniper right to each junior water right was not implemented in the model since that would have required that the model represent each of those junior rights. In effect, this alternative would be indistinguishable from the subordination mechanism. DEVELOPMENT OF BASIN NETWORK MODEL 8ackground The Yampa Rivcr basin modcl is an application of Hydrosphere's Central Resource Allocation Model (CRAM). CRAM is a proprietary software package which facilitates the representation of complex water resources systems as networks amenable to solution using mathematical programming methods. This section of the memorandum describes the development of the basin model. A wide variety or resource allocation problems in which commodities must be moved from point to point (either spatially or temporally) can be visualized as networks. Com'modities might be raw materials needed for industrial production or water needcd to meet various demands. Typically the movement of commodities in such problems is to be accomplished in such a way as to maximize value or minimize costs. In general, networks are structured as a system 'of nodes and arcs. [n a water resource application, nodes may serve as points of inflow, outflow and junction of flow while arcs connect nodes and may represent pathways or processes through which water must flow.' The flow along any arc may have a positive or negati,ve unit cost or value' associated with it; the cost is often referred to as a prioritY or a rank.. The solution of the network is the set of arc flows that produces the minimum total cost (or maximum total value) for the entire network. Mathematically, the problem can be stated as follows: minimize Z = 2:2: c..x.. - tJ tJ (1) subject to: (.. < x.. < u.. tJ- tl- tJ 2: x.. - 2: x.. = 0 tJ It (2) (3) where: i = l,...,m j = l,...,n m = n '" the number of nodes X;j is the amount flowing from nodc i to node'j cij is the unit cost (or value) of now from i to j lij is the lowest flow allowed in arc ij (often 0) uij is the highest flow allowed in arc ij , l. :; ,ih.~~.i'.