A Network Flow Model of Mineral Supply

This paper describes a dynamic short-nun mineral supply model that incorporates secondary processing, transportation, mineral market structure, and direct mining and milling costs. The method employed is network flow programming. Empirical tests utilizing domestic phosphate industry data have been conducted by the Bureau of Mines, U.S. Department of the Interior. In the model, nodes represent physical locations such as a mine or port. Arcs represent either a process, such as mining, or movement, such as rail or barge transport. Each arc is described by lower or minims allowable flow bounds, upper or maximum possible flow bands, and variable cost. Mines and previous period inventories represent potential supply. The model is optimized via a cost minimizing algorithm, which attempts to fulfill stated total demand at the minimum possible system cost given the arc constraints. An optimal solution of the model will predict production patterns by mineral property for each prespecified level of demand. A mineral property is defined as a separate accounting entity such as a mine. The results of serial optimizations are used to construct the short-run supply curve. Dynamic policy analysis can be conducted by altering the arc constraints.