A method and tool is provided to obtain an optimistic estimate or exact optimal value of an operational parameter for a realistic
system model under investigation. The realistic
system model includes components and paths arranged to process continuous or discrete commodities. The
system could be a model of a manufacturing system with different machines (some of which may be identical)
processing multiple job types, with different sequences of operations with different
processing rates on the different machines at different stages. A network flow model of the realistic
system model under investigation is generated. Constraints are applied to the abstracted network flow model, and a plurality of
steady state network flows, which take into consideration the applied constraints, are performed. The network flows are combined or cascaded into an aggregate network flow, which captures a transformation of the commodities from a first state to a final output state. The network flow problem is solved using a
general purpose or custom
solver. The optimistic estimate or exact optimal value operational parameter estimate of the realistic
system model under investigation is then returned. The method can be used to perform tradeoff studies between
machine allocations, job mixes, operating costs, reliability and
throughput, or to speed up scheduling and
machine control.