Time-bounds for production networks

Lower and upper time bounds are established for completing a task using a system that can be structurally represented by a digraph in which the nodes are production components. Each component is assumed to execute a known number of operations and each operation is assumed to require a known delay. The algorithms presented provide a rapid means for computing an objective function when optimizing a system using a method that requires the objective function to be evaluated an extremely large number of times, such as a simulated annealing or genetic algorithm.