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In this article the author focuses on the problem of maximizing the flow through a network in which the nodes and arcs have limited capacity. Each arc has a positive rational capacity representing the maximum amount of flow that may pass across it, and each node has a positive rational capacity representing the maximum amount of flow that may enter or leave it. The author also describes the linear program that maximizes flow through the network and illustrates how cut sets are used to solve the problem. He also use illustrations and diagrams to emphasize his point. The author remarks that the problem of maximizing flow, through a network with node and arc capacities can be formulated as a linear program. The linear formulation has been presented and the relations between variables has been explained by the author. The author has also described the algorithm for finding a maximum flow pattern that starts out with a flow of zero on all arcs. The algorithm attempts to find a chain from source to sink with unused capacity on all of its arcs and nodes.

An algorithm for the determination of the economic design of X-charts based on Duncan's model is described in this paper. This algorithm consists of solving an implicit equation in design variables n (sample size) and k (control limit factor) and an explicit equation for h (sampling interval). The use of this algorithm not only yields the exact optimum but also provides valuable information so that the sensitivity of the optimum loss-cost (L*) can be evaluated. Loss-cost contours are used to discuss the nature of the loss-cost surface and the effect of the design variables. The effect of two parameters, the delay factor (e), and the average time for an assignable cause to occur (1/lambda), on the optimum design is evaluated. Numerical examples are used for illustrations. [ABSTRACT FROM AUTHOR]