Bottleneck Problems, Functional Equations, and Dynamic Programming

Abstract : A 'bottleneck problem' in the sense that the level of economic activity will be determined by the resource in shortest supply is discussed. A typical problem of the bottleneck type involving the auto industry, the steel industry and the tool industry is presented. The problem is formulated mathematically employing a discrete approximation. After a short discussion of the difficulties of this approach, a continuous approximation is advanced. Finally, the functional equation approach is applied to the theory of dynamic programming.