STUDIES ON BOTTLENECK PROBLEMS IN PRODUCTION PROCESSES
Abstract
Two papers are given, their purpose being to study in detail some representative problems which occur in the study of interindustry processes. The general techniques will be those of the theory of dynamic programming. The first paper considers a simple mathematical model of the interaction of two independent industries engaged in the production of one item. For convenience, the auto and steel industries are considered. The second paper treats the problem of maximizing x sub 2 (T) given the equations: dx sub 2/dt = a sub 2 z sub 2 (t) - z sub 3 (t), x sub 2 (0)<c sub 2, and dx sub 3/dt = b sub 3 gamma sub 3 z sub 3 (t) gamma sub 2 a sub 2 (t), x sub 3 (0) c sub 3, and the constraints: z sub 2, z sub 3 greater than or equal to 0, z sub 2 + z sb 3 less than or equal to x sub 2, and gamma sub 2 z sub 2+ gamma sub 3 z sub 3 less than or equal to x sub 3, where a sub 2, b sub 2, gamma sub 2, and gamma sub 3 are positive constants.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 25, 1954
- Accession Number
- AD0293677
Entities
People
- R. Sherman Lehman
- Richard E. Bellman
Organizations
- RAND Corporation