The pull multi-stage production scheduling and inventory control system is a way of implementing the just-in-time doctrine. In the pull system the production schedule of the final stage is transmitted back to all the upstream stages. This is achieved by keeping a certain amount of parts at each stage, with succeeding stages withdrawing parts from preceding ones only to the extent that they are needed;A stochastic model for the pull multi-stage production system is developed for two situations. The first situation is that a single machine (server) with non-zero inventory. The second situation is that of several machines with zero inventory;The model is studied and analyzed in the light of several measures of system performance and effectiveness. Allocation of parts among stages, and the effect of processing rates are investigated;A stochastic model for the push multi-stage production system is also developed and compared to the pull model. A new method, which reduced the number of Markovian states, is developed to model the blocking phenomenon in push system. A duality phenomenon between the pull and a specially defined push model is presented and discussed;The confluent system, with "made" parts processed in house into subassemblies, and then into final assemblies, is also modeled under the pull system. WIP allocation is studied as for the series system, and the possibility is explored of analyzing a process through its "sub-process";Although processing and demand are assumed exponential, the limitation imposed by stage capacity will cause the output process not to be poisson. For this reason, closed form solution for equilibrium probabilities of the system are not available and approximation and numerical methods were investigated, and compared;The proposed model can be applied to flexible manufacturing systems, assembly lines, and flow shops.