A New Approach for Analyzing Queuing Models of Material Control Strategies in Manufacturing Systems

This paper discusses a new approach for analyzing queuing models of material control strategies such as kanban, CONWIP and POLCA in manufacturing systems. In practice, these strategies regulate the flow of jobs at various stations of the manufacturing system using a combination of card loops and authorization signals. Queuing models of such systems are composed of closed queuing networks corresponding to the different card loops. Fork/join stations are used to represent the synchronization constraints imposed on jobs, cards and authorization signals. Analyzing these networks involves solving a set of multi-class closed queuing networks with fork/join synchronization stations and stations with general processing times. Since these networks cannot be solved exactly, approximate methods have been investigated. We propose a new approximate approach based on the node decomposition technique. We study the underlying semi-markov processes at each station in the network and use the two moment renewal approximations to describe arrival and departure processes at each station. One of the new contributions here is the development of a two-moment approximation for fork/join stations fed by independent arrival streams. This approximation allows us to better model the synchronization constrains typical of material control strategies. Then, we use constraints on flow of jobs in the closed network to develop closed form expressions linking the arrival and departure process parameters at the different stations. These equations are then solved using an iterative algorithm.