Stochastic Modeling and Analysis of Generalized Kanban Controlled Unsaturated finite capacitated Multi-Stage Production System

In recent years, variants of Kanban mechanisms are proposed to deal with different levels of uncertainties commonly exist in a typical production system. Among them, generalized Kanban control (Buzacott [1989]) mechanism gained popularity as it is able to deal with uncertainties effectively while maintaining pull philosophy. In literature, many models are developed to gain insights on the design of generalized Kanban control mechanism however they were developed under the assumption that external demand for finished products of a production system in its control is very large, known as saturated condition. In the present globalization of market, most of the products face finite rate of demand, known as unsaturated condition and stochastic. In the present paper, Generalized Kanban Control unsaturated finite capacitated Multi-Stage Production of serial type (GKCMP) system has been considered with uncertainties in external demand and processing times. A model of decomposition Continuous Time Markov Chain (CTMC) type is developed for analyzing the considered system for the performance measures, namely, fill rate, average inventory and throughput. The model is then validated with stochastic discrete event simulation model at 95 % confidence level. Insights on the issues relevant to deployment of safety stocks, such that specified fill rate is achieved with minimum average inventory, have been presented. It is found analytical results are in close agreement with simulation results and uniform increasing Kanban allocation pattern is dominant over uniform allocation pattern for the specified criteria.