Just-in-Time (JIT) production is a philosophy that calls for reducing work-in-process (WIP) inventory to aid process improvement and reduce process variability. The basic idea of JIT production is to produce the right amount of product at the right time. Unfortunately JIT production has been misinterpreted by some as a method that can achieve zero or minimal WIP with a lot size of one. There are no models or theories to achieve the JIT goals and, in particular, to help determine when and where to maintain this minimal inventory. A kanban system acts as the nerve of a JIT production system whose functions are to direct materials just-in-time to workstations in stages of manufacturing, and to pass information as what and how much to produce for workstations in the preceding stage. Indeed, the number of kanbans between two adjacent workstations describes the inventory level of that pair of workstations. With the objective to minimize WIP inventory level, one model dealing with two cases of production configuration is developed for deciding the optimum number of kanbans between two adjacent workstations. One case is for the one station to one station configuration. The other case is for the multiple station to one station configuration. This model is then solved using a Markov Process approach. The reason for using a Markov process is that the authors consider the demand of finished products and the production rates of stations as stochastic processes with exponential distribution. In this paper, the model and solution procedure are detailed along with numerical examples.
