A STOCHASTIC-MODEL OF AN UNRELIABLE KANBAN PRODUCTION SYSTEM

We analyze a stochastic model of a production line with k stations (machines) in series. There are finite-capacity buffers between the machines and at the end of the line. The movement of the workpieces through the line is demand-driven, i.e. we deal with a pull (kanban) production system. Processing times are assumed to be deterministic and constant. There are two sources of randomness in the model: Demand for workpieces from outside is stochastic, and the machines may break down (and then be repaired) with a given probability. A demand from outside is lost if the final buffer is empty. This system is described by a discrete-time Markov chain. The steady-state distribution is given for k = 1. This is the basis of a decomposition algorithm which approximates the throughput of the line and the percentage of satisfied demand for arbitrary k. A comparison with simulation results shows that this algorithm is very accurate.