A stochastic model of an unreliable kanban production system

Abstract

We analyze a stochastic model of a production line withk stations (machines) in series. There are finitecapacity 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 steadystate 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 arbitraryk. A comparison with simulation results shows that this algorithm is very accurate.