The stability of supply chains

A continuous time version of the well-known beer game model is derived and its stability and robust stability properties are investigated. Novelty originates from the treatment of pure process delays rather than exponential lags and it is shown that this can lead to diametrically different dynamics to the exponential lag case. The stability properties of the system are shown to support and quantify the qualitative empirical results of the beer game. Additional insight into the influence of certain model parameters is attained by their interpretation as the degree of mismatch in a Smith predictor regulator. The transient inability to supply all that is demanded is mimicked and shown to constitute an influential source of demand amplification. The analytical nature of these calculations engenders the capacity to improve supply chain dynamics through the synthesis and calibration of strategic supply chain trade-off problems.