Supply-chain modelling and control under proportional inventory-replenishment policies

A novel state-space model of a multi-node supply chain is presented, controlled via local proportional inventory-replenishment policies. The model is driven by a stochastic sequence representing customer demand. The model is analysed under stationarity conditions and a simple recursive scheme is developed for updating its covariance matrix. This allows us to characterise the ‘bullwhip effect’ (demand amplification) in the chain and to solve an optimisation problem for a three-node model involving the minimisation of inventory subject to a probabilistic constraint on downstream demand. Finally, issues related to estimation schemes based on local historical data are briefly discussed.