We present an analytic investigation of the bullwhip effect developing in production-distribution chains. All common considered causes of the effect are excluded and the only mean to induce a bullwhip type of instability is the adoption of an inventory replenishment policy involving a variable target level. The policy is designed to maintain a safety stock that is proportional to the actual demand. In order to achieve our goals we develop a particular discrete model of supply chains by introducing some fresh concepts into the field of supply chain stability. The basic idea is to derive an update scheme describing the status of the whole chain over the entire time-space (period-stage) domain of interest. We prove that the strategy of demand driven target inventory inherently leads to an instability developing in the chain, which is precisely a manifestation of the bullwhip effect. Following the identification of the source and the nature of the instability, we propose a new production plan, which is stable and does not exhibit the bullwhip effect at all. Thus, the amplitude of the variation of the production rate never exceeds the amplitude of the oscillation of the market demand within the entire supply chain. © 2012 ICIC International.