---

This paper explains a model for analyzing and measuring the propagation of order amplifications (i.e. bullwhip effect) for a single-product supply network topology considering exogenous uncertainty and linear and time-invariant inventory management policies for network entities. The stream of orders placed by each entity of the network is characterized assuming customer demand is ergodic. In fact, we propose an exact formula in order to measure the bullwhip effect in the addressed supply network topology considering the system in Markovian chain framework and presenting a matrix of network member relationships and relevant order sequences. The formula turns out using a mathematical method called frequency domain analysis. The major contribution of this paper is analyzing the bullwhip effect considering exogenous uncertainty in supply networks and using the Fourier transform in order to simplify the relevant calculations. We present a number of numerical examples to assess the analytical results accuracy in quantifying the bullwhip effect.

---

This work investigates the effect of different inventory policies of a supply chain model using the system dynamics approach which belongs to the class of Vendor Managed Inventory (VMI), automatic pipeline, inventory and order based production control systems (VMI-APIOBPCS). This work helps management to investigate the effect of different policies such as adding the VMI system or third party logistic (TPL) on the whole cost of the supply chain. To this end, this work applies system dynamics in supply chain with two supplier and one retail channel which consists of VMI system. Moreover, this work studies the performance of the proposed model via three metrics: Bullwhip effect; satisfaction of the end-customer; the amount of the whole inventory of chain.