Supply Chain Modelling and Control Under Proportional Inventory-Replenishment Policies

Abstract

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 analyzed under stationarity conditions and a simple recursive scheme is developed for updating its covariance matrix. This allows us to characterize the "bullwhip effect" (demand amplification) in the chain and to solve an optimization problem for a three-node model involving the minimization of inventory subject to a probabilistic constraint on downstream demand.Finally, issues related to estimation schemes based on local historical data are briefly discussed.

The bullwhip effect: Progress, trends and directions

“…General guidance on tuning the feedback parameters is given by Papanagnou and Halikias (2008). Graves et al (1998), Balakrishnan et al (2004 and Boute and Van Miegham (in press) describe other proportional ordering policies.…”

State-space proportional-integral inventory replenishment practices for bullwhip effect investigation in supply chains

“…By substituting previous equality in (4), it can easily be proved that O 1 * (t) = O 0,1 (t). This is essentially a linearization assumption also made in [12] and [13] which simplifies the subsequent analysis.…”

“…Keeping the inventory level close to set-point SP 1 provides an inventory "buffer" for the system, enabling it to meet varying levels of demand [13]. For a real system exhibiting trends or seasonal variations in demand profiles, the set-points need to be (slowly) time-varying by adapting to the average volume of demand.…”

“…This approach can be considered as an extensive base stock level policy where the replenishment procedure takes place continuously in contrast to traditional periodic review policies (e.g., (S,s) or (R,S) policies) [9], [10]. P or PI continuous policies have been proposed only in recent past by many researchers [11], [12], [13] and they are based on classical control theory. Their main characteristic is that orders take place continuously, rather than being triggered by specific events (e.g., when inventory falls below a certain target level).…”

“…The main methodology used in this research is based on [13]. In this work, Papanagnou and Halikias presented explicit methods for analyzing and predicting the bullwhip effect via covariance analysis of proportional control schemes in stochastic multi-node serial supply chain models of arbitrary complexity.…”