On variance amplification in a three-echelon supply chain with minimum mean square error forecasting

Abstract

Please note: Changes made as a result of publishing processes such as copy-editing, formatting and page numbers may not be reflected in this version. For the definitive version of this publication, please refer to the published source. You are advised to consult the publisher's version if you wish to cite this paper.This version is being made available in accordance with publisher policies. See http://orca.cf.ac.uk/policies.html for usage policies. Copyright and moral rights for publications made available in ORCA are retained by the copyright holders. ACCEPTED FOR OMEGA, AS OF NOVEMBER 2, 20041 On variance amplification in a three-echelon supply chain with minimum mean square error forecasting Takamichi Hosoda † , and Stephen M. Disney AbstractWe analyse a three echelon supply chain model. First-order autoregressive end consumer demand is assumed. We obtain exact analytical expressions for bullwhip and net inventory variance at each echelon in the supply chain. All of the three supply chain participants employ the order-up-to policy with the minimum mean square error forecasting scheme. After demonstrating that the character of the stochastic ordering process observed at each level of the supply chain is mathematically tractable, we show that the upper stream participants have complete information of the market demand process. Then we quantify the bullwhip produced by the system, together with the amplification ratios of the variance of the net inventory levels. Our analysis reveals that the level of the supply chain has no impact upon the bullwhip effect, rather bullwhip is determined by the accumulated lead-time from the customer and the local replenishment lead-time. We also find that the conditional variance of the forecast error over the lead-time is identical to the variance of the net inventory levels and that the net inventory variance is dominated by the local replenishment lead-time. Index TermsBullwhip effect; order-up-to policy; inventory variance; information sharing; supply chain management; minimum mean square error forecast.

The impact of information sharing, random yield, correlation, and lead times in closed loop supply chains

“…It is a periodic review system where both the manufacturer and the remanufacturer employ the same review period. The manufacturer uses an order-up-to policy (Hosoda and Disney 2006) to determine its production quantity. Both the manufacturing and the remanufacturing processes have unlimited capacity.…”

Altruistic behaviour in a two-echelon supply chain with unmatched proportional feedback controllers

“…Each player acts to minimize global inventory costs. To quantify its benefit, this strategy will be compared with other two strategies; 1) a traditional strategy where each player minimizes local inventory costs, Hosoda and Disney (2006a), and 2) an altruistic strategy achieved by the generalized OUT policy with matched feedback controllers, Hosoda and Disney (2006b).…”

“…ISSN 1740-8865. DOI: 10.1504/IJISTA.2009 These expressions for the variances may, in general, be obtained by a variety of ways, from stochastic analysis Hosoda and Disney (2006a) via the frequency domain Dejonckheere et al (2004), control theory Disney and Towill (2003), or state space methods Gaalman and Disney (2006). However we will not provide further details here due to space requirements.…”

Incorporating demand, orders, lead time, and pricing decisions for reducing bullwhip effect in supply chains

“…Several researchers have studied different forecasting methods for reducing that effect (Metters [11], Chen et al [12], Dejonckheere et al [13], Chandra and Grabis [14], Hosoda and Disney [15], Sucky [16], Wang et al [17], Fazel zarandi and Gamasaee [18], Nepal et al [19], Adenso-Díaz et al [20], Ciancimino et al [21], Samvedi and Jain [22], Lau et al [23], and Cho and Lee [24]). Recently, Montanari et al [25] presented a new probabilistic demand forecasting and inventory control model for mitigating BWE.…”