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.
We investigate the impact of advance notice of product returns on the performance of a decentralised closed loop supply chain. The market demands and the product returns are stochastic and are correlated with each other. The returned products are converted into "as-good-as-new" products and used, together with new products, to satisfy the market demand. The remanufacturing process takes time and is subject to a random yield. We investigate the benefit of the manufacturer obtaining advance notice of product returns from the remanufacturer. We demonstrate that lead times, random yields and the parameters describing the returns play a significant role in the benefit of the advance notice scheme. Our mathematical results offer insights into the benefits of lead time reduction and the adoption of information sharing schemes.
We investigate the dynamics of a closed-loop supply chain with first-order auto-regressive (AR(1)) demand and return processes. We assume these two processes are cross-correlated. The remanufacturing process is subject to a random triage yield. Remanufactured products are considered as-goodas-new and used to partially satisfy market demand; newly manufactured products make up the remainder. We derive the optimal linear policy in our closed-loop supply chain setting to minimise the manufacturer's inventory costs. We show that the lead-time paradox can emerge in many cases. In particular, the auto-and cross-correlation parameters and variances of the error terms in the demand and the returns, as well as the remanufacturing lead time, all influence the existence of the lead-time paradox. Finally, we propose managerial recommendations for manufacturers.
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