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Exploring the nonlinear dynamics of the lost-sales order-up-to policy

Disney, Stephen M., Ponte, Borja and Wang, Xun ORCID: 2021. Exploring the nonlinear dynamics of the lost-sales order-up-to policy. International Journal of Production Research 59 (19) , pp. 5809-5830. 10.1080/00207543.2020.1790687

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With most inventory theory investigating linear models, the dynamics of nonlinear inventory systems is not well understood. We explore the dynamics of the order-up-to policy under lost-sales for the case of i.i.d.~normally distributed demand and unit lead times. We consider the ideal minimum mean squared error forecast and two alternative scenarios: partial demand observation and dynamic demand forecasting, providing a broad understanding of the operational performance of lost-sales systems. In each scenario, we obtain analytical expressions for the order, inventory, and satisfied demand distributions. This allows us to quantify the Bullwhip and inventory variance amplification ratios as well as the fill rate and the inventory cover. We show the lost sales nonlinearity induces complex behaviors in inventory systems. Interestingly, lost sales smooth supply chain dynamics, significantly affecting the trade-off between service level and average inventory holding. We also reveal the inventory downsides of demand censoring and the production damages induced by dynamic forecasts. We identify a key parameter, the relative safety margin, that characterizes the performance of lost-sales systems. We finish by offering some prescriptive results for the optimal safety stock and capacity level in both a retail and a manufacturing lost-sales setting.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
Publisher: Taylor & Francis
ISSN: 0020-7543
Date of First Compliant Deposit: 30 June 2020
Date of Acceptance: 27 June 2020
Last Modified: 08 Nov 2023 13:29

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