Inventory management for stochastic lead times with order crossovers

Disney, Stephen M. ORCID: https://orcid.org/0000-0003-2505-9271, Maltz, Arnold, Wang, Xun ORCID: https://orcid.org/0000-0001-7800-726X and Warburton., Roger D. H. 2016. Inventory management for stochastic lead times with order crossovers. European Journal of Operational Research 248 (2) , pp. 473-486. 10.1016/j.ejor.2015.07.047

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Abstract

We study the impact of stochastic lead times with order crossover on inventory costs and safety stocks in the order-up-to (OUT) policy. To motivate our research we present global logistics data which violates the traditional assumption that lead time demand is normally distributed. We also observe that order crossover is a common and important phenomenon in real supply chains. We present a new method for determining the distribution of the number of open orders. Using this method we identify the distribution of inventory levels when orders and the work-in-process are correlated. This correlation is present when demand is auto-correlated, demand forecasts are generated with non-optimal methods, or when certain ordering policies are present. Our method allows us to obtain exact safety stock requirements for the so-called proportional order-up-to (POUT) policy, a popular, implementable, linear generalization of the OUT policy. We highlight that the OUT replenishment policy is not cost optimal in global supply chains, as we are able to demonstrate the POUT policy always outperforms it under order cross-over. We show that unlike the constant lead-time case, minimum safety stocks and minimal inventory variance do not always lead to minimum costs under stochastic lead-times with order crossover. We also highlight an interesting side effect of minimizing inventory costs under stochastic lead times with order crossover with the POUT policy—an often significant reduction in the order variance.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Business (Including Economics) Centre for Advanced Manufacturing Systems At Cardiff (CAMSAC)
Subjects:	H Social Sciences > HD Industries. Land use. Labor
Uncontrolled Keywords:	Stochastic lead-times; Safety stock; Order cross-over; Order-up-to policy; Global supply chains
Additional Information:	Available online 26 July 2015
Publisher:	Elsevier
ISSN:	0377-2217
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	20 July 2015
Last Modified:	08 Nov 2023 01:55
URI:	https://orca.cardiff.ac.uk/id/eprint/74757

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