TY - JOUR
T1 - Inventory management for stochastic lead times with order crossovers
AU - Disney, Stephen M.
AU - Maltz, Arnold
AU - Wang, Xun
AU - Warburton, Roger D H
N1 - Publisher Copyright:
© 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
PY - 2016/1/16
Y1 - 2016/1/16
N2 - 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.
AB - 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.
KW - Global supply chains
KW - Order cross-over
KW - Order-up-to policy
KW - Safety stock
KW - Stochastic lead-times
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U2 - 10.1016/j.ejor.2015.07.047
DO - 10.1016/j.ejor.2015.07.047
M3 - Article
AN - SCOPUS:84942295417
SN - 0377-2217
VL - 248
SP - 473
EP - 486
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -