Inventory management for stochastic lead times with order crossovers

Stephen M. Disney, Arnold Maltz, Xun Wang, Roger D H Warburton

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)473-486
Number of pages14
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Jan 16 2016


  • Global supply chains
  • Order cross-over
  • Order-up-to policy
  • Safety stock
  • Stochastic lead-times

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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