Impact of Correlated Procurement Lead Times on Reorder Point Decisions with Cycle Service Level Thresholds

Supply chain disruptions make procurement lead time (PLT) uncertain, so a reorder point that meets a target customer service level must be set against several sources of risk at once, including disruption-induced abnormal replenishment lead times. This paper models the abnormal PLT as a stochastic amplification of the normal PLT, LTA=LTN×DP with DP>1 by construction and extends the Normal Approximation Method (NAM) and the Compound Normal Distribution Method (CNDM) to this dependence structure under a cycle service level (CSL) constraint. The extended NAM uses the complete two-component mixture variance, including the between-state term that the classical variance average omits. For the extended CNDM the stationary points of the reorder point with respect to normal PLT volatility solve H(R)=0 under the within-state normal approximation of the two lead-time demand distributions, which has one or three simple roots on the non-degenerate parameter region; the two mean-based levels are reference values rather than thresholds. The service level and the reorder point are therefore linked through several distinct thresholds at which the effect of volatility changes sign, and the sign alternates across adjacent thresholds, which accounts for the procurement lead time paradox: a reduction in volatility need not lower the required inventory and raises the reorder point in some service-level regions. Monte Carlo experiments over sixty non-degenerate scenarios support this reading, with the CNDM showing a lower average absolute error than the NAM at all five target service levels while the NAM is closer in some individual scenarios. Lead time improvement measures should therefore be evaluated jointly with the service-level target, and reorder points should not be treated as one-off calibrations of a stable environment, because they need review when the disruption probability changes.