A (Q, R) inventory replenishment model with two delivery modes

•Analysis of an inventory replenishment model with two transportation modes.•Demonstrates potential benefits of delivery mode splitting.•Strategic use of quick response supplier to reduce inventory cost.

Although splitting shipments across multiple delivery modes typically increases total shipping costs as a result of diseconomies of scale, it may offer certain benefits that can more than offset these costs. These benefits include a reduction in the probability of stockout and in the average inventory costs. We consider a single-stage inventory replenishment model that includes two delivery modes: a cheaper, less reliable mode, and another, more expensive but perfectly reliable mode. The high-reliability mode is only utilized in replenishment intervals in which the lead time of the less-reliable mode exceeds a certain value. This permits substituting the high-reliability mode for safety stock, to some degree. We characterize optimal replenishment decisions with these two modes, as well as the potential benefits of simultaneously using two delivery modes.