Continuous review inventory models where random lead time depends on lot size and reserved capacity

The processing time of large orders is, in many industries, longer than tha t of small orders. This renders supply lead times in such settings to be in creasing in the order size. Yet that pattern is not reflected in existing i nventory control models, especially those allowing for random lead times. T his work aims at rectifying the situation. Our setting is an order-quantity /reorder-point model with backordering, where the shortage penalty is incur red per unit per unit time. The processing time of each unit is random; the processing time of a lot is correlated with its size. For the case where l ead time is proportional to the lot size, we obtain a closed-form solution. That is, unlike the classical (Q, r) model (where lead time is independent of lot size), no iterations are required here. We also analyze a case wher e the processing time exhibits economies of scale in the lot size. Finally, we consider a situation where a customer can secure shorter processing tim es by reserving capacity at the supplier's manufacturing facility. (C) 2000 Elsevier Science B.V. All rights reserved.