A note on "lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand"

Glock [2012. Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand. International Journal of Production Economics 136, 37-44] recently presented an integrated inventory model where the lead time can be reduced by crashing the setup and transportation time, by increasing the production rate, or by decreasing the lot size. In this note, we introduce a more realistic lead time crashing cost and propose a modified integrated inventory model by adding the transportation time as a decision variable and assuming that there are two different safety stocks. Furthermore, we give some numerical examples to illustrate the advantages of the modified model.