This paper develops an inventory-transport model where demand, lead ti
me and freight loss and damage are all stochastic. An exact formulatio
n, as well as a set of approximations, of a shipper's average logistic
s cost are derived. They are tested on numerical examples and the resu
lts are discussed in terms of the performance of the approximations, t
he impacts of freight loss and damage, and the relationships between l
oss and damage control and reductions of the mean and variance of lead
time.