A bi-modal inventory study with random lead times

the long version

A single-product continuous review inventory problem is formulated and solved. The chief virtue of the formulation is that the probability distribution of lead times is general. It is found that the optimal order size differs from the Wilson EOQ when holding costs or deterioration rate (both are lumped into a single discount rate) are large, and that it may even be a non-unique quantity. The second (fast) shipment mode enters in the same manner as a stockout cost. (Author)