An (s,q) inventory model with stochastic and interrelated lead times

In this article the authors introduce a lead time mechanism that allows simultaneous order arrivals. This mechanism ensures that orders never cross each other. For the continuous review (s,q) inventory system with constant demand, the authors show that the allowance of batch arrivals gives rise to a discontinuous cost function. By exploiting the special structure of this cost function, a search algorithm is derived that yields the optimal order strategy in a reasonable amount of time. The search is restricted to integer order strategies only. The authors also consider an approximate method of solution that is based on a related model with a continuous cost function. The results obtained by this approximation are, in general, very satisfactory.