Continuous review cyclic inventory models with emergency order

Many kinds of reorder point-reorder quantity policies with an emergency order, in which we can decide when the expedited order point is reached and then we place an expedited replenishment order, have been presented in earlier contributions. Very few studies on cyclic inventory control with an emergency order, however, have been reported. The purpose of this paper is to establish some analytical results on the continuous review cyclic inventory policy with two kinds of lead times. The authors derive necessary and sufficient conditions for the existence of the optimal ordering time which minimizes the long-run average or the expected total discounted costs. Also, they give explicit formulae of the expected costs by specifying demand processes. Poisson and Brownian motion processes are assumed as the demand processes. Finally, the authors numerically calculate the optimal ordering time and the optimal order quantity, and refer to the sensitivity of model parameters for the optimal policy.