CONTINUOUS-TIME INVENTORY CONTROL FOR WIENER PROCESS DEMAND

This paper discusses a continuous time inventory system without backlogging allowed under the condition that the demand follows a Wiener process. We propose the explicit formula of the expected total discounted cost for an infinite time span by applying the familiar technique of optimal stopping problem. Further, it is shown that the asymptotic value of the expected total discounted cost by perturbation of the discount rate gives the long-run average cost. Finally, the optimal inventory policies, which are given as the optimal stock levels minimizing the expected total discounted and the long-run average costs, are numerically obtained and compared with ones in the deterministic inventory system. It is made apparent that the discount rate and the diffusion parameter of the demand process are very sensitive for the optimal inventory policies.