Dacheng Yao

TL;DR: In this article, the authors consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control, and they find an adjustment policy that balances the holding cost and adjustment cost to minimize the long-run average cost.

Abstract: We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a three-step lower-bound approach to solving the optimal control problem under a discounted cost criterion. In addition, we prove that a four-parameter control band policy is optimal among all feasible policies. A key step is the constructive proof of the existence of a unique solution to the free boundary problem. The proof leads naturally to an algorithm to compute the four parameters of the optimal control band policy.

TL;DR: This work considers a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift, and proposes a selection procedure for computing the optimal policy parameters when thesetup cost is a step function.

TL;DR: In this paper, the demand process is modeled as a Brownian motion and the optimal control policy is a generalized (s, S) policy consisting of a sequence of (si, Si ).

TL;DR: In this article, an infinite horizon, continuous-review, stochastic inventory system is considered, where the cumulative customers' demand is price dependent and is modeled as a Brownian motion, and the objective is to simultaneously determine a pricing strategy and an inventory control strategy to maximize the expected long run average profit.