In this paper, we consider an infinite horizon, continuous-review, stochasticinventory system in which cumulative customers' demand is price-dependent andis modeled as a Brownian motion. Excess demand is backlogged. The revenue isearned by selling products and the costs are incurred by holding/shortage andordering, the latter consists of a fixed cost and a proportional cost. Ourobjective is to simultaneously determine a pricing strategy and an inventorycontrol strategy to maximize the expected long-run average profit.Specifically, the pricing strategy provides the price $p_t$ for any time$t\geq0$ and the inventory control strategy characterizes when and how much weneed to order. We show that an $(s^*,S^*,p^*)$ policy is optimal and obtain theequations of optimal policy parameters, where $p^*=\{p_t^*:t\geq 0\}$.Furthermore, we find that at each time $t$, the optimal price $p_t^*$ dependson the current inventory level $z$, and it is increasing in $[s^*,z^*]$ and isdecreasing in $[z^*,\infty)$, where $z^*$ is a negative level.
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机译：在本文中，我们考虑了一个无限视野，连续审查的随机库存系统，在该系统中，累积客户需求与价格有关，并被建模为布朗运动。需求积压。收入是通过销售产品来赚取的，而成本则是通过持有/短缺和订购而产生的，后者包括固定成本和比例成本。我们的目标是同时确定定价策略和库存控制策略，以最大化预期的长期平均利润。具体来说，定价策略提供任何时间的价格$ p_t $$ t \ geq0 $，而库存控制策略则描述了何时以及如何表征非常需要订购。我们证明了$（s ^ *，S ^ *，p ^ *）$策略是最优的，并获得了最优策略参数的等式，其中$ p ^ * = \ {p_t ^ *：t \ geq 0 \} $。此外，我们发现在每次$ t $时，最优价格$ p_t ^ * $取决于当前库存水平$ z $，并且它以$ [s ^ *，z ^ *] $递增，而以$ [ z ^ *，\ infty）$，其中$ z ^ * $是负值。
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