In this paper, we study a periodic-review joint inventory and pricing optimization problem in a stochastic price-sensitive demand framework with lost sales. We contribute to the existing literature from three aspects: generalizing the form of demand functions, developing the technique of proving concavity preservation, and extending the scope of optimality conditions. Specifically, we set the demand in our model as a general function. In order to obtain the optimality condition under general demands, we first introduce the concept of Price Elasticity of the Slope (PES) and transform the original PES condition between sales and profit in literature into a PES condition between sales and demand. Then, we obtain the lower bound of the PES difference between sales and profit by utilizing our transformed condition. With the non-negativity of the lower bound, we obtain two groups of easy-to-verify conditions which consist of the mean demand and the probability distribution of the demand. Under specific demand forms, the obtained conditions are reduced to constraints on the distribution of price-free uncertainty and the deterministic functions of price, respectively. Compared with the existing literature, our study therefore extends the scope of optimality conditions and includes non-concave demand functions when adapting a base-stock list-price (BSLP) policy in a joint inventory-pricing problem. Our conditions ensure that more types of products (e.g., the products of which the price elasticity of demand is constant) meet the optimality of the BSLP strategy, and more retailers can make pricing and replenishment decisions based on this strategy.

在本文中，我们研究了具有销售损失的随机价格敏感需求框架中的定期审查联合库存和定价优化问题。我们从三个方面对现有文献做出贡献：推广需求函数的形式，开发证明凹性保持的技术，以及扩展最优条件的范围。具体来说，我们将模型中的需求设置为通用函数。为了得到一般需求下的最优条件，我们首先引入斜率价格弹性（PES）的概念，将文献中销售与利润之间的原始PES条件转化为销售与需求之间的PES条件。然后，我们利用转换后的条件获得销售额和利润之间 PES 差异的下限。利用下界的非负性，我们得到了两组易于验证的条件，即均值需求和需求的概率分布。在特定的需求形式下，所获得的条件分别简化为对无价格不确定性分布和价格确定性函数的约束。因此，与现有文献相比，我们的研究扩展了最优条件的范围，并在联合库存定价问题中采用基本库存定价 (BSLP) 政策时包括非凹需求函数。我们的条件保证了更多种类的产品（如需求价格弹性不变的产品）满足BSLP策略的最优性，更多的零售商可以基于该策略进行定价和补货决策。我们得到两组易于验证的条件，包括平均需求和需求的概率分布。在特定的需求形式下，所获得的条件分别简化为对无价格不确定性分布和价格确定性函数的约束。因此，与现有文献相比，我们的研究扩展了最优条件的范围，并在联合库存定价问题中采用基本库存定价 (BSLP) 政策时包括非凹需求函数。我们的条件保证了更多种类的产品（如需求价格弹性不变的产品）满足BSLP策略的最优性，更多的零售商可以基于该策略进行定价和补货决策。我们得到两组易于验证的条件，包括平均需求和需求的概率分布。在特定的需求形式下，所获得的条件分别简化为对无价格不确定性分布和价格确定性函数的约束。因此，与现有文献相比，我们的研究扩展了最优条件的范围，并在联合库存定价问题中采用基本库存定价 (BSLP) 政策时包括非凹需求函数。我们的条件保证了更多种类的产品（如需求价格弹性不变的产品）满足BSLP策略的最优性，更多的零售商可以基于该策略进行定价和补货决策。