对同时运营线上与线下销售渠道的垄断型制造商, 在同时考虑过度生产损失和缺货机会损失的情况下, 研究其在随机需求下的最优生产与定价决策. 以最大化期望利润为目标函数, 建立了制造商的随机决策规划模型. 基于两个销售渠道随机需求的概率密度函数恒正的假设, 证明了在最大化期望利润的情况下, 每个渠道的生产量都是两个渠道销售价格的二元函数. 在分析模型解的过程中:对于目标函数最大值在可行域边界取得的情形, 提出了渠道妥协的概念;对于目标函数最大值在可行域内部取得的情形, 给出了必要和充分的判定条件. 进一步地, 分别对备货量关于销售价格的不同函数表达形式给出了当目标函数最大值在可行域边界取得时最大期望利润的求解方法.

This paper considers production and pricing issues of a monopolistic manufacturer who possesses dual sales channels in the presence of stochastic demands. Both overproduction loss and opportunity loss of stock-out are taken into account. A stochastic programming model is constructed, aiming to maximize the manufacturer's expected profit.Under the assumption that probability density functions of stochastic demands of the two sales channels are positive, we demonstrate that the production quantity for each channel is a mapping of sales prices of the two channels while maximizing the total profit. The conception of a channel's compromise is proposed during analyzing the solution of the model. Moreover, both a necessary condition and a sufficient condition are presented for cases in which the maximal expected profit realizes in the interior of the feasible region. Further, methods are proposed for obtaining the solution when the maximal expected profit realizes on one boundary.