中文摘要：

对时效性商品的定价问题进行了研究。基于一种负二项分布的离散需求函数，并在利润最大化原则下，建立了时效商品最优定价模型。由于该模型涉及多个随机变量的概率分布，常规函数极值算法难以获得问题解析解，引入粒子群优化算法，对模型进行演化求解，并给出算例分析。结果表明：利用粒子群算法，可以快速有效得到不同库存量情况下应采取的最优定价。最后提出需要进一步解决的若干问题。

英文摘要：

The problem of pricing for perishable commodities is mainly studied. According to the principle of profit maximization and based on a discrete demand function which can be represented as a negative binomial distribution, the optimal pricing model for the perishable products is established. Since the model involves some different stochastic distributions of several variables, which is difficult for the normal numerical methods to solve, the particle swarm optimization （PSO） algorithm is introduced for the first time to settle it, and a numerical example is studied then. The result indicated that. by using the PSO method, the optimal prices for different inventory levels can be derived quickly and effectively. In the end some possible extensions to the current study that need further investigations are presented.