Inventory management is a crucial task for any industry. In this paper, we have determined the optimum profit and economical order quantity under variety of assumptions such as the demand per unit time follows either a log-normal or a generalized exponential distribution. Parametric relationship between these two distributions, the proposed models become comparable. For modeling, we consider the expected demand and variable deterioration. Under these probabilistic assumptions, inventory models are developed for situations like no, complete and partial backlogging. Classical methods are unable to solve these situations under these assumptions. Thus genetic algorithm is proposed to solve these models. Economic order quantity is obtained for maximizing the total profit for the respective demand per unit time distributions. A real-world case study of a deteriorated product is presented to illustrate the procedures of the proposed inventory models.

库存管理是任何行业的一项关键任务。在本文中，我们在各种假设下确定了最佳利润和经济订货量，例如单位时间的需求服从对数正态分布或广义指数分布。这两个分布之间的参数关系，使提出的模型具有可比性。对于建模，我们考虑了预期需求和变量恶化。在这些概率假设下，库存模型是针对无积压、完全积压和部分积压等情况开发的。在这些假设下，经典方法无法解决这些情况。因此提出遗传算法来解决这些模型。经济订货量是为了使单位时间分配的各个需求的总利润最大化而获得的。