随机需求下多品种易腐品的联合补货优化

Optimization of Multi Variety Perishable Products’ Joint Replenishment Problem under Random Demand Conditions

摘要: 本文研究了在无限时间范围内，需求为服从某一分布的随机函数，多品种易腐品联合补货的库存模型，采用(T,S)策略，目标是通过确定每种产品的补货周期，使得单位时间内，零售商的总成本最小。本文的难点有两个：首先，联合补货问题是个N-P HARD问题，且由于本文考虑缺货损失的影响，使得模型非常复杂；第二，在随机需求下，零售商的成本模型是不确定的，随着需求函数的变化而变化。针对以上难点，本文首先对模型中存在的指数及对数函数进行泰勒展开实现简化，同时应用了文献[1]的差分进化算法，为易腐品的零售商在实施联合补货时提供有益的管理建议。

Abstract: In this paper, We studied the inventory model of multiple perishable goods combined with a random function of a certain distribution in an infinite time range. The model uses the (T, S) strategy; the goal is to determine the replenishment cycle of each product, making the total cost per unit time of the retailer minimum. The difficulty of this paper has two aspects: First of all, the joint replenishment problem is a N-P HARD problem, and the model becomes more complex because of the effect of the loss of the stock; second, under stochastic demand, the cost model of retailers is uncertain, with the change of demand function changes. In view of the above difficulties, we first simplify the Taylor expansion of exponential and logarithmic functions in the model, and apply the differential evolution algorithm based on [1] to provide useful management recommendations for retailers with perishable goods when implementing joint replenishment.