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考虑一个报童模型中多类顾客的库存分配问题,将顾客按照他们愿意支付价格的高低划分为不同级别。零售商在销售期初决定产品订货量,并在销售期内决定接受或者拒绝不同顾客的需求,以最大化销售期内的期望总利润。将销售期分成大量足够小的时间单位,通过建立一个反向Bellman动态规划方程,以优化每个时间单位内的库存分配策略,并得到了零售商最优的期初订货量。通过与没有库存分配策略下零售商的期望利润进行比较,算例分析得出库存分配策略可以大幅提高零售商的利润。这主要是因为通过库存分配可以使得零售商从高端顾客中获取更多利润,同时能够减小期初的订货量,以节约采购成本和库存持有成本。
Consider the inventory allocation of multiple types of customers in a newsboy model, and divide the customers into different grades according to the price they are willing to pay. The retailer determines the order quantity of the product at the beginning of the sales period and decides to accept or reject the needs of different customers during the sales period in order to maximize the expected total profit during the sales period. The sales period is divided into a large number of small enough time units to optimize the inventory allocation strategy in each time unit by establishing an inverse Bellman dynamic programming equation and obtain the optimal initial order quantity for the retailer. By comparing the retailer’s expected profit with the non-inventory allocation strategy, the case study shows that the inventory allocation strategy can greatly increase the retailer’s profit. This is mainly because retailers can obtain more profits from high-end customers by allocating inventory, meanwhile, can reduce the order quantity at the beginning of the period to save purchasing cost and inventory holding cost.