This paper investigates a dual-channel retailer’s inventory and pricing integrated decision-making problem over multiple periods. The quantity-sales mode is adopted in the online channel while the unit-sales mode is used offline. The customer demand of each sales channel is stochastic, and depends on visit costs, customer return costs, sales modes and pricing levels. To achieve the long-term profit maximization, the dual-channel retailer needs to optimize the pricing levels of both channels and the ordering quantity. For this problem, we first formulate a stochastic dynamic programming model, and then prove the joint concavity and the supermodularity of the objective function. With these properties, the optimality of the base-stock policy is proved, and the optimum price policy is characterized. Specifically, if the retailer’s optimum stock is neither too low nor too high, both sales channels need to be operated simultaneously, otherwise, only operating one channel is optimal. The online price is invariant with the retailer’s stock level while the offline price is decreasing in the retailer’s stock level. Finally, numerical results show that the quantity-sales mode, dual-channel sales model, and the multi-period dynamic decisions could benefit the dual-channel retailer. In addition, influences of cost parameters on the total profit are verified numerically.

中文翻译：

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量销模式下双渠道零售商多期库存与定价策略

本文研究了一个双渠道零售商的多时期库存和定价综合决策问题。线上渠道采用量销模式，线下渠道采用单位销售模式。每个销售渠道的客户需求是随机的，取决于访问成本、客户退货成本、销售方式和定价水平。为实现长期利润最大化，双渠道零售商需要优化双渠道的定价水平和订货量。对于这个问题，我们首先制定了一个随机动态规划模型，然后证明了目标函数的联合凹性和超模性。利用这些性质，证明了基础库存政策的最优性，并表征了最优价格政策。具体来说，如果零售商的最优库存既不太低也不太高，则需要同时经营两个销售渠道，否则只经营一个渠道是最优的。线上价格与零售商的库存水平保持不变，而线下价格随着零售商的库存水平而下降。最后，数值结果表明，数量销售模式、双渠道销售模式和多期动态决策可以使双渠道零售商受益。此外，数值验证了成本参数对总利润的影响。数值结果表明，数量销售模式、双渠道销售模式和多期动态决策可以使双渠道零售商受益。此外，数值验证了成本参数对总利润的影响。数值结果表明，数量销售模式、双渠道销售模式和多期动态决策可以使双渠道零售商受益。此外，数值验证了成本参数对总利润的影响。