Dual-Channel Retailer’s Multi-Period Inventory and Pricing Policy with the Quantity-Sales Mode

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.