Mathematical Modeling of Pricing and Service in the Dual Channel Supply Chain Considering Underservice

The retailer cannot often identify consumers’ preference for personalized and refined services. This poses a lower service than the consumer expects, which will lead to a decline in consumers’ satisfaction and loyalty. To cope with this problem, we consider a dual-channel supply chain composed of a manufacturer who has the online channel and an offline retailer and introduce the concept of underservice into the framework of pricing and service decision. The influence of consumers’ service expectations and the sensitive coefficient of consumers’ perceptive service on optimal decision-making were explored by optimization theory. First, the mathematical model of profit functions of the offline retailer and the manufacturer was developed by taking into account the service expectation respectively. Based on this, the Stackelberg game was adopted to prove that there is a linkage mechanism between the optimal retail price and the optimal service level under certain conditions. Second, we examined the conditions under which underservice occurs and the factors that influence them. Finally, we explored the stability condition under which the offline retailer’s optimal service level is against pricing. Results show that for newly launched products, the offline retailer will take the risk of increased service costs to adopt a strategy of high profit and good sales as a result of underservice. With regard to expiring products, it is impossible for the offline retailer to provide a lower-than-expected service level. Therefore, the offline retailer will adopt a strategy of small profits but quick turnover. In addition, the optimal service level of the offline retailer is stable against the optimal retail price, which greatly simplifies the service decision of the offline retailer, that is, the offline retailer does not need to consider the pricing strategy of the manufacturer and only needs to offer a level of service equal to the consumers’ service expectation.