Designing Shipping Policies with Top-up Options to Qualify for Free Delivery

Motivated by the growing significance of contingent free shipping (CFS) policies in the e-commerce industry, we investigate the optimal CFS and pricing decisions for online retailers. Under a CFS policy, consumers enjoy free shipping for orders exceeding a certain threshold value; otherwise, they are charged a flat fee for orders below this threshold. We adopt a utility-based model to capture consumers' behavior of purchasing additional items to qualify for free shipping under a CFS policy and analyze its impact on policy structure and consumer surplus. We characterize the retailer's optimal pricing and CFS policy as functions of consumer mix. When consumer heterogeneity is large enough, the optimal policy induces some consumers to top up and may allow some others to ship for free. In this case, the retailer can charge a high profit margin. Otherwise, a top-up option is unnecessary and a flat-rate shipping fee policy is optimal. Moreover, while the optimal policy never induces all consumers to top up when they are rational, it is possible to do so when consumers associate a psychological disutility with the shipping fee. Surprisingly, the total consumer surplus under the optimal policy may increase in the latter case. Lastly, we show that a subscription program, in addition to the CFS policy, can improve profits when consumers' order size and frequency are negatively correlated. We find that consumer heterogeneity explains the existence of different forms of shipping policy in reality. The CFS policy is a more effective discrimination mechanism in extracting consumer surplus compared to the flat-rate shipping fee policy. The retailer should utilize the CFS policy especially when consumer heterogeneity is significant. Our findings reveal important insights regarding the impact of consumers' top-up behavior on a retailer's optimal operational and marketing decisions