Optimal pricing and return policy and the value of freight insurance for a retailer facing heterogeneous consumers with uncertain product values

We study the optimal pricing and return policy, and the value of freight insurance for a retailer selling a product to heterogeneous consumers with uncertain values of the product. For the case with no return freight cost, we find that the optimal sale price and refund depend on the heterogeneity of consumers and the proportion of high-value consumers. When consumer heterogeneity is relatively high and the proportion of high-value consumers is very high, the retailer should not adopt the return policy; otherwise, the retailer should adopt it. For the case with a positive return freight cost, the retailer has to set a higher refund or a lower price, hurting its profit. When consumer heterogeneity is relatively high and the proportion of high-value consumers is very high, the optimal price is unchanged, but the optimal refund increases. In other situations, the retailer needs to reduce the price or increase the refund to attract consumers. Further considering the case where the retailer provides return freight insurance for the consumers, we find that whether freight insurance benefits the retailer depends on the unit insurance premium and the return freight cost.