Advancements in digital technologies have catalyzed the emergence of the ship-then-shop subscription service, which offers consumers a personalized shopping experience. Using this service, consumers could either receive products regularly at a fixed frequency, i.e., fixed shipment frequency service (FSF), or place orders as needed under on-demand service (ODS) by paying a service fee for each shipment. Nevertheless, suppliers' service portfolio design is challenged by the information of consumers' demand occurrence rates, particularly on service fee and service capacity. In this regard, this study strives to understand this problem by developing a tractable model comprising a supplier and a consumer. Consumer demand rate, either high or low, remains private information, leading to the classification of consumers in high and low types. When the difference in reservation utility is moderate, a first-best result can manifest amid information asymmetry. However, when the reservation utility of the H-type consumer is small (large), the supplier must strategically distort the service portfolio to encourage honest choices from consumers. Besides, ODS does not necessarily benefit the supplier even though the exact demand rate information is common knowledge. As the reservation utility of H-type consumers rises, the supplier's preference for FSF initially grows but subsequently declines. Moreover, it is not necessarily the case that symmetric demand rate information proves strictly better off for the supplier when the reservation utility of the H-type consumer is extremely low. The two preceding findings elucidate the reasons for the coexistence of ODS and FSF modes in practice. Finally, information asymmetry may endow information rent to the H-type consumer.