Channel selection is a critical trade-off for digital products firms whose products are characterized by network externality. This work develops the models of consumers’ utility impacted by the network externality for two channel strategies of the digital product firms in the two-sided market: direct channel strategy and platform channel strategy. Deriving from the consumers’ utility, the optimization models of the two channel strategies are presented. The optimization models are solved through the Lagrangian method, and the comparative statics analysis is conducted to investigate the effect of network externality on optimality. Mathematical results show that if the intensity of network externality in the online platform surpasses that in the direct channel, the platform channel strategy dominates the other channel strategy; otherwise, the direct channel strategy is the firms’ optimal decision. In addition, the two channels share the equal optimal price, and the firms’ profit (and demand) would be positively impacted by the network effect and the products’ features but negatively impacted by the consumers’ learning cost. This work provides decision support for the digital product firms on channel selection in the context of the two-sided market.

“Freemium” is a popular business model adopted by the vendors of digital products, and it has aroused extensive attention in the academia. The existing research studies commonly explore the business model from the perspective of network effect, but lack the attention to the small-world features of network effect. In order to explore the effect of the small-world network, the current work presents a two-period optimization model of monopolist. The optimization model is incorporating with the Freemium model and the small-world feature of consumer base. The optimization model is solved analytically, and the comparative static results show that if the integrating network effect caused by the strong and weak relationship group is sufficiently high (or the small-world feature of the user group is prominent), the user group network exerts a positive effect; if the integrating network effect is not sufficiently high (or the small-world feature of the user group is not prominent), the user group network exerts a negative effect; especially, if the integrating network effect is low or moderate, the premium product is supposed to be free for the consumers. The conclusions enrich the understanding on the operation of digital products firms in the academia and industry.

Successive release is a common strategy adopted by mobile app providers, and determining the launch timing of new app versions presents an important challenge to these providers. Network effect and consumers' perceived value are significant factors that influence the decisions of providers. By focusing on a monopoly market, we develop an optimization model that incorporates the two factors to determine the optimal launch timing of new versions of mobile apps. The model is solved by Lagrangian method, and the closed-form results indicate that the monopoly provider launches new app versions as soon as possible if the consumers' perceived value is not sufficiently high. Otherwise, the new version is launched after (or before) the sales of its former version reach maturity if the network effect is (or not) sufficiently high. Moreover, the monopoly app vendor delays the launch of a new version when the consumers enjoy a large network externality; however, the same vendor accelerates the release of upgrades if the consumers have a high perceived value of the app. This paper presents a novel mathematical formulation to analyze the launching policy of digital products.

This paper develops a joint strategy of condition-based maintenance and spare ordering for a multistate system which is subject to competing failures due to external shocks and self-degradation. Failures of this system are hidden and can be divided into two types: a one-stage hard failure and a two-stage soft failure. The states of the system are identified by periodic inspections and replacement is executed preventively or correctively in response to the defective or failed state. When the operating time of the system is reached the predetermined threshold τ, the spare is ordered. Furthermore, a threshold level z is introduced to postpone the preventive replacement (PR) when the ordered spare is delivered before the defective state is first detected. Depending on the state of the ordered spare when replacement is required and the fault cause of the system when a corrective replacement (CR) is needed, all possible renewal events are analyzed to establish the joint optimization model. A modified artificial bee colony algorithm and discrete simulation algorithm are adopted to find the optimal solutions, and the correctness of the proposed model is verified by a numerical example. Moreover, the results from the numerical example indicate that the proposed strategy is superior to the comparative model, thus the applicability and effectiveness of the proposed model is illustrated.INDEX TERMS Multistate competing failure, hidden failures, condition-based maintenance, spare ordering, delay-time model