A duo hierarchical graph model for conflict resolution is developed to investigate market competition between Airbus and Boeing over aircraft sales in the Asia Pacific region. The duo hierarchical graph model, a significant extension of the graph model for conflict resolution methodology, contains two common decision makers, who take part in two related subconflicts, as well as local decision makers, who participate in only one subconflict. New stability definitions are proposed to describe forms of sanction unique to the hierarchical model. The interrelationships between stabilities in the overall graph model and in the two local models are investigated. Then the duo hierarchical graph model is applied to the competition between Airbus and Boeing in both the wide and narrow body markets in the Asia-Pacific region. The two types of Asian airlines have different operating strategies, so that the two markets constitute sub-competitions that can be modelled naturally using the duo hierarchical graph model. The stability results indicate a resolution for all decision makers that implies marketing strategies for the aircraft manufacturers and guidelines for aircraft purchase by the airlines. Thus, this model provides decision makers with a comprehensive understanding of the dynamics of the competition and guidance in identifying beneficial actions.

Reliability is a desirable performance indicator of many real-world systems to measure the quality level. One general method for evaluating multi-state reliability is using d-minimal paths (d-MPs). However, being an NP-hard problem, searching for all d-MPs is a rather challenging task. This paper proposes an improved algorithm to solve the d-MP problem. To reduce the search space of d-MPs, a concept of lower capacity bound is introduced into the d-MP problem, and an effective technique is developed to find lower capacity bounds. Meanwhile, the fast enumeration method which is a recent improvement to the traditional enumeration method is employed to solve d-MPs. In addition, by introducing the operation of transforming undirected edges into directed edges, the proposed algorithm is applicable to solving both directed networks and undirected networks. Through numerical experiments, it is found that the proposed algorithm holds a distinct advantage over the existing methods in solving all d-MPs.

This article explores bundling and pricing decisions for two complementary products in a two-layer supply chain consisting of a multi-product manufacturer and a retailer. We establish four different pricing models under cases of decentralized decision, while considering different portfolio-bundling strategies of the manufacturer and the retailer. A game-theoretical method is used to characterize the corresponding equilibrium outcomes in each scenario. By further analyzing and comparing the maximum profits of all four possible scenarios, optimal bundling and pricing decisions for the manufacturer and the retailer are obtained, respectively. Model extensions and numerical examples are enriched to highlight the factors affecting optimal decision-making. Finally, valuable and interesting managerial insights are summarized. Results show that the upstream manufacturer always profits more when he sells complementary products separately. However, the optimal bundling decision of the downstream retailer is jointly determined by product complementarity (as a major factor) and the difference of product profitability (as a secondary factor). Market power cannot exert an influence on both optimal bundling decisions, but it can partly affect pricing decisions.

This article presents the issue of extended warranty and management strategies in a three-echelon competing online shopping supply chain with price- and base warranty period-dependent demand. We employ game theory to develop decision models to explore the interactions between component suppliers and the manufacturer, as well as competition between two component suppliers. Products and extended warranty are sold by an online store, which is the leader in the Stackelberg game. Two scenarios are considered: either the manufacturer offers a prepaid extended warranty to customers or doses not. In each scenario, base warranties are assumed to be bundled with products. Our results show that when the manufacturer’s repair costs change in a proper range, providing extended warranty can benefit both the manufacturer and the online store; otherwise, the manufacturer has no incentive to offer the extended warranty. Reducing repair costs, improving component reliability, or shortening the base warranty period allows the manufacturer to realize significantly better value of the extended warranty. High component reliability benefits both the manufacturer and the online store, with the manufacturer reaping more benefit. Extending the length of the base warranty adversely affects profit of the manufacturer and the value of the extended warranty.

This study examines an optimal inventory strategy when a retailer markets a product at different selling prices through a dual-channel supply chain, comprising an online channel and an offline channel. Using the operating pattern of the offline-to-online (O2O) business model, we develop a partial robust optimization (PRO) model. Then, we provide a closed-form solution when only the mean and standard deviation of the online channel demand distribution is known and the offline channel demand follows a uniform distribution (partial robust). Specifically, owing to the good structural properties of the solution, we obtain a heuristic ordering formula for the general distribution case (i.e., the offline channel demand follows a general distribution). In addition, a series of numerical experiments prove the rationality of our conjecture. Moreover, after comparing our solution with other possible policies, we conclude that the PRO approach improves the performance of incorporating the internet into an existing supply chain and, thus, is able to adjust the level of conservativeness of the solution. Finally, in a degenerated situation, we compare our PRO approach with a combination of information approach. The results show that the PRO approach has more “robust” performance. As a result, a reasonable trade-off between robustness and performance is achieved.