Ping Cao

1. E-commerce platforms, leveraging their vast consumer base and extensive data resources, are increasingly involved in product operations beyond merely facilitating transactions between buyers and...

Problem definition: We study advance selling and upgrading in a priority queue setting that emerges in the amusement park industry. Customers choose to buy fast-track or regular tickets depending on their heterogeneous waiting costs. At the park entrance, customers can choose tickets based on the observed congestion levels. Customers who purchase tickets in advance suffer from congestion uncertainty. Upgrading options allow customers to purchase regular tickets in advance and upgrade on-site if the congestion turns out to be high. The seller’s objective is to find the optimal pricing scheme to maximize revenue. Methodology/results: We analyze a two-stage model in a queueing game framework. Under full coverage and fixed regular ticket prices, the seller sets the priority ticket prices to maximize the revenue. We investigate two pricing schemes, both with and without upgrading options, under different scenarios depending on the proportion of customers who have access to advance ticket purchasing. When all customers have access to advance ticket purchasing, our findings indicate that the advance-and-spot selling scheme yields the same maximum revenue as the scheme that includes the upgrading option if the spot regular ticket price is not too large; thus, the upgrading option becomes unnecessary. Otherwise, allowing upgrading generates more revenue (and social welfare). Interestingly, although upgrading options offer consumers greater flexibility, they reduce consumer surplus in scenarios where upgrading increases revenue. When some customers only purchase tickets on the spot, our numerical analysis shows that allowing upgrading results in higher revenue when the probability of high system congestion is large and highlights cases when the revenue gap is significant. Finally, we extend our analysis to account for customers’ balking behavior and the additional waiting time incurred when purchasing tickets on the spot, providing a robust check on scheme comparison. Managerial implications: Our paper is one of the first to investigate—in the context of queueing economics—the advance selling strategy together with upgrading option, taking into account arrival rate uncertainty. Our results offer guidance on selling scheme design for ticket sellers and provide one economic explanation for the various pricing policies seen in the amusement park industry. Funding: Financial support from the National Natural Science Foundation of China [Grants 72101248, 72471215, 72122019, 72471005, and 72031006] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0410 .

Problem definition: This paper considers a tandem queueing system in which stage 1 has one station serving multiple classes of arriving customers with different service requirements and related delay costs, and stage 2 has multiple parallel stations, with each station providing one type of service. Each station has many statistically identical servers. The objective is to design a joint capacity allocation between stages/stations and scheduling rule of different classes of customers to minimize the system’s long-run average cost. Methodology/results: Using fluid approximation, we convert the stochastic problem into a fluid optimization problem and develop a solution procedure. Based on the solution to the fluid optimization problem, we propose a simple and easy-to-implement capacity allocation and scheduling policy and establish its asymptotic optimality for the stochastic system. The policy has an explicit index-based scheduling rule that is independent of the arrival rates, and resource allocation is determined by the priority orders established between the classes and stations. We conduct numerical experiments to validate the accuracy of the fluid approximation and demonstrate the effectiveness of our proposed policy. Managerial implications: Tandem queueing systems are ubiquitous. Our results provide useful guidelines for the allocation of limited resources and the scheduling of customer service in those systems. Our proposed policy can improve the system’s operational efficiency and customers’ service quality. Funding: Z. Zhong’s research is partially supported by the Fundamental Research Funds for the Central Universities [Grant 2023ZYGXZR074] and the Hunan Provincial Natural Science Foundation of China [Grant 2022JJ40109]. P. Cao’s research is partially supported by the National Natural Science Foundation of China [Grant 72122019]. J. Huang’s research is partially supported by the Hong Kong Research Grants Council General Research Fund [CUHK-14501621] and the National Natural Science Foundation of China [Grant 72222023]. S. X. Zhou’s research is partially supported by the Hong Kong Research Grants Council General Research Fund [CUHK-14500921], the National Natural Science Foundation of China [Grant 72394395], and the Asian Institute of Supply Chains and Logistics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0266 .

With the advancement of online‐ordering technology, an increasing number of service providers are transforming to sell services through online channels alongside traditional offline stores. Our paper studies this emerging business model (also known as omnichannel services) in which customers can choose between online and offline ordering. We develop a queueing‐game‐theoretic model to evaluate the performance of omnichannel systems in terms of throughput and social welfare when customers strategically choose their ordering channels in the presence of service valuation uncertainty. We also contrast omnichannel services with single‐channel services, that is, online‐only and offline‐only services. Our analysis yields the following main insights. First, although customers run the risk of making suboptimal decisions and suffering from unexpected losses when they are uncertain about their service valuations, we find that all customers would be better off in expectation with an increasing level of service valuation uncertainty. Second, while social welfare improves as ordering online becomes more convenient in some cases, it (even online customer welfare) can also be worse off in others, especially when the system operates under heavy congestion, because customers' self‐interested channel choice behavior would impose significant negative congestion externalities among customers. Third, despite the fact that omnichannel services provide customers with an additional, more convenient ordering channel option in comparison with conventional offline‐only services, we find that, somewhat surprisingly, adopting omnichannel services does not necessarily guarantee improvement in social welfare. Finally, we discuss two alternative modeling assumptions to demonstrate the robustness of our main insights.