I n many services, the quality or value provided by the service increases with the time the service provider spends with the customer. However, longer service times also result in longer waits for customers. We term such services, in which the interaction between quality and speed is critical, as customer-intensive services. In a queueing framework, we parameterize the degree of customer intensity of the service. The service speed chosen by the service provider affects the quality of the service through its customer intensity. Customers queue for the service based on service quality, delay costs, and price. We study how a service provider facing such customers makes the optimal "quality-speed trade-off." Our results demonstrate that the customer intensity of the service is a critical driver of equilibrium price, service speed, demand, congestion in queues, and service provider revenues. Customer intensity leads to outcomes very different from those of traditional models of service rate competition. For instance, as the number of competing servers increases, the price increases, and the servers become slower.
We examine a possibly capacitated, periodically reviewed, single-stage inventory system where replenishment can be obtained either through a regular fixed lead time channel, or, for a premium, via a channel with a smaller fixed lead time. We consider the case when the unsatisfied demands are backordered over an infinite horizon, introducing the easily implementable, yet informationally rich dual-index policy. We show very general separability results for the optimal parameter values, providing a simulation-based optimization procedure that exploits these separability properties to calculate the optimal inventory parameters within seconds. We explore the performance of the dual-index policy under stationary demands as well as capacitated production environments, demonstrating when the dual-sourcing option is most valuable. We find that the optimal dual-index policy mimics the behavior of the complex, globally optimal state-dependent policy found via dynamic programming: the dual-index policy is nearly optimal (within 1% or 2%) for the majority of cases, and significantly outperforms single sourcing (up to 50% better). Our results on optimal dual-index parameters are generic, extending to a variety of complex and realistic scenarios such as nonstationary demand, random yields, demand spikes, and supply disruptions.
Companies in a variety of industries (e.g., airlines, hotels, theaters) often use last-minute sales to dispose of unsold capacity. Although this may generate incremental revenues in the short term, the long-term consequences of such a strategy are not immediately obvious: More discounted last-minute tickets may lead to more consumers anticipating the discount and delaying the purchase rather than buying at the regular (higher) prices, hence potentially reducing revenues for the company. To mitigate such behavior, many service providers have turned to opaque intermediaries, such as Hotwire.com, that hide many descriptive attributes of the service (e.g., departure times for airline tickets) so that the buyer cannot fully predict the ultimate service provider. Using a stylized economic model, this paper attempts to explain and compare the benefits of last-minute sales directly to consumers versus through an opaque intermediary. We utilize the notion of rational expectations to model consumer purchasing decisions: Consumers make early purchase decisions based on expectations regarding future availability, and these expectations are correct in equilibrium. We show that direct last-minute sales are preferred over selling through an opaque intermediary when consumer valuations for travel are high or there is little service differentiation between competing service providers, or both; otherwise, opaque selling dominates. Moreover, contrary to the usual belief that such sales are purely mechanisms for disposal of unused capacity, we show that opaque selling becomes more preferred over direct last-minute selling as the probability of having high demand increases. When firms randomize between opaque selling and last-minute selling strategies, they are increasingly likely to choose the opaque selling strategy as the probability of high demand increases. When firms with unequal capacities use the opaque selling strategy, consumers know more clearly where the opaque ticket is from and the efficacy of opaque selling decreases.distribution channels, competition, revenue management, strategic consumer behavior, rational expectations
Consumers often purchase goods that are "hard to find" to conspicuously display their exclusivity and social status. Firms that produce such conspicuously consumed goods such as designer apparel, fashion goods, jewelry, etc., often face challenges in making optimal pricing and production decisions. Such firms are confronted with precipitous tradeoff between high sales volume and high margins, due to the highly uncertain market demand, strategic consumer behavior, and the display of conspicuous consumption. In this paper, we propose a model that addresses pricing and production decisions for a firm, using the rational expectations framework. We show that, in equilibrium, firms may offer high availability of goods despite the presence of conspicuous consumption. We show that scarcity strategies are harder to adopt as demand variability increases, and we provide conditions under which scarcity strategies could be successfully adopted to improve profits. Finally, to credibly commit to scarcity strategy, we show that firms can adopt sourcing strategies, such as sourcing from an expensive production location/supplier or using expensive raw materials, that signal deeper investment in unit production costs.
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