Two Essays on Dynamic Pricing in Service and Behavioral Operations Management


Student thesis: Doctoral Thesis

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Award date5 Aug 2022


In this thesis, we study two dynamic pricing problems, and present the results in two essays. In the first essay, we consider the dynamic pricing for a service system under a finite horizon with time-varying demand. Customers are price and congestion sensitive, and have uniform valuations. In the existing literature, dynamic pricing for service systems is focused on the long-run behavior with stationary demand. However, in practice service providers typically operate on a short-run basis with time-varying demand. We formulate the problem as a Markov decision process. We propose an approximation scheme, which is asymptotically optimal as the probability that the system is idle or extremely congested goes to zero. Under our approximation scheme, we obtain an explicit quadratic form of the value function for the continuous time counterpart, and a congestion based linear pricing rule, which is easy to implement. We show that the intertemporal effect under the pricing rule can be captured by the congestion pricing and the idling pricing. We quantify how the different arrival patterns and parameters affect the pricing rule. Moreover, by exploiting the results under the uniform distribution, we also construct the lowerbound and upperbound systems for a general valuation distribution through the piecewise linear approximations. Our findings provide guidelines on how to design simple and effective pricing policies, in particular surge pricing policies, for service systems under short run with time-varying demand. Our approximation scheme also serves as a benchmark to tackle more general queueing systems.

In the second essay, motivated by the consumer habituation behavior, we investigate the optimal dynamic pricing strategy to maximize the total discounted long run profit. Consumers are myopic and their willingness-to-pay is determined by their habitual level of consumption. We formulate the seller's continuous time profit maximization problem by adopting the exponential smoothing consumer habituation dynamics. We find that given any initial habituation level, under the optimal dynamic pricing policy, there always exists an equilibrium habitual level. Whether the equilibrium habitual level is medium is determined by how the willingness-to-pay depends on the habitual level. When the equilibrium level is medium, it is optimal for the seller to price to the willingness-to-pay when the habitual level is less than the optimal switchover level and to price out the consumers otherwise. In the equilibrium, the seller prices out customers with a positive probability to mitigate the habituation effect. When the equilibrium level is fully habituated, then it is always optimal for the seller to induce customers to purchase. Before reaching the equilibrium level, the optimal pricing strategy can be described by a first penetration then skimming price strategy. Once reaching the equilibrium state, the optimal pricing strategy is either a periodic discount or fixed pricing strategy. We further investigate different equilibria behavior and consumption patterns under the optimal pricing strategy. We find that the equilibrium outcome under the dynamic pricing is structurally different from that under the fixed pricing. Moreover, we numerically show that dynamic pricing can reap significant value against fixed pricing. Our findings provide a new explanation of the popularity of penetration pricing, skimming pricing, periodic discounts, and their variants in practice. We also provide guidelines on how to carry out dynamic pricing in the presence of customer habituation.