The benefits of dynamic pricing methods have long been known in industries, such as airlines, hotels, and electric utilities, where the capacity is fixed in the short-term and perishable. In recent years, there has been an increasing adoption of dynamic pricing policies in retail and other industries, where the sellers have the ability to store inventory. Three factors contributed to this phenomenon: (1) the increased availability of demand data, (2) the ease of changing prices due to new technologies, and (3) the availability of decision-support tools for analyzing demand data and for dynamic pricing. This paper constitutes a review of the literature and current practices in dynamic pricing. Given its applicability in most markets and its increasing adoption in practice, our focus is on dynamic (intertemporal) pricing in the presence of inventory considerations.

Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions

In this paper, we examine the research and results of dynamic pricing policies and their relation to revenue management. The survey is based on a generic revenue management problem in which a perishable and nonrenewable set of resources satisfy stochastic price sensitive demand processes over a finite period of time. In this class of problems, the owner (or the seller) of these resources uses them to produce and offer a menu of final products to the end customers. Within this context, we formulate the stochastic control problem of capacity that the seller faces: How to dynamically set the menu and the quantity of products and their corresponding prices to maximize the total revenue over the selling horizon.

https://pages.stern.nyu.edu/~rcaldent/papers/Abstract-Survey-Paper-MSOM.pdf

Commissioned Paper: An Overview of Pricing Models for Revenue Management

This paper develops a model of dynamic pricing with endogenous inter-temporal demand. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically in order to maximize revenue. Customers arrive continually over the duration of the selling season. At each point in time, customers may purchase the product at current prices, remain in the market at a cost in order to purchase later, or exit, and they wish to maximize individual utility. The customer population is heterogeneous along two dimensions: they may have different valuations for the product and different degrees of patience (waiting costs). We demonstrate that heterogeneity in both valuation and patience is important because they jointly determine the structure of optimal pricing policies. In particular, when high-value customers are proportionately less patient, markdown pricing policies are effective because the high-value customers would buy early at high prices while the low-value customers are willing to wait (i.e. they are not lost). On the other hand, when the high-value customers are more patient than the low-value customers, prices should increase over time in order to discourage inefficient waiting. Contrary to intuition, we find that strategic waiting by customers may sometimes benefit the seller: when low-value customers wait, they compete for availability with high-value customers and thus increase their willingness to pay. Our results also shed light on how the composition of the customer population affects optimal revenue, consumer surplus, and social welfare. Finally, we consider the long run problem of selecting the optimal initial stocking quantity.

/pdf/inter-temporal-pricing-with-strategic-customer-behavior-v1l9e3265h.pdf

Inter-temporal Pricing with Strategic Customer Behavior

This paper develops a model of dynamic pricing with endogenous intertemporal demand. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically to maximize revenue. Customers arrive continually over the duration of the selling season. At each point in time, customers may purchase the product at current prices, remain in the market at a cost to purchase later, or exit, and they wish to maximize individual utility. The customer population is heterogeneous along two dimensions: they may have different valuations for the product and different degrees of patience (waiting costs).

We demonstrate that heterogeneity in both valuation and patience is important because they jointly determine the structure of optimal pricing policies. In particular, when high-value customers are proportionately less patient, markdown pricing policies are effective because the high-value customers would buy early at high prices while the low-value customers are willing to wait (i.e., they are not lost). On the other hand, when the high-value customers are more patient than the low-value customers, prices should increase over time to discourage inefficient waiting. Contrary to intuition, we find that strategic waiting by customers may sometimes benefit the seller: when low-value customers wait, they compete for availability with high-value customers and thus increase their willingness to pay. Our results also shed light on how the composition of the customer population affects optimal revenue, consumer surplus, and social welfare. Finally, we consider the long-run problem of selecting the optimal initial stocking quantity.

/pdf/intertemporal-pricing-with-strategic-customer-behavior-56yxv84egn.pdf

Intertemporal Pricing with Strategic Customer Behavior

Recent years have seen scores of retail and manufacturing companies exploring innovative pricing strategies in an effort to improve their operations and ultimately the bottom line. Firms are employing such varied tools as dynamic pricing over time, target pricing to different classes of customers, or pricing to learn about customer demand. The benefits can be significant, including not only potential increases in profit, but also improvements such as reduction in demand or production variability, resulting in more efficient supply chains.

Coordination of Pricing and Inventory Decisions: A Survey and Classification

We consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon. Customers, whose reservation price distribution changes over time, arrive according to a nonhomogeneous Poisson process. We show that at any given time, the optimal price decreases with inventory. We also identify a sufficient condition under which the optimal price decreases over time for a given inventory level. This sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time. In addition to shedding managerial insight, these structural properties enable efficient computation of the optimal policy.Numerical studies are conducted to show the revenue impact of dynamic price policies. Price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price. For the former, our examples show that using optimal dynamic optimal policies achieves 2.4--7.3% revenue improvement over the optimal single price policy. For the latter, the revenue increase can be as high as 100%. These results explain why yield management has become so essential to fashion retailing and travel service industries.

Wen Zhao

Papers

Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand