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Cyclic Pricing with Strategic Waiting Customers and Population Dynamics

Cyclic Pricing with Strategic Waiting Customers and Population Dynamics
Author: Zheyi Li
Publisher:
Total Pages: 0
Release: 2022
Genre:
ISBN:

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We consider continuous-time dynamic pricing in the presence of strategic waiting customers and their population dynamics. The firm makes the pricing decision with a finite menu of prices each time. Customers arrive at a constant rate with heterogeneous valuations. Customers purchase if the current price is less than their corresponding valuations. The remaining customers are strategic: they may leave or wait for future clearance sales, and the leaving rate can be population-contingent. The firm has the option to offer a clearance price to attract all waiting customers to purchase. We build a continuous-time model by exploiting impulse control. For a two-price menu, the optimal pricing policy is a cyclic pricing strategy that starts with a regular price and ends at a clearance price. For a multi-price menu, in contrast to the existing literature, we show that the optimal dynamic pricing policy can be either a textit{pump and dump cyclic} or textit{generalized pump and dump cyclic} strategy. Which strategy is optimal is determined by the sign of the effective marginal leaving rate. We provide analytical solutions for the cycle length and the optimal pricing path. Our results provide new explanations for the popularity of periodic clearance sales with penetration pricing and skimming pricing in practice. Our findings also provide guidelines on carrying out dynamic pricing with the customer leaving behaviors. Numerically, we show that ignoring cyclic pricing in the presence of strategic waiting customers can lead to a significant profit loss.


Intertemporal Price Discrimination

Intertemporal Price Discrimination
Author: Omar Besbes
Publisher:
Total Pages: 0
Release: 2015
Genre:
ISBN:

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We study a firm's optimal pricing policy under price commitment. The firm's objective is to maximize its long-term average revenue given a steady arrival of strategic customers. In particular, customers arrive over time, are strategic in timing their purchases and are heterogeneous along two dimensions: their valuation for the firm's product and their willingness to wait before purchasing or leaving. The customers' patience and valuation may be correlated in an arbitrary fashion. For this general formulation, we prove that the firm may restrict attention to cyclic pricing policies, which have length at most twice the maximum willingness to wait of the customer population. To efficiently compute optimal policies, we develop a dynamic programming approach which uses a novel state space which is general, enabling to handle arbitrary problem primitives, and that generalizes to finite horizon problems with non-stationary parameters. We analyze the class of monotone pricing policies and establish their suboptimality in general. Optimal policies are, in a typical scenario, characterized by nested sales, where the firm offers partial discounts throughout each cycle, offers a significant discount halfway through the cycle, with the largest discount offered at the end of the cycle. We further establish a form of equivalence between the problem of pricing for a stream of heterogeneous strategic customers and pricing for a pool of heterogeneous customers who may stockpile units of the product.


Cyclic Pricing When Customers Queue with Rating Information

Cyclic Pricing When Customers Queue with Rating Information
Author: Fengfeng Huang
Publisher:
Total Pages: 0
Release: 2019
Genre:
ISBN:

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Consider a situation where a service provider serves two types of customers, sophisticated and naive. Sophisticated customers are well-informed of service-related information and make their joining-or-balking decisions strategically, whereas naive customers do not have such information and rely on online rating information to make such decisions. We demonstrate that under certain conditions a service provider can increase its profitability by simply `dancing' its price, that is, replacing the static pricing strategy with a high-low cyclic pricing strategy. The success of this strategy relies on two key conditions: the potential market size is large enough so that congestion is a key concern in the service system, and the rating provides the average price and average utility information. Finally, we show that the cyclic pricing strategy is not socially optimal.


The Cyclicality of Sales, Regular and Effective Prices

The Cyclicality of Sales, Regular and Effective Prices
Author: Mr.Olivier Coibion
Publisher: International Monetary Fund
Total Pages: 75
Release: 2012-08-01
Genre: Business & Economics
ISBN: 1475505574

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We study the cyclical properties of sales, regular price changes and average prices paid by consumers ("effective" prices) in a dataset containing prices and quantities sold for numerous retailers across a variety of U.S. metropolitan areas. Both the frequency and size of sales fall when local unemployment rates rise and yet the inflation rate for effective prices paid by consumers declines significantly with higher unemployment. This discrepancy can be reconciled by consumers reallocating their expenditures across retailers, a feature of the data which we document and quantify. We propose a simple model with household shopping effort and store-switching consistent with these stylized facts and document its implications for business cycles and policymakers.


Inter-Temporal Pricing with Strategic Customer Behavior

Inter-Temporal Pricing with Strategic Customer Behavior
Author: Xuanming Su
Publisher:
Total Pages: 0
Release: 2012
Genre:
ISBN:

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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.


Dynamic Pricing with Heterogeneous Patience Levels

Dynamic Pricing with Heterogeneous Patience Levels
Author: Ilan Lobel
Publisher:
Total Pages: 28
Release: 2017
Genre:
ISBN:

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We consider the problem of dynamic pricing in the presence of patient consumers. We call a consumer patient if she is willing to wait a certain number of periods for a lower price and will purchase as soon as the price is equal to or below her valuation. We allow for arbitrary joint distributions of patience levels and valuations. We propose an efficient dynamic programming algorithm for finding optimal pricing policies. The dynamic program requires a larger state space than its counterpart for a strategic consumers model. We find numerically that optimal policies can take the form of incomplete cyclic policies, combining features of both nested sales policies and decreasing cyclic policies.


Synchronizing Pricing and Replenishment to Serve Forward-Looking Customers with Lost Sales

Synchronizing Pricing and Replenishment to Serve Forward-Looking Customers with Lost Sales
Author: Ying-Ju Chen
Publisher:
Total Pages: 34
Release: 2018
Genre:
ISBN:

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[Problem Definition] We incorporate heterogeneous customer valuation and the strategic customer behavior in the classical economic order quantity (EOQ) setting. The seller incurs setup costs when replenishing inventory, and can set the prices differently over time and implement capacity rationing. [Academic/ Practical Relevance] While similar ideas of market segmentation and intertemporal price discrimination can be carried over from the travel industries to other industries, there are new aspects when applying these concepts to retail outlets and supermarkets, because they usually face inventory replenishment problems. This makes the joint inventory replenishment and revenue management problem imperative. [Methodology] We adopt the mechanism design and dynamic programming approaches. [Results] We establish the optimality of cyclic intertemporal price discrimination, even if the customers are endowed with homogeneous valuations. Under the optimal policy, the replenishments and price promotions are synchronized, and the seller adopts the highest selling price when the inventory level is the lowest and plans discontinuous price discount at the replenishment point when the inventory is the highest. We also show that, under inventory-based pricing there is a direct mapping between deterministic and stochastic arrivals scenarios, and randomness on the arrivals per se does not alter the structure of the optimal policy. [Managerial Implications] This cyclic pricing scheme offers a stark contrast to the "low-price-every-day" scheme and achieves overall higher profit because customer strategic behavior offers additional flexibility to the seller in managing his inventory. Furthermore, because strategic customers are willingly backlogged, this creates opportunities for the seller to work with the customers to achieve a lower operational cost and a higher overall profit.


Adaptive Strategies and Population Ecology of Northern Grouse

Adaptive Strategies and Population Ecology of Northern Grouse
Author: A. T. Bergerud
Publisher: U of Minnesota Press
Total Pages: 836
Release: 1988
Genre: Adaptation (Biology).
ISBN: 0816614695

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"Adaptive Strategies and Population Ecology of Northern Grouse" was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. This book is at once a major reference to the species of grouse that inhabit North America and the Holarctic and a synthesis of all the available data on their ecology, sociobiology, population dynamics, and management. The book undertakes to answer two long-standing questions in population ecology: what actually regulates the numbers within a population, and what are the breeding and survival strategies evolved in this northern environment? For Volume I, editors Arthur T. Bergerud and Michael W. Gratson have drawn together their own work and that of colleagues in North America, Iceland, and Norway--in all, eleven research studies, averaging six years' duration, on eight species of grouse. These studies deal with the blue and ruffed grouse of the forest habitat; the sharp-tailed grouse, prairie chicken, and sage grouse of the prairie or steppe; and the white-tailed, rick, and willow ptarmigan found in alpine and arctic tundras. The authors describe the rich repertoire of behavior patterns developed by the hen and the cock to achieve their two primary objectives--first, to stay alive, and then to breed. Volume II, primarily the work of Bergerud, synthesizes the evidence in Volume I and in the grouse research literature from a theoretical perspective. Several potentially controversial sociobiological hypotheses are advanced to account for flocking behavior, migration, dispersal, roosting and feeding behavior, mate choice and mating systems. The demographic analysis provides new insights into cycles of abundance, the limitation of numbers, and the demographic factors that determine densities. The contributors, besides Bergerud and Gratson: R.C. Davies, A. Gardarson, J.E. Hartzler, R.A. Huempfner, D.A. Jenni, D.H. Mossop, S. Myrberget, R.E. Page, R.K. Schmidt, W.D. Svedarsky, and J.R. Tester.


INFORMS Annual Meeting

INFORMS Annual Meeting
Author: Institute for Operations Research and the Management Sciences. National Meeting
Publisher:
Total Pages: 644
Release: 2009
Genre: Industrial management
ISBN:

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Adaptive Strategies and Population Ecology of Northern Grouse: Volume 1: Population Studies

Adaptive Strategies and Population Ecology of Northern Grouse: Volume 1: Population Studies
Author: Arthur T. Bergerud
Publisher: U of Minnesota Press
Total Pages: 446
Release: 1988
Genre: Adaptation (Biology)
ISBN: 1452908052

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Adaptive Strategies and Population Ecology of Northern Grouse was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. This book is at once a major reference to the species of grouse that inhabit North America and the Holarctic and a synthesis of all the available data on their ecology, sociobiology, population dynamics, and management. The book undertakes to answer two long-standing questions in population ecology: what actually regulates the numbers within a population, and what are the breeding and survival strategies evolved in this northern environment? For Volume I, editors Arthur T. Bergerud and Michael W. Gratson have drawn together their own work and that of colleagues in North America, Iceland, and Norway—in all, eleven research studies, averaging six years' duration, on eight species of grouse. These studies deal with the blue and ruffed grouse of the forest habitat; the sharp-tailed grouse, prairie chicken, and sage grouse of the prairie or steppe; and the white-tailed, rick, and willow ptarmigan found in alpine and arctic tundras. The authors describe the rich repertoire of behavior patterns developed by the hen and the cock to achieve their two primary objectives—first, to stay alive, and then to breed. Volume II, primarily the work of Bergerud, synthesizes the evidence in Volume I and in the grouse research literature from a theoretical perspective. Several potentially controversial sociobiological hypotheses are advanced to account for flocking behavior, migration, dispersal, roosting and feeding behavior, mate choice and mating systems. The demographic analysis provides new insights into cycles of abundance, the limitation of numbers, and the demographic factors that determine densities. The contributors, besides Bergerud and Gratson: R.C. Davies, A. Gardarson, J.E. Hartzler, R.A. Huempfner, D.A. Jenni, D.H. Mossop, S. Myrberget, R.E. Page, R.K. Schmidt, W.D. Svedarsky, and J.R. Tester.