Research

Is Your Price Personalized? Alleviating Customer Concerns with Inventory Availability Information

with Q. Zhang

Operations Research, 74(1):181-198, January 2026

Topics: personalized pricing, customer protection, inventory availability information, and price discrimination concerns.

Summary: A high price can look like either popularity or personalization. The paper shows that a simple low-versus-high inventory signal can separate the two and, in the right settings, make both customers and the firm better off.

Extant literature has shown that personalized pricing (PP), i.e., customizing prices for individual customers, can benefit firms and some customers. However, customer concerns about being targeted by such practices have raised debates on PP tactics. Using a Bayesian persuasion framework, we study whether and under what conditions price can signal such PP implementation to customers. We also investigate whether disclosing inventory availability information can alleviate customer concerns and benefit the stakeholders, including the firm and customers. We consider a dynamic personalized pricing and information provisioning game between a firm and a market of heterogeneous customers. In the first period, the firm sets the price to learn the customer valuations and maximize revenue. In the second period, the firm may implement PP using customer purchase history. Customers are uncertain about the inventory availability and implementation of PP. Therefore, they may not precisely identify whether their purchase history will be used for pricing. However, they update their beliefs about the possibility of PP upon receiving new information. We first study myopic customers who only consider their immediate utility when purchasing. We then transition to strategic customers who take their future utility into account. We show that price alone cannot always signal PP, hurting the firm and customers. We establish conditions under which a binary inventory signal, where the firm marks the inventory as scarce when it is less than a threshold, increases firm revenue and benefits customers. Thus, firms can create transparency over their pricing strategies by disclosing inventory availability information.

Allocation of Nonprofit Funds among Program, Fundraising, and Administration

with T. Kotsi, G. Aydin, and A.J. Pedraza-Martinez

Manufacturing & Service Operations Management, Vol. 25, No. 5, September-October 2023

Topics: nonprofit operations, fundraising, administration, resource allocation, and the starvation cycle.

Summary: Low-overhead pressure can push nonprofits into a starvation cycle. The paper shows when spending more on fundraising and administration can actually raise long-run mission value by building capacity and protecting against uncertain future needs.

Problem definition: U.S. nonprofits declare three types of expenses in their IRS 990 forms: program spending to meet beneficiaries' needs; fundraising spending to raise donations; and administration spending to build and maintain capacity. Charity watchdogs, however, expect nonprofits to prioritize program spending over other categories. We study when such expectations may lead to the "starvation cycle" or underspending on administration and fundraising. Methodology/results: We characterize optimal budget allocations to program, fundraising, and administration spending categories using a two-period model, which also includes the nonprofit's capacity, return on program spending (the net value of program spending to beneficiaries), and beneficiaries' uncertain future needs. We find that the nonprofit's capacity plays a significant role in the optimal allocation. The nonprofit should (a) at high capacity, spend only the necessary amount on administration to maintain its current capacity; (b) at moderate capacity, maintain its current capacity while limiting program spending in favor of fundraising; and (c) at low capacity, increase administration spending to expand its future capacity. When we compare the optimal allocations prescribed by our model to the actual spending levels reported by a foodbank network, we find that the foodbank underspends on administration and fundraising, suggesting the forces that lead to the starvation cycle may be in play. Another possibility is that the nonprofit's own estimate of its return on program spending is higher than our estimate. At higher estimates of return on program, the gap between our prescribed solutions versus actual spending levels decreases. Managerial implications: Our paper introduces an important discussion on nonprofits' starvation cycle and finds conditions that justify prioritizing administration and fundraising expenses. It also highlights that watchdogs should consider nonprofits' return on program spending in addition to their capacity and future needs when evaluating them.

Competition and Collaboration on Fundraising for Short-Term Disaster Response: The Impact on Earmarking and Performance

with A.J. Pedraza-Martinez

Manufacturing & Service Operations Management, Vol. 25, No. 4, July-August 2023

Topics: disaster response fundraising, earmarking, collaborative fundraising, and nonprofit performance.

Summary: Competition for donors tends to increase earmarking and fundraising costs. The paper shows that when money is scarce, partial collaboration works better, but when money is abundant, full collaboration is the stronger fix.

Problem definition: Most humanitarian organizations (HOs) allow donors to earmark their donations, i.e., designate their contributions to a specific purpose. Allowing earmarking may increase donations, however, it creates operational inefficiencies that undermine the impact of those donations. Extant literature has mainly studied earmarking and its operational consequences in the absence of funding competition. We examine how competition for funding impacts earmarking decisions, fundraising costs, and HO performance in short-term disaster response. In addition to the competition model, we analyze two collaborative fundraising models: (i) full collaboration, where HOs contact donors as a unit and donors cannot donate to specific HOs on the fundraiser, and (ii) partial collaboration, where HOs contact donors as a unit and donors choose among the contacting HOs. Methodology/results: We use game theory to model the interactions between multiple HOs and a market of donors and build a multinomial logit model for the donor choice problem. We find that competition for funding contributes to the prevalence of earmarked donations, increases fundraising costs, and hurts HO performance and utility. We show the two collaborative fundraising models can mitigate these issues depending on the availability of funding resources. When funding is abundant, full collaboration improves HO utility and reduces earmarking and fundraising costs. When funding is scarce, partial collaboration reduces fundraising costs and improves performance and HO utility. When funding is intermediate, these two forms of collaboration do not necessarily benefit HOs. Managerial implications: We illustrate how funding availability drives earmarking and fundraising decisions and key performance metrics of different funding models during short-term disaster response. Using data from the 2010 Haiti earthquake, our numerical study indicates that partial collaboration benefits response to disasters with funding shortage, while full collaboration suits disaster response with sufficient funding. HOs competing for funds can use our insights to improve their response effectiveness.

• Finalist, INFORMS PSOR Best Paper Award, 2022
• Finalist, POMS HOCM Best Paper Award, 2022

Inventory Integration with Rational Consumers

with R. Swinney

Operations Research, Vol. 69, No. 4, July-August 2021

Topics: strategic consumers, inventory integration, rational consumers, and purchase timing.

Summary: Pooling inventory is not always a free operational win: if integration makes clearance inventory easier to find, rational consumers may wait for markdowns and wipe out the benefit.

We study the value of inventory integration (or pooling) for a firm selling a seasonal good over two periods: in the first period the firm charges a high price, and in the second period the firm charges a low price to clear remaining inventory. Consumers are rational and decide when to visit the firm based on the price of the product and its anticipated availability. We show that integration, which combines inventory from distinct selling channels or geographic regions, for example, online and offline channels or two physical locations, into a single virtual stock from which any consumer demand may be fulfilled, possesses both operational and behavioral value in this setting. The operational value, which results from better matching of supply and demand, is always positive; however, the behavioral value, which results from the way integration influences inventory availability and hence consumer purchasing incentives, can be positive or negative. Negative behavioral value occurs when integration increases inventory availability in the second period and encourages more consumers to delay a purchase to obtain a lower price; this may significantly reduce, and even make negative, the total value of integration. We show that negative behavioral value of integration is most likely to occur when demand variability is high, the underlying markets are sufficiently correlated, and the salvage value-to-cost ratio is low. We also consider how three additional factors influence the value of integration, and find that the behavioral value of integration is more likely to be negative when the clearance price is endogenously determined as opposed to fixed ex ante or when the component market demands are more asymmetric; however, behavioral value is more likely to be positive when consumers incur visit costs. We conclude that rational consumer behavior can play a substantial role in determining the value of inventory integration.

Becoming Strategic: Endogenous Consumer Time Preferences and Multiperiod Pricing

with P. Feldman and R. Swinney

Operations Research, Vol. 68, No. 4, July-August 2020

Topics: strategic consumers, multiperiod pricing, endogenous consumer time preferences, and price commitment.

Summary: Making strategic waiting harder can actually help everyone. The paper shows that a higher cost of being strategic can raise profit, consumer surplus, and social welfare, and that price commitment can backfire by encouraging more waiting.

Pricing over multiple periods under forward-looking, strategic consumer purchasing behavior has received significant recent research attention; however, whether consumers actually benefit from this behavior and would voluntarily choose to be strategic has not been previously considered. We explore this question by developing a model of endogenous time preferences, consistent with microeconomic theories of boundedly rational intertemporal decision making, in which consumers choose to become strategic by exerting costly effort. We show three key implications of this choice. First, considering the consumer choice to be strategic can have a significant impact on firm and consumer decisions, in particular, qualitatively impacting the firm's optimal pricing policy. Second, it is possible to increase firm profit, consumer surplus, and social welfare simultaneously by increasing the cost of strategic behavior, suggesting that firms can, essentially, force consumers to be myopic and make all parties better off; this helps explain how firms that do the most to make strategic behavior difficult are able to attract more demand and be successful in the marketplace. And third, efforts to mitigate strategic consumer waiting by committing to future prices instead of pricing dynamically may decrease the cost of strategic behavior and backfire, encouraging more consumers to be strategic; hence, in contrast to most previous research, price commitment may yield lower profit than dynamic pricing if consumers can choose to be strategic.

Humanitarian Funding in a Multi-Donor Market with Donation Uncertainty

with A.J. Pedraza-Martinez

Production and Operations Management, Vol. 25, No. 7, July 2016

Topics: humanitarian operations, donation uncertainty, multi-donor markets, and non-earmarked donations.

Summary: Earmarking can attract donations but reduce operational flexibility. The paper shows that raising awareness of development programs can increase non-earmarked donations and improve disaster-response efficiency under donation uncertainty.

This study analyzes the trade-off between funding strategies and operational performance in humanitarian operations. If a Humanitarian Organization (HO) offers donors the option of earmarking their donations, HO should expect an increase in total donations. However, earmarking creates constraints in resource allocation that negatively affect HO's operational performance. We study this trade-off from the perspective of a single HO that maximizes its expected utility as a function of total donations and operational performance. HO implements disaster response and development programs and it operates in a multi-donor market with donation uncertainty. Using a model inspired by Scarf's minimax approach and the newsvendor framework, we analyze the strategic interaction between HO and its donors. The numerical section is based on real data from 15 disasters during the period 2012-2013. We find that poor operational performance has a larger effect on HO's utility function when donors are more uncertain about HO's expected needs for disaster response. Interestingly, increasing the public awareness of development programs helps HO to get more non-earmarked donations for disaster response. Increasing non-earmarked donations improves HO's operational efficiency, which mitigates the impact of donation uncertainty on HO's utility function.

On the Harmonious Colouring of Trees II

with S. Akbari, D.S. Eskandani, M. Jamaali, and H. Ravanbod

Ars Combinatoria, Vol. 128, July 2016

Topics: graph theory, harmonious colouring, and trees.

Summary: Shows that when a tree has a very high maximum degree, its harmonious chromatic number is exactly one more than that maximum degree, and for the union of two such trees the paper gives a corresponding upper bound that is two more than the maximum degree.

Let G be a simple graph. A harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. In this paper, it is shown that if T is a tree of order n and Delta(T) >= n/2, then h(T) = Delta(T) + 1, where Delta(T) denotes the maximum degree of T. Let T1 and T2 be two trees of order n1 and n2, respectively, and F = T1 union T2. In this paper, it is shown that if Delta(Ti) = Deltai and Deltai >= ni/2, for i = 1, 2, then h(F) <= Delta(F) + 2. Moreover, if Delta1 = Delta2 = Delta and Delta >= ni/2, for i = 1, 2, then h(F) = Delta + 2.

On Harmonious Colouring of Trees I

with S. Akbari, K.J. Edwards, D.S. Eskandani, M. Jamaali, and H. Ravanbod

The Electronic Journal of Combinatorics, 19(1), 2012

Topics: graph theory, harmonious colouring, and combinatorics on trees.

Summary: Shows that when a tree has a very high maximum degree, its harmonious chromatic number is exactly one more than that maximum degree; otherwise, the paper gives an upper bound of one more than half the number of vertices, with every color used at most twice.

Let G be a simple graph and Delta(G) denote the maximum degree of G. A harmonious colouring of G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring. In this paper it is shown that if T is a tree of order n and Delta(T) > n/2, then there exists a harmonious colouring of T with Delta(T) + 1 colours such that every colour is used at most twice. Thus h(T) = Delta(T) + 1. Moreover, we prove that if T is a tree of order n and Delta(T) <= ceil(n/2), then there exists a harmonious colouring of T with ceil(n/2) + 1 colours such that every colour is used at most twice. Thus h(T) <= ceil(n/2) + 1.

Are All Cause Contributions Created Equal? Operational and Competitive Implications of Transactional and Non-Transactional Cause Marketing

with E. Gal-Or, M. Gordon, J. Shang, and E. Xing

Major revision at POM

Topics: cause marketing, competitive strategy, and transactional versus non-transactional campaigns.

Summary: Shows that cause marketing is not one strategic tool but two: transactional and non-transactional campaigns can lead to meaningfully different competitive and operational outcomes.

In Cause Marketing (CM), a firm invests in a cause to attract prosocial customers. CM investments (donations) can be broadly categorized as Transactional CM (T-CM), where donations are linked to sales, and Non-Transactional CM (N-CM), where donations are independent of customer purchases. We study how these CM instruments perform under competition and how endogenizing the CM-type choice shapes outcomes for firms, consumers, nonprofits, and society. Two vertically and horizontally differentiated firms decide whether to engage in CM, which CM type to adopt, and how much to donate, and then compete on price. We show that T-CM and N-CM differ structurally: unlike N-CM, equilibrium T-CM donations are insensitive to competition intensity, allowing T-CM to act as a commitment device that softens price competition and can raise firm profits and total donations. Yet firms may select N-CM in equilibrium, yielding a prisoner's dilemma in which all stakeholders would be better off if both firms coordinated on T-CM. We also show that stronger competition and greater enthusiasm for CM can trigger CM-type switching that reduces total donations and social welfare. These findings imply that nonprofits and social planners should treat T-CM and N-CM as distinct instruments and tailor partnership and policy strategies accordingly.

Rating Systems under Customer Disconfirmation Bias: Asymptotic Behavior and Granularity

with Q. Zhang

Under revision

Topics: rating systems, customer disconfirmation bias, asymptotic behavior, and review granularity.

Summary: Tracks what happens when ratings reflect both experience and disappointed expectations. The paper shows that coarse systems can learn the wrong quality, while sufficiently granular systems can recover correct learning.

Customers and platforms increasingly rely on online ratings to assess the quality of products and services. However, customer ratings are susceptible to various biases. Disconfirmation bias is a specific form where customers incorporate the discrepancy between their prior expectations and post-purchase experiences into their ratings. We study the asymptotic behavior of ratings in the presence of disconfirmation bias in three rating systems: (i) complete system, where customers observe the entire rating history; (ii) aggregate system, where only the frequency of each rating option is available; and (iii) average ratings, where customers solely use the average of past ratings. Customers are Bayesian and update their quality beliefs upon observing the ratings. After experiencing the product, they rate it according to their heterogeneous ex-post utility and disconfirmation bias. In complete and aggregate systems, we show that customer beliefs converge to the intrinsic quality when disconfirmation bias is small. When this bias is large, there will be a discrepancy between converged beliefs and the intrinsic quality, although this discrepancy could be arbitrarily small. When the disconfirmation bias is intermediate, beliefs may diverge significantly from the intrinsic quality or not converge. However, we establish that the platform can guarantee correct learning by designing a sufficiently granular rating system, i.e., a system with more rating options. We confirm all these results in the system with average ratings, albeit with a bias-correcting rule. Finally, we characterize the learning speed in the aggregate system.

An Attribute-Based Multi-Item Demand Model with Constrained Machine Learning: Theory and Estimation

with D. Eskandani and S. Wu

Topics: multi-item demand estimation, constrained machine learning, and attribute-based demand modeling.

Summary: Separates category demand from within-assortment allocation, which keeps substitution disciplined under counterfactual price and availability changes while still allowing flexible assortment interactions and forecasting for newly introduced products.

Demand models guide core retail decisions such as pricing, promotions, assortments, and inventory planning. Yet we show that many widely used empirical specifications can behave poorly in counterfactual analysis. For example, cross-price interactions can imply higher total sales after a price increase. Structural choice models impose discipline on substitution and often yield more coherent counterfactuals. However, baseline forms can be too rigid for large, dynamic assortments. Moreover, common attempts to add flexibility, such as enriching utilities with cross-price terms in the presence of an outside option, can reintroduce unrealistic market-expansion effects. We propose a demand model that combines empirical flexibility with disciplined substitution via a two-stage decomposition. In each period, we first model total category demand, which captures purchase incidence as a function of prices, the offered assortment, and covariates. We then distribute this total demand across items using conditional shares generated from an item-level attractiveness index and a softmax mapping. By separating incidence from allocation, the model cleanly isolates market expansion from within-assortment substitution and delivers regularity guarantees that preclude unbounded substitution and demand creation under counterfactual price and availability changes. At the same time, the attribute-based specification accommodates rich assortment interactions and supports forecasting demand for newly introduced products when their characteristics are observed. Methodologically, we develop a scalable estimation procedure that exploits grouped sparsity in high-dimensional attribute indicators, uses simple transformations that accommodate zero sales to linearize share estimation, and performs feature selection via constrained regularization while preserving the model's guarantees. Using proprietary weekly data from a national apparel retailer, the model achieves strong out-of-sample accuracy. Total category demand forecasts attain a test-set MAPE of 12.8% (MAD = 1.4). At the SKU level, it correctly predicts zero sales with probability 0.91 and achieves an F1 score of 0.75 on zero-versus-positive diagnostics, with an MAD of 0.33 across item-week observations.

Selling Roses on Online Dating Platforms

with M. Hamilton, K. Tari, and E. Xing

Topics: online dating platforms, virtual products, platform monetization, and pay-to-message design.

Summary: Compares how roses should be priced and sold one period at a time, in bundles, or through a mixed menu, and finds that maximally effective roses sold a la carte can outperform bundles on revenue while also improving user surplus and social welfare.

Dating apps offer users the opportunity to match with potential partners, but the mechanisms through which this opportunity is monetized, what is free and what is offered at cost, vary widely across platforms. Many popular dating apps in the United States generate revenue by offering suites of virtual products that increase a user's chances of matching. These products may improve candidate recommendations based on private platform data, expand the user's range of matches by displaying their profile to others at a higher rate, or increase visibility to one specific potential match of interest. We investigate this final category of virtual products, which we refer to as roses, and consider how they should be implemented and offered to users. Methodology / Results. In a multi-period model with forward-looking customers, we consider three selling mechanisms: offering roses separately in each period, offering a bundle of roses only in the first period, and offering a menu of both options. Under each mechanism we characterize the utility-maximizing user behavior and derive the revenue-maximizing pricing and design for offering roses. In each case, we find that increasing the efficacy of the rose, and then appropriately pricing them, monotonically increases platform revenue. Further, under these maximal roses, we find that offering them separately in each period dominates the revenue, user surplus, and social welfare of bundle selling and is nearly equal to the more involved mixed mechanism across all three metrics. Managerial Implications. Our results yield actionable guidelines for the design and monetization of dating apps. In particular, when the platform offers maximally effective roses, the system reduces to an a la carte setting where users can only message via a rose. Thus our work lends support for pay-to-message platforms like Match.com as a platform design choice that can increase both revenue and user welfare.

Signaling Quality with Delayed Incentives

with B. Kadiyala and D. Shin

Topics: quality signaling, delayed incentives, and consumer response.

Summary: Studies how delayed incentives, instead of immediate promotions, can signal quality to customers.

Examines whether delayed incentives can communicate product quality more credibly than immediate promotions. It studies how the timing of incentives shapes customer inference and when waiting to reward the customer can itself become a quality signal.

Optimal Fashionability for Seasonal Products

with R. Swinney

Topics: seasonal products, fashionability, and product strategy.

Summary: Shows that design, pricing, and inventory choices have to move together when style value decays quickly, especially under dynamic pricing.

Studies products whose fashion appeal decays over a season and links design choice to pricing and inventory decisions. It shows how optimal fashionability depends on selling horizon, markdown timing, and dynamic pricing considerations.