publications

Volunteers, the primary workforce for many charities, represent a complex labor pool; they are unreliable and exhibit substantial heterogeneity in both performance and affinity to the organization. Additionally, many volunteers engage not only to contribute but also to immerse themselves in a volunteering experience that, if rewarding, can inspire them to become future donors. However, practical approaches to volunteer management commonly neglect these traits and the consequential impact that tactical decision-making can have on nurturing potential future donations. Building on a previous study, we propose a forward-looking volunteer scheduling model that accounts for the heterogeneity among volunteers, mitigates both understaffing and overstaffing costs, and explicitly correlates individual time contribution with their monetary donations. We provide analytical solutions when the charity can reliably estimate distributions (e.g., uniform distribution) from data and suggest a distribution-free method to offer actionable insights where data are limited or uncertain. At the strategic level, by viewing volunteers as potential donors, the optimal staffing strategy balances meeting the charity’s labor needs and maximizing volunteers’ satisfaction, as this satisfaction influences their likelihood of becoming future donors. We show that charities could avert substantial losses by adopting an integrative approach, thereby challenging conventional organizational structures that compartmentalize volunteer and donor management. Our model suggests that building robust data infrastructures can significantly advance the charity’s core mission. Paradoxically, efforts to increase labor productivity may inadvertently undermine this objective. At the operational level, we provide an Excel-based decision support tool and a decision-tree framework to navigate optimal policies, determining when and how a charity can rely on episodic (less reliable) volunteers. Our results confirm that reducing uncertainty in volunteer turnout benefits charities. However, we also find that when labor value is low, episodic volunteers are preferred, whereas formal (reliable) volunteers are favored when labor value is high.

Too Good To Go (TGTG) has emerged as a global leader in reducing food waste by connecting consumers with retailers’ surplus food through "surprise bags." While TGTG provides both environmental and economic benefits, participating stores face significant operational challenges in determining the optimal number of bags to offer. Specifically, stores must decide on the number of surprise bags before knowing the actual surplus for the day. Additionally, key questions such as whether to include regular sale items in the bags and how to allocate food across bags are critical for balancing customer satisfaction and profitability. We explore these challenges and model the stores’ decision-making process by stochastic dynamic programming. Our analysis reveals that the commonly adopted practice of evenly distributing surplus food across all surprise bags may not maximize consumer satisfaction, particularly when customer utility functions are non-concave. We propose an alternative-offering up to two types of bags-that achieves maximal consumer satisfaction while still remaining simple to implement. Determining the optimal number of bags and the total food volume to allocate at each period is a non-convex two-stage stochastic optimization problem. To address both the analytical and computational complexities, we propose two approximation policies that are computationally efficient with intutive managerial insights and provable performance guarantees. Our findings provide practical guidance for stores in balancing revenue generation, customer satisfaction, and sustainability objectives, thereby enhancing the long-term viability of TGTG’s mission to reduce food waste.

We study the problem faced by the Philippine Department of Social Welfare (DSWD) in prepositioning relief items before landfall of an oncoming typhoon whose future outcome (trajectory and wind speed) is uncertain. The importance of prepositioning was a hard lesson learned from Super Typhoon Haiyan that devastated the Philippines in 2013, when many affected by the typhoon did not have immediate access to food and water. In a typhoon-prone country, it is important to build resilience through an effective prepositioning model. By engaging with DSWD, we developed a practically relevant stochastic prepositioning model. The probability models of municipality-level demand and of supply damage are both dependent on the typhoon outcome. A linear mixed effects model is used to estimate the dependence of demand on the typhoon outcome using a large data set that includes the municipality-level impact of West Pacific typhoons during 2008–2019. The model has two objectives motivated from the practical realities of the Philippine network: prioritizing regions with high demand and prepositioning in all affected regions proportional to their total demand. We find that the choice of the demand model significantly impacts the distributed relief items in the Philippine setting where it is challenging to adjust region-level supply after a typhoon. By using the historical data on past typhoons, we show that in this setting, our stochastic demand model provides the best distribution to date of any existing demand models. There currently exists a gap between theory and practice in the management of relief inventories. We contribute toward bridging this gap by engaging with DSWD to develop a practically relevant relief distribution model. Our work is an effective example of collaboration with government and nongovernment agencies in developing a relief distribution model.

We study assortment and price optimization under the \emphContextual Concavity (CC) model introduced by \citekivetz2004alternative, which subsumes the well-known \emphMulti-attribute Loss Aversion (MLA) model. Most existing work relies on context-independent choice models that assume product utilities are independent of the presence or absence of other alternatives in the assortment (i.e., the “context”). In contrast, the CC model offers a multi-attribute, context-dependent framework that incorporates reference points across multiple attributes and captures prominent context effects (e.g., the compromise effect) well-documented in the empirical literature. We analytically study the structure of the optimal assortment in several settings. More generally, we show that the pure assortment problem under the CC model can be reformulated as a mixed-integer linear program (MILP) that is polynomial in the number of products for a fixed number of attributes. When price is jointly optimized alongside the assortment, we prove that the optimal assortment consists of all products. Although the classic same-markup pricing policy is no longer optimal, we are able to derive the structure of the optimal prices and use it to develop an approximation algorithm for computing a near-optimal solution. We conduct numerical simulations that compare the optimal assortment policies under the CC model with those under a misspecified MNL model that ignores contextual effects, and demonstrate their implications for assortment structure, firm profitability, and customer surplus: (i) In settings with few attributes, the CC model may select smaller assortments than the misspecified model, whereas for larger number of attributes the opposite trend can emerge; (ii) The model misspecification can lead to significant revenue losses; (iii) The model misspecification may benefit customers in settings with few attributes but reduces customer surplus as the number of attributes increases.

When underlying demand follows a complex stochastic process, pricing problems are difficult to solve. In such cases, certainty equivalent (CE) policies, based on the solution to the deterministic relaxation of the stochastic pricing problem, can be used as practical alternatives. CE policies have lighter computational and informational requirements compared with solving the problem to optimality. Although the effectiveness of CE pricing policies has been theoretically studied when demands are independent, performance is not well known when demands are state-dependent and price-changing opportunities are limited. This paper analyzes the performance of CE policies in a pricing problem where future demand depends on sales and inventory, and the firm has limited opportunities to change prices. We show that CE policies are asymptotically optimal; as the problem scale (denoted by m) becomes large, the percentage revenue loss decreases at the rate of ⁢Θ(\sqrtm). We also extend the result to the joint pricing and (initial) inventory problem.

Social media influencer marketing has become a prevalent strategy to promote products. This paper examines the benefit of using an influencer to promote products in a social learning setting in which followers generate information and share with other followers organically. We adopt an information design framework and answer the question of how a firm should value a given influencer in terms of that influencer’s ability to persuade her followers to purchase the product. This persuasion includes how followers learn from the information the influencer shares and possibly social learning among themselves. We analyze how the value of an influencer’s information changes with respect to the accuracy of an influencer’s historical information strategy (what we call informativeness) and how exclusively followers rely on the influencer to update their beliefs about the product rather than learning socially (what we call charisma). Surprisingly, we find that (i) social learning can sometimes amplify the value of influence; and (ii) the optimal information structure under social learning is more informative than that without social learning. We also provide a method for a firm to strategically choose from a large selection of diverse influencers to determine a given product’s "ideal" influencer by characterizing optimal information strategies with and without social learning.

This paper addresses operational challenges faced by retailers offering free return policies. We consider a general system with lost-sales, positive lead time, periodic review, Binomial demand, and an arbitrary restriction on price change frequency. We study the joint pricing and inventory decisions in the presence of stochastic returns. Specifically, when an item is purchased, it can be returned at a future random time and may be restocked for resale after passing an inspection. We assume a general stationary return time distribution. A key challenge in both policy design and analysis arises from the dynamic coupling introduced by returns being restocked over time. To address this, we propose a simple yet effective policy that combines a simple inventory policy with adaptive pricing based on observed sales and returns. Our results provide insights into how uncertainty in both demand and returns can be managed through adaptive pricing under various price change constraints. The analysis can be extended to more general settings, including: (1) return fees and partial refunds, (2) non-stationary demand, and (3) service level constraints. We also show numerically that mis-specifying the return time distribution can lead to significant losses, even in a fully deterministic system without randomness.

Designing effective operational strategies requires a good understanding of customer behavior. The classic economic theory of customer choice has long been the paradigm in the operations literature. However, the rise of online marketplaces such as e-commerce has triggered considerable efforts in academia and industry to develop alternative models that not only provide a good approximation of customer behavior but also are easily scalable for large-scale implementations. In this paper, we consider a multiproduct dynamic pricing problem with limited inventories under the so-called cascade click model, which is one of the most popular click models used in practice and has been intensively studied in the computer science literature. We present some fundamental results. First, we derive a sufficiently general characterization of the optimal pricing policy and show that it has a different structure than the optimal policy under the standard pricing model. Second, we show that the optimal expected total revenue under the cascade click model can be upper bounded by the objective value of an approximate deterministic pricing problem. Third, we show that two policies that are known to have strong performance guarantees in the standard revenue management setting can be properly adapted (in a nontrivial way) to the setting with cascade click model while retaining their strong performance. Finally, we also briefly discuss the joint ranking and pricing problem and provide an iterative heuristic to calculate an approximate ranking. Taking into account customers’ click-and-search behavior leads to different structures of the optimal pricing policy, and some common insights under the standard pricing models may no longer hold. Moreover, our simulation studies show that pricing under a (misspecified) classic choice model that is oblivious to customers click-and-search behavior can severely impact profitability.

Decisions regarding new products are often difficult to make, and mistakes can have grave consequences for a firm’s bottom line. Often, firms lack important information about a new product, such as its potential market size and the speed of its adoption by consumers. One of the most popular frameworks that has been used for modeling new product adoption is the Bass model. Although the Bass model and its many variants are used to study dynamic pricing of new products, the vast majority of these models require a priori knowledge of parameters that can only be estimated from historical data or guessed using institutional knowledge. In this paper, we study the interplay between pricing and learning for a monopolist whose objective is to maximize the expected revenue of a new product over a finite selling horizon. We extend the generalized Bass model to a stochastic setting by modeling adoption through a continuous-time Markov chain with which the adoption rate depends on the selling price and on the number of past sales. We study a pricing problem in which the parameters of this demand model are unknown, but the seller can utilize real-time demand data for learning the parameters. We propose two simple and computationally tractable pricing policies with ⁡⁡O(\ln m) regret, where m is the market size.

We study a joint product framing and order fulfillment problem with both inventory and cardinality constraints faced by an e-commerce retailer. There is a finite selling horizon and no replenishment opportunity. In each period, the retailer needs to decide how to “frame” (i.e., display, rank, price) each product on his or her website as well as how to fulfill a new demand. E-commerce retail is known to suffer from thin profit margins. Using the data from a major U.S. retailer, we show that jointly planning product framing and order fulfillment can have a significant impact on online retailers’ profitability. This is a technically challenging problem as it involves both inventory and cardinality constraints. In this paper, we make progress toward resolving this challenge. We use techniques such as randomized algorithms and graph-based algorithms to provide a tractable solution heuristic that we analyze through asymptotic analysis. Our proposed randomized heuristic policy is based on the solution of a deterministic approximation to the stochastic control problem. The key challenge is in constructing a randomization scheme that is easy to implement and that guarantees the resulting policy is asymptotically optimal. We propose a novel two-step randomization scheme based on the idea of matrix decomposition and a rescaling argument. Our numerical tests show that the proposed policy is very close to optimal, can be applied to large-scale problems in practice, and highlights the value of jointly optimizing product framing and order fulfillment decisions. When inventory across the network is imbalanced, the widespread practice of planning product framing without considering its impact on fulfillment can result in high shipping costs, regardless of the fulfillment policy used. Our proposed policy significantly reduces shipping costs by using product framing to manage demand so that it occurs close to the location of the inventory.

We study a single-period (i.e., one replenishment cycle) joint assortment and inventory problem in a general model with Poisson arrivals, dynamic substitution, the Multinomial Logit (MNL) choice model, and an arbitrary set of capacity constraints. Motivated by business practices in the retail industry, we consider a setting where the initial inventory levels of some products (i.e., before ordering) could be positive and we allow the existence of a set of products whose inventory levels cannot be adjusted (e.g., the retailer does not wish to replenish these products because of out-of-season). The retailer makes a one-time assortment and inventory decisions at the beginning of the period and does not have a direct control over the assortment of the products throughout the remaining of the period (i.e., within the period, product availability is assumed to evolve naturally over time depending on realized sales). Computing the order quantities in the stated model at the beginning of the period is a practically relevant yet technically challenging problem. The main technical challenge here arises because customer substitution behavior is affected by product availability, which makes it difficult to characterize the impact of order quantities on the total sales of each product. In this paper, we develop a linear programming (LP)-based algorithm to compute a provably near-optimal (asymptotically optimal) solution. We start by considering the deterministic (fluid) version of the model and show that, in general, an optimal solution to this model can be computed by solving a sequence of M+1 linear programs (LPs), where M is the number of products. We then show that the rounded version of this solution is asymptotically optimal for the original stochastic model as the market size grows large.

Omnichannel retail refers to a seamless integration of an e-commerce channel and a network of brick-and-mortar stores. An example is cross-channel fulfillment, which allows a store to fulfill online orders in any location. Another is price transparency, which allows customers to compare the online price with store prices. This paper studies a new and widespread problem resulting from omnichannel retail: price optimization in the presence of cross-channel interactions in demand and supply, where cross-channel fulfillment is exogenous. We propose two pricing policies that are based on the idea of “partitions” to the store inventory that approximate how this shared resource will be utilized. These policies are practical because they rely on solving computationally tractable mixed integer programs that can accept various business and pricing rules. In extensive simulation experiments, they achieve a small optimality gap relative to theoretical upper bounds on the optimal expected profit. The good observed performance of our pricing policies results from managing substitutive channel demands in accordance with partitions that rebalance inventory in the network. A proprietary implementation of the analytics is commercially available as part of the IBM Commerce markdown price solution. The system results in an estimated 13.7% increase in clearance-period revenue based on causal model analysis of the data from a pilot implementation for clearance pricing at a large U.S. retailer.

Expected utility models in portfolio optimization are based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance, and support information. No additional restrictions on the type of distribution such as normality is made. The investor’s utility is modeled as a piecewise-linear concave function. We derive exact and approximate optimal trading strategies for a robust (maximin) expected utility model, where the investor maximizes his worst-case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Extensions of the model to capture asymmetry using partitioned statistics information and box-type uncertainty in the mean and covariance matrix are provided. Using the optimized certainty equivalent framework, we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst-case risk under distributional ambiguity. New closed-form results for the worst-case optimized certainty equivalent risk measures and optimal portfolios are provided for two- and three-piece utility functions. For more complicated utility functions, computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.

We consider the data-driven newsvendor problem in which a manager makes inventory decisions sequentially and learns the unknown demand distribution based on observed samples of continuous demand (no truncation). We study the widely used sample average approximation (SAA) approach and analyze its performance with respect to regret, which is the difference between its expected cost and the optimal cost of the clairvoyant who knows the underlying demand distribution. We characterize how the regret performance depends on a minimal separation assumption that restricts the local flatness of the demand distribution around the optimal order quantity. In particular, we consider two separation parameters, γand ε, where γ denotes the minimal possible value of the density function in a small neighborhood of the optimal quantity and εdefines the size of the neighborhood. We establish a lower bound on the worst case regret of any policy that depends on the product of the separation parameters γεand the time horizon N. We also show a finite-time upper bound of SAA that matches the lower bound in terms of the separation parameters and the time horizon (up to a logarithmic factor of N). This illustrates the near-optimal performance of SAA with respect to not only the time horizon, but also the local flatness of the demand distribution around the optimal quantity. Our analysis also shows upper bounds of ⁡O(\log N) and O(\sqrtN) on the worst case regret of SAA over N periods with and without the minimal separation assumption. Both bounds match the lower bounds implied by the literature, which illustrates the asymptotic optimality of the SAA approach.

We study a multilocation newsvendor network when the only information available on the joint distribution of demands are the values of its mean vector and covariance matrix. We adopt a distributionally robust model to find inventory levels that minimize the worst-case expected cost among the distributions consistent with this information. This problem is NP-hard. We find a closed-form tight bound on the expected cost when there are only two locations. This bound is tight under a family of joint demand distributions with six support points. For the general case, we develop a computationally tractable upper bound on the worst-case expected cost if the costs of fulfilling demands have a nested structure. This upper bound is the optimal value of a semidefinite program whose dimensions are polynomial in the number of locations. We propose an algorithm that can approximate general fulfillment cost structures by nested structures, yielding a computationally tractable heuristic for distributionally robust inventory optimization on general newsvendor networks. We conduct experiments on networks resembling U.S. e-commerce distribution networks to show the value of a distributionally robust approach over a stochastic approach that assumes an incorrect demand distribution.

An omnichannel retailer with a network of physical stores and online fulfillment centers facing two demands (online and in-store) has to make important, interlinked decisions—how much inventory to keep at each location and where to fulfill each online order from, as online demand can be fulfilled from any location with available inventory. We consider inventory decisions at the start of the selling horizon for a seasonal product, with online fulfillment decisions made multiple times over the horizon. To address the intractability in considering inventory and fulfillment decisions together, we relax the problem using a hindsight-optimal bound, for which the inventory decision can be made independent of the optimal fulfillment decisions, while still incorporating virtual pooling of online demands across locations. We develop a computationally fast and scalable inventory heuristic for the multilocation problem based on the two-store analysis. The inventory heuristic directly informs dynamic fulfillment decisions that guide online demand fulfillment from stores. Using a numerical study based on a fictitious network embedded in the United States, we show that our heuristic significantly outperforms traditional strategies. The value of centralized inventory planning is highest when there is a moderate mix of online and in-store demands leading to synergies between pooling within and across locations, and this value increases with the size of the network. The inventory-aware fulfillment heuristic considerably outperforms myopic policies seen in practice, and is found to be near-optimal under a wide range of problem parameters.

A basic assumption of the classical newsvendor model is that the probability distribution of the random demand is known. But in most realistic settings, only partial distribution information is available or reliably estimated. The distributionally robust newsvendor model is often used in this case where the worst-case expected profit is maximized over the set of distributions satisfying the known information, which is usually the mean and covariance of demands. However, covariance does not capture information on asymmetry of the demand distribution. In this paper, we introduce a measure of distribution asymmetry using second-order partitioned statistics. Semivariance is a special case with a single partition of the univariate demand. With mean, variance, and semivariance information, we show that a three-point distribution achieves the worst-case expected profit and derive a closed-form expression for the distributionally robust order quantity. For multivariate demand, the distributionally robust problem with partitioned statistics is hard to solve, but we develop a computationally tractable lower bound through the solution of a semidefinite program. We demonstrate in numerical experiments that asymmetry information significantly reduces expected profit loss particularly when the true distribution is heavy tailed. In computational experiments on automotive spare parts demand data, we provide evidence that the distributionally robust model that includes partitioned statistics outperforms the model that uses only covariance information.

Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments. This bound reveals that the demand distribution’s weighted mean spread affects the accuracy of the SAA heuristic.

Nowadays customers are becoming important partners of product innovation, with firms using customer feedback to guide product quality improvements. Soliciting customer feedback not only supports product innovation, it also cultivates loyalty among customers who feel that their voice can lead to change. However, soliciting informative feedback could be costly, leading to complicated tensions in the decision of whether to solicit feedback or not. In this paper, we analyze the dynamic policy for soliciting feedback that is informative for product quality improvement under two different settings where (i) the firm continually invests and (ii) the firm jointly decides when to invest in product quality improvement respectively. In setting (i), we find that the optimal policy has a monotone-threshold structure, which suggests the firm should initially engage in soliciting customer feedback, until either the amount of solicited feedback is sufficient or the product quality reaches a certain level, indicating the termination of solicitation. The policy is very easy to implement in practice. In setting (ii), the problem is extended to be the joint optimization of feedback solicitation and quality improvement, where we propose a simple but effective heuristic that only needs three thresholds. We run numerical experiments to verify the performance of the heuristic. By modeling the dynamics of product innovation, our study provides simple and effective practical solutions for dynamic customer feedback solicitation to better facilitate product quality improvement. Moreover, our numerical experiments reveal the importance of ensuring adequate customer engagement before committing resources to product innovation, where just a little coordination between feedback solicitation and product innovation can go a long way.

This paper studies inventory commingling in third-party (3P) marketplaces, a fulfillment practice where identical items from different sellers are pooled and shipped interchangeably. While commingling improves efficiency for both the platform and the sellers, it creates quality risks when sellers differ in product quality and this information is privately held. We develop a game-theoretic model of a platform that sets its fulfillment fee while sellers, differentiated by quality, decide whether to participate in commingling. We characterize the resulting equilibrium outcomes and uncover a form of market stratification: lower-quality sellers either avoid the platform entirely or join only by commingling, whereas higher-quality sellers always remain but in some cases may opt out of commingling to shield their customers from quality spillovers. We show that commingling consistently improves the profits of the platform and lower-quality sellers. However, it may hurt higher-quality sellers, even if they opt out: not through quality risk, but via the platform’s endogenous increase of the fulfillment fee. Importantly, we identify market conditions where commingling improves outcomes for all parties. Our paper provides platform managers with a framework to evaluate \textitwhen and \textithow to offer inventory commingling. By pinpointing market conditions where commingling boosts profits, expands seller participation, or threatens product quality, we offer actionable guidance for aligning fulfillment design with strategic objectives.

In this paper, we describe both applied and analytical work in collaboration with a large multistate gas utility. The project addressed a major operational resource allocation challenge that is typical to the industry. We study the resource allocation problem in which some of the tasks are scheduled and known in advance, and some are unpredictable and have to be addressed as they appear. The utility has maintenance crews that perform both standard jobs (each must be done before a specified deadline) as well as respond to emergency gas leaks (that occur randomly throughout the day and could disrupt the schedule and lead to significant overtime). The goal is to perform all the standard jobs by their respective deadlines, to address all emergency jobs in a timely manner, and to minimize maintenance crew overtime. We employ a novel decomposition approach that solves the problem in two phases. The first is a job scheduling phase, where standard jobs are scheduled over a time horizon. The second is a crew assignment phase, which solves a stochastic mixed integer program to assign jobs to maintenance crews under a stochastic number of future emergencies. For the first phase, we propose a heuristic based on the rounding of a linear programming relaxation formulation and prove an analytical worst-case performance guarantee. For the second phase, we propose an algorithm for assigning crews that is motivated by the structure of an optimal solution. We used our models and heuristics to develop a decision support tool that is being piloted in one of the utility’s sites. Using the utility’s data, we project that the tool will result in a 55% reduction in overtime hours.