arXiv subjects

Chamsi Hssaine

Publications and source records attributed to Chamsi Hssaine.

10 recordsLinked to original sources

arXiv2026

On The Limited Cost of Consistency In Points-Based Rewards Programs

Points-based rewards programs are a prevalent way to incentivize customer loyalty. In theory, the effective design of these programs is shaped by two important considerations. Customer heterogeneity suggests that tailoring thresholds to different customer types may yield revenue gains, while demand uncertainty creates incentives to update thresholds over time as the seller learns how customers respond to the program. In practice, however, there may be nontrivial operational and customer-facing benefits associated with maintaining consistency along both of these dimensions. Setting a single threshold across customer types can facilitate transparent communication and reduce the legal, reputational, and operational risks associated with personalization, while avoiding threshold increases prevents the devaluation of customers' previously earned points. Motivated by these considerations, this paper studies the cost of consistency in points-based rewards programs. We study this question within the context of the popular ``Buy $N$, Get One Free'' (BNGO) rewards programs. We first bound the value of personalization of these programs, proving that the revenue of the optimal single-threshold program is within a factor of $\frac{π^2}{6}$ of that of the optimal personalized strategy. We then tackle the problem of designing devaluation-free learning algorithms --- i.e., algorithms that never increase the redemption threshold --- in the presence of demand uncertainty. Toward this goal, we first design a greedy learning algorithm that incurs $\widetilde{O}(\sqrt{T})$ regret in expectation over a horizon of length $T$; this guarantee is optimal, up to polylogarithmic factors. We then provide a devaluation-free modification of this algorithm, and show that this results in only a constant factor loss in regret.

cs.LG↗

arXiv2026

Online Fair Allocation of Perishable Resources

We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and the decision-maker must commit to an allocation for these individuals before moving on to the next round. The goal is to construct a sequence of allocations that is envy-free and efficient. Our work makes two important contributions toward this problem: we first derive strong lower bounds on the optimal envy-efficiency trade-off, demonstrating that a decision-maker is fundamentally limited in what she can hope to achieve relative to the no-perishing setting; we then design an algorithm achieving these lower bounds which takes as input (i) a prediction of the perishing order, and (ii) a desired bound on envy. Given the remaining budget in each period, the algorithm uses forecasts of future demand perishing to adaptively choose from one of two carefully constructed guardrail quantities. We demonstrate our algorithm's strong numerical performance, and state-of-the-art, perishing-agnostic algorithms' inefficacy, on simulations calibrated to a real-world dataset.

math.OC↗

arXiv2026

The Data-Driven Censored Newsvendor Problem

We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.

math.OC↗

arXiv2025

Online Allocation of Throughput-Constrained Resources Using Proxy Assignments

We study a variation of the canonical online resource allocation problem in which resources are throughput, rather than budget, constrained. As in the classical setting, the decision-maker must assign sequentially arriving jobs to one of multiple available resources. However, in addition to the assignment costs incurred from these decisions, the decision-maker is also penalized for deviating from exogenous, time-varying target assignment rates for each resource, which represent the resources' respective throughput capacities throughout the horizon. The goal is to minimize the total expected assignment and deviation penalty costs incurred throughout the horizon when the distribution of assignment costs is unknown. We first show that naive extensions of state-of-the-art algorithms for classical budget-constrained resource allocation problems can fail dramatically when applied to throughput-constrained resource allocation. We then propose a novel ``proxy assignment" primal-dual algorithm that uses current arrivals to simulate the effect of future arrivals. We prove that our algorithm achieves the optimal $O(\sqrt{T})$ regret bound when the assignment costs of the arriving jobs are drawn i.i.d. from a fixed distribution. We demonstrate the practical performance of our approach by conducting numerical experiments on synthetic datasets, as well as real-world datasets from retail fulfillment operations.

math.OC↗

arXiv2025

Sequential Fair Allocation With Replenishments: A Little Envy Goes An Exponentially Long Way

We study the trade-off between envy and inefficiency in repeated resource allocation settings with stochastic replenishments, motivated by real-world systems such as food banks and medical supply chains. Specifically, we consider a model in which a decision-maker faced with stochastic demand and resource donations must trade off between an equitable and efficient allocation of resources over an infinite horizon. The decision-maker has access to storage with fixed capacity $M$, and incurs efficiency losses when storage is empty (stockouts) or full (overflows). We provide a nearly tight (up to constant factors) characterization of achievable envy-inefficiency pairs. Namely, we introduce a class of Bang-Bang control policies whose inefficiency exhibits a sharp phase transition, dropping from $Θ(1/M)$ when $Δ= 0$ to $e^{-Ω(ΔM)}$ when $Δ> 0$, where $Δ$ is used to denote the target envy of the policy. We complement this with matching lower bounds, demonstrating that the trade-off is driven by supply, as opposed to demand uncertainty. Our results demonstrate that envy-inefficiency trade-offs not only persist in settings with dynamic replenishment, but are shaped by the decision-maker's available capacity, and are therefore qualitatively different compared to previously studied settings with fixed supply.

math.OC↗

arXiv2025

On the Power of Delayed Flexibility: Balls, Bins, and a Few Opaque Promotions

Effective load balancing lies at the heart of many applications in operations. Frequently tackled via the balls-into-bins paradigm, seminal results established the power of two choices in load balancing: a limited amount of costly flexibility goes a long way in order to maintain an approximately balanced load throughout the decision-making horizon. In many applications, however, balance across time may be too stringent a requirement; rather, the only desideratum is approximate balance at the {\it end} of the horizon. Motivated by this observation, in this work we design "delayed-flexibility" algorithms tailored to such settings. For the canonical balls-into-bins problem, we show that a simple policy that begins exerting flexibility toward the end of the time horizon - namely, when $Θ\left(\sqrt{T\log T}\right)$ periods remain - suffices to achieve an approximately balanced load, i.e., a maximum load within $O(1)$ of the average load. Moreover, with just a small amount of adaptivity, a threshold policy achieves the same result, while only exerting flexibility in $O\left(\sqrt{T}\right)$ periods, thus matching a natural lower bound. We leverage these results to study the design of opaque selling strategies in retail settings, a topic recently identified as a key application of the power of two choices paradigm. For this problem, we prove that late-stage opaque selling strategies achieve the optimal trade-off between exerting costly flexibility - i.e., offering the opaque product at a discount - and achieving inventory cost savings through load balancing. We demonstrate the robustness of our insights via extensive numerical experiments, for a variety of customer choice models.

math.OC↗

arXiv2024

Price Competition Under A Consider-Then-Choose Model With Lexicographic Choice

The sorting and filtering capabilities offered by modern e-commerce platforms significantly impact customers' purchase decisions, as well as the resulting prices set by competing sellers on these platforms. Motivated by this practical reality, we study price competition under a flexible choice model: Consider-then-Choose with Lexicographic Choice (CLC). In this model, a customer first forms a consideration set of sellers based on (i) her willingness-to-pay and (ii) an arbitrary set of criteria on items' non-price attributes; she then chooses the highest-ranked item according to a lexicographic ranking in which items with better performance on more important attributes are ranked higher. We provide a structural characterization of equilibria in the resulting game of price competition, and derive an economically interpretable condition, which we call gradient dominance, under which equilibria can be computed efficiently. For this subclass of CLC models, we prove that distributed gradient-based pricing dynamics converge to the set of equilibria. Extensive numerical experiments show robustness of our theoretical findings when gradient dominance does not hold.

cs.GT↗

arXiv2024

Fair Incentives for Repeated Engagement

We study a decision-maker's problem of finding optimal monetary incentive schemes for retention when faced with agents whose participation decisions (stochastically) depend on the incentive they receive. Our focus is on policies constrained to fulfill two fairness properties that preclude outcomes wherein different groups of agents experience different treatment on average. We formulate the problem as a high-dimensional stochastic optimization problem, and study it through the use of a closely related deterministic variant. We show that the optimal static solution to this deterministic variant is asymptotically optimal for the dynamic problem under fairness constraints. Though solving for the optimal static solution gives rise to a non-convex optimization problem, we uncover a structural property that allows us to design a tractable, fast-converging heuristic policy. Traditional schemes for retention ignore fairness constraints; indeed, the goal in these is to use differentiation to incentivize repeated engagement with the system. Our work (i) shows that even in the absence of explicit discrimination, dynamic policies may unintentionally discriminate between agents of different types by varying the type composition of the system, and (ii) presents an asymptotically optimal policy to avoid such discriminatory outcomes.

cs.GT↗

arXiv2021

Real-Time Approximate Routing for Smart Transit Systems

We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its fleet of cars as a feeder to connect passengers to its high-capacity fleet, which operates on fixed routes. Our goal is to find the optimal set of (bus) routes and corresponding frequencies to maximize the social welfare of the system in a given time window. This generalizes the Line Planning Problem, a widely studied topic in the transportation literature, for which existing solutions are either heuristic (with no performance guarantees), or require extensive computation time (and hence are impractical for real-time use). To this end, we develop a $1-\frac{1}{e}-\varepsilon$ approximation algorithm for the Real-Time Line Planning Problem, using ideas from randomized rounding and the Generalized Assignment Problem. Our guarantee holds under two assumptions: $(i)$ no inter-bus transfers and $(ii)$ access to a pre-specified set of feasible bus lines. We moreover show that these two assumptions are crucial by proving that, if either assumption is relaxed, the Real-Time Line Planning Problem does not admit any constant-factor approximation. Finally, we demonstrate the practicality of our algorithm via numerical experiments on real-world and synthetic datasets, in which we show that, given a fixed time budget, our algorithm outperforms Integer Linear Programming-based exact methods.

math.OC↗

arXiv2019

Information Signal Design for Incentivizing Team Formation

We study the use of Bayesian persuasion (i.e., strategic use of information disclosure/signaling) in endogenous team formation. This is an important consideration in settings such as crowdsourcing competitions, open science challenges and group-based assignments, where a large number of agents organize themselves into small teams which then compete against each other. A central tension here is between the strategic interests of agents who want to have the highest-performing team, and that of the principal who wants teams to be balanced. Moreover, although the principal cannot choose the teams or modify rewards, she often has additional knowledge of agents' abilities, and can leverage this information asymmetry to provide signals that influence team formation. Our work uncovers the critical role of self-awareness (i.e., knowledge of one's own abilities) for the design of such mechanisms. For settings with two-member teams and binary-valued agents partitioned into a constant number of prior classes, we provide signaling mechanisms which are asymptotically optimal when agents are agnostic of their own abilities. On the other hand, when agents are self-aware, then we show that there is no signaling mechanism that can do better than not releasing information, while satisfying agent participation constraints.

cs.GT↗