Hanzhang Qin

Stochastic optimization often restricts recourse decisions to affine parameterizations for computational tractability, potentially creating a substantial and irreducible approximation gap. Large language models (LLMs) offer new opportunities to discover richer problem-specific structures that can help narrow this gap. We propose Generative Stochastic Optimization (GenSO), a framework that uses LLMs to discover representations for adaptive recourse while preserving the rigor and tractability of optimization models. The key component of GenSO is the Generative Linear Decision Rule (GenLDR), in which recourse decisions are expressed as linear combinations of closed-form nonlinear basis functions generated by LLMs from problem structure and domain knowledge. Consequently, GenSO increases the expressiveness of recourse decisions without compromising tractability and interpretability. We establish finite-sample guarantees for fixed generated representations and further derive a performance bound under the assumption motivated by empirical scaling laws of LLMs. We evaluate GenSO on a multi-period newsvendor problem and a data center location problem with multi-period job scheduling calibrated using real-world datasets. Across both settings, GenSO consistently outperforms existing benchmarks in out-of-sample evaluations while uncovering interpretable nonlinear decision structures that are difficult to identify through conventional manual design.

We develop a min-cut certificate approach to sparse process-flexibility design. The classical long-chain theory relies on complementarity among flexible arcs, but that mechanism breaks down once each plant can serve three or more products. The replacement is a product-set certificate: a low-demand set is costly exactly when it traps too many complete plant neighborhoods. This certificate separates demand risk from topology. Ancillary fixed-design diagnostics relate the same certificate to generalized chaining gaps and marginal-sales certificates. For chain designs with a fixed neighborhood degree, the certificate becomes an interval problem, which gives finite-size monotonicity, normalized risk-pooling monotonicity, diminishing returns in the flexibility degree, and efficient finite-system computation. The same certificate also explains when chains are the wrong topology. Exact pair-spread designs are certificate-profile optimal for all small bottleneck sets q<2k-1. For projective-plane designs with n=k^2-k+1, this distribution-free profile result yields a coefficient separation under binary 0/2 demand: the design improves on the k-chain by n(k-2)p^{k+1}(1-p)^{n-k-1}+O(p^{k+2}), with the Fano-plane theorem as the k = 3 instance. Numerical experiments show that low-codegree balanced topologies improve on chain designs in general.

We consider a fundamental problem in revenue management: feature-based pricing, where a firm needs to make a pricing decision to maximize the expected revenue for a single product based on feature information. Historical data with price, covariates, and uncensored sales, is available for demand estimation. Our model assumes a linear relationship between price and demand while simultaneously capturing the impact of covariates through a nonparametric shape-restricted function. We develop a Three-Step Semi-Parametric Estimation algorithm to estimate the demand and foster provably near-optimal data-driven pricing decisions. From a non-asymptotic perspective, we derive finite sample regret bounds, showcasing the efficacy of our algorithm in achieving near-optimal revenue, even under potential misspecification of the demand model. The numerical results demonstrate that the decision performance of our algorithm is comparable to the Double Machine Learning method, while significantly outperforming a naive two-step iterative learning method as well.

Motivated by logistical problems faced by a large supply chain software company, the paper, “A New Approach for Vehicle Routing with Stochastic Demand: Combining Route Assignment with Process Flexibility,” studies a vehicle routing problem where some routes are allowed to overlap. The paper proposes a class of simple and effective strategies to design overlapped routes with customer sharing, which combines ideas from the process flexibility in manufacturing and traditional vehicle routing literatures. Through theoretical analysis and numerical simulations, the paper illustrates the advantage of an overlapped routing strategy with a small amount of customer overlaps. In particular, it shows that such a strategy can provide consistent route assignments to drivers, while achieving a similar expected travel distance as the theoretical benchmark in the fully reoptimized setting. The strategy is in contrast to the traditional fixed routing strategy, which provides consistent route assignments to drivers, but incurs a much higher expected travel distance.

We study the classic multiperiod joint pricing and inventory control problem in a data-driven setting. In this problem, a retailer makes periodic decisions on the prices and inventory levels of a product that she wishes to sell. The retailer’s objective is to maximize the expected profit over a finite horizon by matching the inventory level with a random demand, which depends on the price in each period. In reality, the demand functions or random noise distributions are usually difficult to know exactly, whereas past demand data are relatively easy to collect. We propose a data-driven approximation algorithm that uses precollected demand data to solve the joint pricing and inventory control problem. We assume that the retailer does not know the noise distributions or the true demand functions; instead, we assume either she has access to demand hypothesis sets and the true demand functions can be represented by nonnegative combinations of candidate functions in the demand hypothesis sets, or the true demand function is generalized linear. We prove the algorithm’s sample complexity bound: the number of data samples needed in each period to guarantee a near-optimal profit is [ ], where T is the number of periods, and ϵ is the absolute difference between the expected profit of the data-driven policy and the expected optimal profit. In a numerical study, we demonstrate the construction of demand hypothesis sets from data and show that the proposed data-driven algorithm solves the dynamic problem effectively and significantly improves the optimality gaps over the baseline algorithms. This paper was accepted by J. George Shanthikumar, big data analytics.

This work is inspired by the daily operations of Hema supermarket, which is a recently established “new retail” model by Alibaba Group, China. In a Hema supermarket store, a single SKU may be presented with demand in the form of multiple channels. The challenge facing Hema is the question of how many units to stock in total between the warehouse and the store-front in advance of uncertain demand that arises in several consecutive time frames, each 30 minutes long. In this work, we provide the first distributionally robust optimization study in the setting of omnichannel inventory management, wherein we are to make a stocking decision robust to an adversary's choice of coupling of available (marginal) demand distributions by channel and by time frame. The adversary's coupling decision amounts to designing a random mathematical program with equilibrium constraints (MPEC). And we provide both a structural analysis of the adversary's choice of couplingas well as an efficient procedure to find this coupling. In general, the overall distributionally robust stocking problem is non-concave. We provide sufficient conditions on the cost parameters under which this problem becomes concave, and hence tractable. Finally, we conduct experiments with Hema's data. In these experiments, we compare and contrast the performance of our distributionally robust solution with the performance of a naive Newsvendor-like solution on various SKUs of varying sales volume and number of channels on a 5-hour time window from 2pm - 7pm on weekends. Numerical experiments show that the distributionally robust solutions generally outperform the stochastic Newsvendor-like solution. Furthermore, and interestingly, in all of our experiments, the distributionally robust inventory decision problems presented by the historical data provided by Hema are in fact concave.