A Column Generation Algorithm for Choice-Based Network Revenue Management

Contributors

Contributors

New Algorithms Advance Revenue Management with Demand Learning A new study by Sentao Miao (University of Colorado Boulder), Yining Wang (University of Texas at Dallas), and Jiawei Zhang (New York University) introduces efficient algorithms for revenue management when firms face limited resources and uncertain demand. Revenue management, used in industries such as airlines, hotels, and retail, requires dynamic decisions on pricing and product assortments, whereas resources such as seats or inventory cannot be replenished. Traditional approaches often struggle with complexity or weak theoretical guarantees. The authors propose a primal-dual learning framework that combines optimization with machine learning’s upper confidence bound method. Their approach achieves near-optimal regret bounds, remaining computationally efficient even in large or infinite decision spaces. Applications include dynamic assortment selection, network revenue management with generalized linear demand, and joint pricing–assortment optimization. Numerical experiments show the methods consistently outperform benchmarks, offering practical, scalable solutions for data-driven industries.

Generic Model Base Design for Decision Support Systems in Revenue Management: Applications to Hotel and Health Care Sectors

One of the most prevalent demand models in the revenue management literature is based on dividing the selling horizon into a number of time periods such that there is at most one customer arrival at each time period. This demand model is equivalent to using a discrete-time approximation to a Poisson process, but it has an important shortcoming. If the mean number of customer arrivals is large, then the coefficient of variation of the number of customer arrivals has to be small. In other words, large demand volume and large demand variability cannot coexist in this demand model. In this paper, we start with a revenue management model that incorporates general mean and variance for the number of customer arrivals. This revenue management model has a random selling horizon length, capturing the distribution of the number of customer arrivals. The question we seek to answer is the form of the fluid approximation that corresponds to this revenue management model. It is tempting to construct the fluid approximation by computing the expected consumption of the resource capacities in the constraints and the total expected revenue in the objective function through the distribution of the number of customer arrivals. We demonstrate that this answer is wrong in the sense that it yields a fluid approximation that is not asymptotically tight as the resource capacities get large. We give an alternative fluid approximation where perhaps surprisingly, the distribution of the number of customer arrivals does not play any role in the constraints. We show that this fluid approximation is asymptotically tight as the resource capacities get large. A numerical study also demonstrates that the policies driven by the latter fluid approximation perform substantially better, so there is practical value in getting the fluid approximation right under high-variance demand. This paper was accepted by Omar Besbes, revenue management and market analytics. Funding: The work of the O. El Housni and H. Topaloglu was supported by a seed grant from Urban Tech research hub at Cornell Tech. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2023.4769 .

Column generation is a fundamental technique for solving large-scale combinatorial optimization problems such as unit commitment and vehicle routing, yet its performance is often limited by dual oscillation. This study explores the intrinsic cause of this phenomenon from the perspective of shadow price theory and demonstrates that dual oscillation arises from the lack of marginal interpretability of Lagrange multipliers when multiple dual solutions coexist. To address this issue, an improved column generation framework is proposed in which traditional multipliers are replaced with minimum-norm multipliers that possess clear economic meaning and act as directional shadow prices. A generalized pricing subproblem is formulated, and partial minimum-norm multipliers are obtained through convex quadratic optimization to guide column generation. Numerical experiments on a simplified single-period unit commitment case and large-scale cutting stock problems showed that the proposed approach eliminated invalid column generation and achieved speedy convergence to the optimal solution within only two iterations for the unit commitment case, and the classical column generation exhibited slow convergence with dual oscillation in large-scale scenarios while the improved algorithm achieved fast and stable convergence. The results indicate that the stabilization method enhances the consistency of dual variables and provides a more robust foundation for the theoretical and practical development of column generation algorithms.

Demand management, or revenue management, is commonplace in many industries. In order to enhance revenues, revenue management aims to exploit differences in product preferences between customers by prioritizing service to customers with a higher willingness-to-pay. The key lesson from revenue management is that a company should try to use its scarce capacity for its most valuable customers. Instead of accepting demand first-come, first-serve, it may be beneficial to reserve capacity for more valuable customers that may still arrive in the future. There is a huge body of literature devoted to quantity control policies and dynamic pricing in revenue management (for a review, see Chiang et al. 2007), Talluri and Van Ryzin (2004) and Boyd and Bilegan (2003). Quantity-based control manages the availability of product classes, while price-based control is concerned with the price of products. Note that pricing refers to the whole range of incentives that are available to manage customer demand, e.g. financial rewards for peak travel avoidance (Knockaert et al., Chap. 6). Airlines, hotels and rental car industries represent the most successful applications of revenue management (Chiang et al. 2007). These industries all share some similar business characteristics. In particular, their products are perishable, the availability of capacity is relatively inflexible in the short run, and the variable costs operating costs are small, relative to the fixed costs.

A General Framework for Resource Constrained Revenue Management with Demand Learning and Large Action Space

In this paper, we introduce the Electric Vehicle Routing Problem with Flexible Time Windows (EVRPFTW) in which vehicles are allowed to serve customers before and after the earliest and latest time window bounds, respectively. The objective of this problem is to assign electric vehicles to feasible routes and make schedules with minimum total cost that includes the traveling costs, the costs of using electric vehicles and the penalty costs incurred for earliness and lateness. The proposed mathematical model is solved by a column generation procedure. To generate an integer solution, we solve an integer programming problem using the routes constructed by the column generation algorithm. We further develop a linear programming model to compute the optimal times to start service at each customer for the selected routes. A number of well-known benchmark instances is solved by our solution procedure to evaluate the operational gains obtained by employing flexible time windows.

Masking primal and dual models for data privacy in network revenue management

Column generation is an increasingly popular basic tool for the solution of large-scale mathematical programming problems. As problems being solved grow bigger, column generation may however become less efficient in its present form, where columns typically are not optimizing, and finding an optimal solution instead entails finding an optimal convex combination of a huge number of them. We present a class of column generation algorithms in which the columns defining the restricted master problem may be chosen to be optimizing in the limit, thereby reducing the total number of columns needed. This first article is devoted to the convergence properties of the algorithm class, and includes global (asymptotic) convergence results for differentiable minimization, finite convergence results with respect to the optimal face and the optimal solution, and extensions of these results to variational inequality problems. An illustration of its possibilities is made on a nonlinear network flow model, contrasting its convergence characteristics to that of the restricted simplicial decomposition (RSD) algorithm.

We consider a canonical quantity-based network revenue management problem where a firm accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. Because of the curse of dimensionality, the exact solution to this problem by dynamic programming is intractable when the number of resources is large. We study a family of re-solving heuristics that periodically re-optimize an approximation to the original problem known as the deterministic linear program (DLP), where random customer arrivals are replaced by their expectations. We find that, in general, frequently re-solving the DLP produces the same order of revenue loss as one would get without re-solving, which scales as the square root of the time horizon length and resource capacities. By re-solving the DLP at a few selected points in time and applying thresholds to the customer acceptance probabilities, we design a new re-solving heuristic with revenue loss that is uniformly bounded by a constant that is independent of the time horizon and resource capacities. This paper was accepted by Kalyan Talluri, revenue management and market analytics.

As airlines began forming hub-and-spoke networks, network-based revenue management (RM) systems have increased in overall importance. In an airline’s quest to maximize system revenue, a network RM-based system differentiates between the local (using only one resource) and connecting or flow (using multiple resources) passengers. Although these systems are theoretically optimal, they are difficult to implement in practice directly. Implementation of such systems often requires assumptions that, when not correct, may lead to suboptimal decisions. This article is meant to highlight the major difficulties a practitioner may encounter during the transition to a network-based RM system. We begin with a brief overview of a common set of network-based RM models and then address three areas in which such a system may expose a carrier to revenue leakage, including: (i) forecasting, (ii) optimization and (iii) distribution. The aim of this article is to explain each of these areas and their respective difficulties with implementing a network RM system. Furthermore, we provide significant detail for each of the problem areas such that: (i) fellow researchers may consider these details when working within the field of network RM and (ii) practitioners may decide how to address such issues during the implementation of a network RM system within their organization.

Simulation of stochastic systems : Sheldon M. Ross, College of Engineering, Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, U.S.A.

An effective resource allocation technique is required for each Ready Mixed Concrete (RMC). Finding the optimum solution for large scale RMC dispatching problems with available computing facilities is intractable. Two kinds of techniques have been implemented to deal with this problem: (i) evolutionary techniques and (ii) numerical techniques. For the purposes of this paper we selected a technique from each category and compared them under the same conditions. Robust Genetic Algorithm (Robust-GA) and Column Generation (CG) were selected and tested with different sizes of real RMC problems. The results show that on average CG solutions are obtained with a 20% reduced cost. However, Robust-GA converges 40% faster than CG, while the number of unassigned customers for both the techniques is almost the same.