Margarida Carvalho

Golnoosh Farnadi

2024-03-24

Proceedings of the AAAI Conference on Artificial Intelligence (published)

Solving Combinatorial Pricing Problems using Embedded Dynamic Programming Models

Quang Minh Bui

Jos'e Neto

The combinatorial pricing problem (CPP) is a bilevel problem in which the leader maximizes their revenue by imposing tolls on certain items … (see more)that they can control. Based on the tolls set by the leader, the follower selects a subset of items corresponding to an optimal solution of a combinatorial optimization problem. To accomplish the leader's goal, the tolls need to be sufficiently low to discourage the follower from choosing the items offered by the competitors. In this paper, we derive a single-level reformulation for the CPP by rewriting the follower's problem as a longest path problem using a dynamic programming model, and then taking its dual and applying strong duality. We proceed to solve the reformulation in a dynamic fashion with a cutting plane method. We apply this methodology to 2 distinct dynamic programming models, namely, a novel formulation designated as selection diagram and the well-known decision diagram. We also produce numerical results to evaluate their performances across 3 different specializations of the CPP and a closely related problem that is the knapsack interdiction problem. Our results showcase the potential of the 2 proposed reformulations over the natural value function approach, expanding the set of tools to solve combinatorial bilevel programs.

2024-03-19

ArXiv (preprint)

The Sample Average Approximation Method for Solving Two-Stage Stochastic Programs with Endogenous Uncertainty

Maria Bazotte

Thibaut Vidal

Real-world decision-making problems involve Type 1 decision-dependent uncertainty, where the probability distribution of the stochastic proc… (see more)ess depends on the model decisions. However, few studies focus on two-stage stochastic programs with this type of endogenous uncertainty, and those that do lack general methodologies. We thus propose herein a general method for solving a class of these programs based on the transformation of random variables, a technique widely employed in probability and statistics. The proposed method is tailored to large-scale problems with discrete or continuous endogenous random variables. The random variable transformation allows the use of the sample average approximation (SAA) method, which provides optimality convergence guarantees under certain conditions. We show that, for some classical distributions, the proposed method reduces to solving mixed-integer linear or convex programs. Finally, we validate this method by applying it to a network design and facility-protection problem, considering distinct decision-dependent distributions for the random variables. Whereas most distributions result in a nonlinear nonconvex deterministic equivalent program, the proposed method solves mixed-integer linear programs in all cases. In addition, it produces attractive performance estimators for the SAA method in a reasonable computational time and outperforms the case in which the endogenous distribution defines a mixed-integer deterministic equivalent.

2024-02-23

ArXiv (preprint)

Computing Approximate Nash Equilibria for Integer Programming Games

Aloïs Duguet

Gabriele Dragotto

Sandra-ulrich Ngueveu

2024-02-06

ArXiv (preprint)

Asymmetry in the complexity of the multi-commodity network pricing problem

Quang Minh Bui

Jos'e Neto

2024-01-03

Mathematical Programming (published)

Penalties and Rewards for Fair Learning in Paired Kidney Exchange Programs

Alison Caulfield

Yi Lin

Adrian Vetta

A kidney exchange program, also called a kidney paired donation program, can be viewed as a repeated, dynamic trading and allocation mechani… (see more)sm. This suggests that a dynamic algorithm for transplant exchange selection may have superior performance in comparison to the repeated use of a static algorithm. We confirm this hypothesis using a full scale simulation of the Canadian Kidney Paired Donation Program: learning algorithms, that attempt to learn optimal patient-donor weights in advance via dynamic simulations, do lead to improved outcomes. Specifically, our learning algorithms, designed with the objective of fairness (that is, equity in terms of transplant accessibility across cPRA groups), also lead to an increased number of transplants and shorter average waiting times. Indeed, our highest performing learning algorithm improves egalitarian fairness by 10% whilst also increasing the number of transplants by 6% and decreasing waiting times by 24%. However, our main result is much more surprising. We find that the most critical factor in determining the performance of a kidney exchange program is not the judicious assignment of positive weights (rewards) to patient-donor pairs. Rather, the key factor in increasing the number of transplants, decreasing waiting times and improving group fairness is the judicious assignment of a negative weight (penalty) to the small number of non-directed donors in the kidney exchange program.

2023-12-31

Web and Internet Economics (published)

When Nash Meets Stackelberg

Gabriele Dragotto

Felipe Feijoo

Andrea Lodi

Sriram Sankaranarayanan

2023-12-22

Management Science (published)

Maximum flow-based formulation for the optimal location of electric vehicle charging stations

Pierre-Luc Parent

Miguel F. Anjos

Ribal F. Atallah

With the increasing effects of climate change, the urgency to step away from fossil fuels is greater than ever before. Electric vehicles (EV… (see more)s) are one way to diminish these effects, but their widespread adoption is often limited by the insufficient availability of charging stations. In this work, our goal is to expand the infrastructure of EV charging stations, in order to provide a better quality of service in terms of user satisfaction (and availability of charging stations). Specifically, our focus is directed towards urban areas. We first propose a model for the assignment of EV charging demand to stations, framing it as a maximum flow problem. This model is the basis for the evaluation of user satisfaction with a given charging infrastructure. Secondly, we incorporate the maximum flow model into a mixed‐integer linear program, where decisions on the opening of new stations and on the expansion of their capacity through additional outlets is accounted for. We showcase our methodology for the city of Montreal, demonstrating the scalability of our approach to handle real‐world scenarios. We conclude that considering both spacial and temporal variations in charging demand is meaningful when solving realistic instances.

2023-12-10

ArXiv (preprint)

Accelerated Benders Decomposition and Local Branching for Dynamic Maximum Covering Location Problems

Steven Lamontagne

Ribal F. Atallah

The maximum covering location problem (MCLP) is a key problem in facility location, with many applications and variants. One such variant is… (see more) the dynamic (or multi-period) MCLP, which considers the installation of facilities across multiple time periods. To the best of our knowledge, no exact solution method has been proposed to tackle large-scale instances of this problem. To that end, in this work, we expand upon the current state-of-the-art branch-and-Benders-cut solution method in the static case, by exploring several acceleration techniques. Additionally, we propose a specialised local branching scheme, that uses a novel distance metric in its definition of subproblems and features a new method for efficient and exact solving of the subproblems. These methods are then compared through extensive computational experiments, highlighting the strengths of the proposed methodologies.

2023-09-01

ArXiv (preprint)

Optimising Electric Vehicle Charging Station Placement Using Advanced Discrete Choice Models

Steven Lamontagne

Emma Frejinger

Bernard Gendron

Miguel F. Anjos

Ribal Atallah

D'epartement d'informatique et de recherche op'erationnelle

U. Montr'eal

S. O. Mathematics

U. Edinburgh

Institut de Recherche d'Hydro-Qu'ebec

We present a new model for finding the optimal placement of electric vehicle charging stations across a multiperiod time frame so as to maxi… (see more)mise electric vehicle adoption. Via the use of stochastic discrete choice models and user classes, this work allows for a granular modelling of user attributes and their preferences in regard to charging station characteristics. We adopt a simulation approach and precompute error terms for each option available to users for a given number of scenarios. This results in a bilevel optimisation model that is, however, intractable for all but the simplest instances. Our major contribution is a reformulation into a maximum covering model, which uses the precomputed error terms to calculate the users covered by each charging station. This allows solutions to be found more efficiently than for the bilevel formulation. The maximum covering formulation remains intractable in some instances, so we propose rolling horizon, greedy, and greedy randomised adaptive search procedure heuristics to obtain good-quality solutions more efficiently. Extensive computational results are provided, and they compare the maximum covering formulation with the current state of the art for both exact solutions and the heuristic methods. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by Hydro-Québec and the Natural Sciences and Engineering Research Council of Canada [Discovery grant 2017-06054; Collaborative Research and Development Grant CRDPJ 536757–19]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0185 .

2023-09-01

INFORMS Journal on Computing (published)

Capacity Planning in Stable Matching: An Application to School Choice

Federico Bobbio

Andrea Lodi

Ignacio Rios

Alfredo Torrico

Centralized mechanisms are becoming the standard approach to solve several assignment problems. Examples include the allocation of students … (see more)to schools (school choice), high-school graduates to colleges, residents to hospitals and refugees to cities. In most of these markets, a desirable property of the assignment is stability, which guarantees that no pair of agents has incentive to circumvent the matching. Using school choice as our matching market application, we introduce the problem of jointly allocating a school capacity expansion and finding the best stable matching for the students in the expanded market. We analyze theoretically the problem, focusing on the trade-off behind the multiplicity of student-optimal assignments, and the problem complexity. Since the theoretical intractability of the problem precludes the adaptation of classical approaches to solve it efficiently, we generalize existent mathematical programming formulations of stability constraints to our setting. These generalizations result in integer quadratically-constrained programs, which are computationally hard to solve. In addition, we propose a novel mixed-integer linear programming formulation that is exponentially-large on the problem size. We show that the stability constraints can be separated in linear time, leading to an effective cutting-plane method. We evaluate the performance of our approaches in a detailed computational study, and we find that our cutting-plane method outperforms mixed-integer programming solvers applied to existent formulations extended to our problem setting. We also propose two heuristics that are effective for large instances of the problem. Finally, we use the Chilean school choice system data to demonstrate the impact of capacity planning under stability conditions. Our results show that each additional school seat can benefit multiple students. On the one hand, we can focus on access by prioritizing extra seats that benefit previously unassigned students; on the other hand, we can focus on merit by allocating extra seats that benefit several students via chains of improvement. These insights empower the decision-maker in tuning the matching algorithm to provide a fair application-oriented solution.

2023-07-07

Proceedings of the 24th ACM Conference on Economics and Computation (published)

Integer Programming Games: A Gentle Computational Overview

Gabriele Dragotto

Andrea Lodi

Sriram Sankaranarayan

2023-06-05

ArXiv (preprint)