arXiv subjects

Virginie Lurkin

Publications and source records attributed to Virginie Lurkin.

8 recordsLinked to original sources

arXiv2026

Logic-Based Benders Decomposition for Time Slot Management with Mixed Logit Demand

This paper develops an exact solution framework for the choice-based time slot management problem under mixed logit demand in attended home delivery systems. The problem jointly optimizes delivery slot offerings, price discounts, and routing decisions, with customer choices endogenously modeled through a simulation-based mixed logit formulation embedded via sample average approximation, resulting in a large-scale stochastic mixed-integer program. To address this complexity, we propose a logic-based Benders decomposition (LBBD) that separates strategic assortment and pricing decisions, together with customer choice, from scenario-specific vehicle routing subproblems. We derive problem-specific optimality cuts that exploit the routing structure to provide stronger bounds than generic cuts, and establish their validity. To enhance computational performance, we introduce and systematically evaluate several strengthening strategies, including relaxation-based cut generation and capacity- and flow-based valid inequalities. Computational experiments on benchmark instances show that the proposed framework significantly extends the range of solvable instances compared to direct MILP approaches. The method yields proven optimal solutions for instances with up to 10 customers and consistently tight optimality gaps for instances with 15-20 customers. For larger instances, the approach provides meaningful upper bounds, while remaining computationally challenging for larger problem sizes. Overall, the results highlight the interaction between stochastic choice modeling, routing complexity, and decomposition design, and demonstrate the potential of LBBD for solving integrated choice-based optimization problems.

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arXiv2025

A tactical time slot management problem under mixed logit demand

We study the tactical time slot management problem under mixed logit demand for attended home delivery in subscription settings. We propose a static mixed-integer linear programming model that integrates delivery slot assortment, price discount decisions, and routing optimization while capturing customer heterogeneity through the mixed logit model. To overcome the computational challenges posed by simulation-based choice probabilities, we develop a simulation-based Adaptive Large Neighborhood Search method aligned with a Sample Average Approximation reformulation. Computational experiments on large-scale instances demonstrate the effectiveness of our approach in capturing stochastic customer behavior and preference heterogeneity, providing a scalable and flexible method for optimizing time slot management under complex demand structures.

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arXiv2024

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes.

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arXiv2023

An exact algorithm for the static pricing problem under discrete mixed logit demand

Price differentiation is a common strategy in many markets. In this paper, we study a static multiproduct price optimization problem with demand given by a discrete mixed multinomial logit model. By considering a mixed logit model that includes individual-specific variables in the utility specification, our pricing problem reflects well the discrete choice models used in practice. To solve this pricing problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. The effectiveness of our algorithm is demonstrated on a parking services pricing case, and a benchmark against solvers and existing contributions in the literature are performed.

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arXiv2022

Fighting Pickpocketing using a Choice-based Resource Allocation Model

Inspired by European actions to fight organised crimes, we develop a choice-based resource allocation model that can help policy makers to reduce the number of pickpocket attempts. In this model, the policy maker needs to allocate a limited budget over local and central protective resources as well as over potential pickpocket locations, while keeping in mind the thieves' preferences towards potential pickpocket locations. We prove that the optimal budget allocation is proportional in (i) the thieves' sensitivity towards protective resources and (ii) the initial attractiveness of the potential pickpocket locations. By means of a numerical experiment, we illustrate how this optimal budget allocation performs against various others budget allocations, proposed by policy makers from the field.

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arXiv2021

Stable allocations for choice-based collaborative price setting

Horizontal agreements can fall within the scope of exemptions to antitrust competition if they are expected to create pro-consumer benefits. Inspired by such horizontal agreements, we introduce a cooperative game in which a set of transport operators can collectively decide at what price to offer sustainable urban mobility services to a pool of travelers. The travelers choose amongst the mobility services according to a multinomial logit model, and the operators aim at maximizing their joint profit under a constant market share constraint. After showing that various well-known allocation rules (i.e., proportional rules and the Shapley value) do not always generate core allocations, we present a core-guaranteeing allocation rule, the market share exchange rule. This rule first allocates to each transport operator the profit he or she generates under collaboration, and then subsequently compensates those transport operators that lose part of their market share, which is paid by the ones that receive some extra market share. This exchange of market share is facilitated by a unique price, which can be expressed as the additional return by cooperating per unit of market share. Finally, we show that, under some natural conditions, the market share exchange rule still sustains the collaboration when the transport operators need to pay back part of the joint profit to society.

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arXiv2020

Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms

The emergence of Big Data has enabled new research perspectives in the discrete choice community. While the techniques to estimate Machine Learning models on a massive amount of data are well established, these have not yet been fully explored for the estimation of statistical Discrete Choice Models based on the random utility framework. In this article, we provide new ways of dealing with large datasets in the context of Discrete Choice Models. We achieve this by proposing new efficient stochastic optimization algorithms and extensively testing them alongside existing approaches. We develop these algorithms based on three main contributions: the use of a stochastic Hessian, the modification of the batch size, and a change of optimization algorithm depending on the batch size. A comprehensive experimental comparison of fifteen optimization algorithms is conducted across ten benchmark Discrete Choice Model cases. The results indicate that the HAMABS algorithm, a hybrid adaptive batch size stochastic method, is the best performing algorithm across the optimization benchmarks. This algorithm speeds up the optimization time by a factor of 23 on the largest model compared to existing algorithms used in practice. The integration of the new algorithms in Discrete Choice Models estimation software will significantly reduce the time required for model estimation and therefore enable researchers and practitioners to explore new approaches for the specification of choice models.

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arXiv2020

Enhancing Discrete Choice Models with Representation Learning

In discrete choice modeling (DCM), model misspecifications may lead to limited predictability and biased parameter estimates. In this paper, we propose a new approach for estimating choice models in which we divide the systematic part of the utility specification into (i) a knowledge-driven part, and (ii) a data-driven one, which learns a new representation from available explanatory variables. Our formulation increases the predictive power of standard DCM without sacrificing their interpretability. We show the effectiveness of our formulation by augmenting the utility specification of the Multinomial Logit (MNL) and the Nested Logit (NL) models with a new non-linear representation arising from a Neural Network (NN), leading to new choice models referred to as the Learning Multinomial Logit (L-MNL) and Learning Nested Logit (L-NL) models. Using multiple publicly available datasets based on revealed and stated preferences, we show that our models outperform the traditional ones, both in terms of predictive performance and accuracy in parameter estimation. All source code of the models are shared to promote open science.

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