Abstracts
Elena Fernández:
The Synchronized Users Preferences Problem
In this talk, we introduce the Synchronized Users’ Preferences Problem (SUP), with particular emphasis on its potential applications. The SUP can be modeled as a bilevel optimization problem involving both location-allocation and routing decisions. It aims at synchronizing users’ preferences regarding service times and locations. We analyze several properties of the SUP and exploit them to derive a single-level mixed-integer linear programming formulation. Results from a real-world application are presented and analyzed, and insights for decision-makers are discussed.
Alfredo Marín:
The problem of opposing p-centers
In the p-center problem, a single decision-maker typically determines both the location of the centers and the assignment of demand points to those centers.
In this presentation, we study a model involving two different agents: one decides the location and the other the assignment, each with their own cost matrix.
In this scenario, the first agent must take into account that the second agent may choose from multiple optimal assignments,
not all of which are favorable to the first agent.
Justo Puerto:
Twenty years of Ordered Optimization with applications to Machine learning, Finance, Location and Routing
Ordered measures form a powerful and flexible modeling paradigm that encompasses a wide range of objective functions, including fairness indices, risk and robustness criteria, and other aggregation operators. Despite their practical importance, incorporating ordering operations into optimization models is inherently challenging: they are interdependent and cannot be treated in isolation from the underlying decision variables.
This talk presents a unified optimization framework for computing and optimizing a broad class of ordered measures within a common algebraic structure. The framework accommodates linear, quadratic, and nested ordered measures, yielding compact, strengthened mixed-integer programming formulations that generalize many existing results in the literature. We also revisit the structural properties of these formulations and discuss the modeling insights that arise from alternative representations of ordering constraints.
The versatility of the proposed framework is illustrated through representative application domains: location-routing problems, machine learning and enhanced indexation in portfolio optimization.
Yolanda Hinojosa Bergillos:
Hub Location with Protection under Inter-hub Link Failures
In this work, we study the design of hub backbone networks that remain operational when inter-hub links fail. We propose two mathematical programming models that minimize the set-up costs of activated hubs and inter-hub links, together with the expected routing costs of the commodities.
In both models, each commodity has an original routing path and a backup path that can be used in case of failure. The first model explicitly constructs a backup path containing a single inter-hub arc. The second model follows a more flexible approach: instead of constructing backup paths explicitly, it guarantees their existence by imposing a given level of connectivity on the backbone network. In this case, alternative paths may use several inter-hub links.
We present the results of an extensive computational study to compare the performance of both models and to analyse the impact of different parameters. Finally, we study the price of robustness, evaluating the additional design cost required to obtain networks that are better protected against failures and their ability to reroute demand under different failure scenarios.
Stefan Nickel:
Towards Data Driven Location Science (DDLS)
In this talk, we will explore the concept of a more data-driven approach to location problems. We will address key questions that arise in the application of location models, algorithm design, and solution strategies. These questions are particularly important when dealing with real-world location problems that have certain temporal contexts and are subject to uncertainty and additional side constraints:
- Which problem aspects should be represented in the model?
- What are the key cost drivers in the model to identify the right objective function(s)?
- Which parts of the solution are performance-critical?
- Which decisions are driven by data structures and remain stable across model variants?
- Which algorithms perform best for a certain location problem, and why?
- How can the algorithm be adapted to the data?
Whenever possible, we will suggest quantitative measures to evaluate the aforementioned aspects.
Several papers have addressed some of these questions, but to our knowledge, there has been limited systematic work on data-driven aspects of location science.
In addition to providing a general overview and review of DDLS, we will present new results for some specific aspects: Data-Driven Interpretation of Solutions for Location Problems, Data-Driven Algorithm Design and Data-Informed Model Choice.
Jessica Rodríguez-Pereira:
Routing with a Plan B: Integrated Site Selection and Routing under Uncertainty
We introduce the Stochastic Assessment Routing Problem (SARP), motivated by post-disaster field assessments where both the locations to visit and the routes to follow must be planned under uncertain site availability. The problem integrates three interrelated decisions: selecting a representative set of primary sites, assigning a backup location to each selected site, and designing routes that account for the possible activation of these backups. Site availability is only revealed upon arrival, and backups are selected to preserve the characteristics of the intended sample.
Francisco Saldanha da Gama:
The latency location-routing problem with stochastic travel times
In vehicle routing problems, latency is defined as the cumulative arrival time across all visited nodes. This is a critical performance measure in application contexts such as disaster operations management. This presentation addresses the latency location-routing problem, in which depot locations and vehicle routes are determined simultaneously under stochastic travel times characterized by a given joint cumulative distribution function. To model a risk-averse decision-maker, objectives based on the Conditional Value-at-Risk as well as on a risk-neutral/risk-averse trade-off are discussed, both allowing for adjustable risk-aversion levels. A mathematical formulation is presented alongside a multi-start variable neighborhood search algorithm tailored for the finite-scenario setting. To handle realistic problem instances where travel time distributions feature very large or infinite support, this metaheuristic is embedded within a sampling framework. An extensive computational analysis is presented to demonstrate algorithmic performance, highlight the managerial importance of explicitly capturing travel time uncertainty, and analyze the structural impact of risk-aversion parameters on optimal solutions.
Martine Labbé:
Solving Chance-Constrained (mixed integer) Linear Optimization Problems with Branch-and Cut
Consider an optimization problem in which some constraints involve random coefficients with known probability distribution. A chance-constraint version of this problem amounts to impose that these constraints must be satisfied with a probability larger than or equal to a given threshold.
Chance-constraint optimization problems (CCOPs) are frequently used to model problems in the domain of energy. They are known to be NP-hard. In the case where objective and constraints are linear and the random data have finite support, the problem can be reformulated as a mixed-integer linear problem by introducing big-M constants.
In this talk, we propose a Branch-and-Cut algorithm for solving linear CCOP. We determine new valid inequalities and compare them to some existing in the literature. Moreover, we state and prove results on the closure of these valid inequalities. Computational experiments validated the quality of these new inequalities.
This is a joint work with Diego Cattaruzza, Matteo Petris, Marius Roland and Martin Schmidt.
Martina Cerulli:
A bilevel approach for compensation and routing decisions in last-mile delivery
Abstract: In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. Since the carriers are not under the platform’s control, the platform has to anticipate their reactions, while deciding how to allocate the delivery operations. In this work, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers together with the compensation paid for each accepted request; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. For the resulting bilevel formulation, we propose a single-level reformulation and an alternative formulation where the lower-level routing variables are projected out. A branch- and-cut algorithm is proposed to solve the bilevel models and extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics.
Markus Leitner:
Compensation, bundling, and driver behavior in crowdsourced delivery
Challenges in last-mile delivery such as high costs, rising customer expectations, and congested urban traffic have encouraged innovative solutions like crowdsourced delivery, in which occasional drivers undertake delivery tasks along their pre-planned trips in exchange for compensation. A key difference from traditional delivery is that the operator controls neither driver availability nor whether offered tasks are accepted. Acceptance can only be influenced indirectly, through the compensation offered and through the way individual tasks are combined into bundles. Both are decisions of the operator rather than exogenous parameters, and both shape driver behavior. We study integrated optimization problems that maximize total expected cost savings by offering bundles of tasks to occasional drivers. To this end, we show how to simultaneously determine the bundles, their assignment to occasional drivers, and the compensation for each bundle-driver pair, while accounting for bundle- and compensation-dependent acceptance probabilities. We first address these integrated challenges in a static setting in which tasks and drivers are known in advance, before extending the problem and our solution method to the case where tasks and drivers arrive dynamically and stochastically.
Claudia Archetti
Profit Sharing in Horizontal Collaboration: An Application to Vehicle Routing Problems
This paper studies a Profit-Sharing Vehicle Routing Game, in which the value of each coalition is determined by solving a Vehicle Routing Problem (VRP). The Framework models collaborative transportation settings where agents coordinate routing decisions and share the resulting profits. To ensure the stability of cooperation, we investigate allocation mechanisms based on cooperative game-theoretic solution concepts. In particular, we study
two optimization problems widely used in the literature: the Least-Core Problem and the Optimal Profit Share Problem. For both problems, we develop mixed-integer programming formulations that explicitly incorporate the routing structure of the underlying VRP. We further extend the analysis by computing the nucleolus of the game, which refines core-based allocations through a lexicographic minimization of coalition dissatisfaction and selects a unique payoff
vector. To this end, we exploit the same routing-based separation problem within an iterative lexicographic scheme. By embedding operational routing decisions within the cooperative game, the proposed approach connects transportation optimization with coalition stability, providing a unified Framework to analyze stable and refined profit-sharing mechanisms in collaborative scenarios.
Joint work with Martina Cerulli, Elena Fernández, and Ivana Ljubic.