2025

Heure:	10:30 - 11:30
Lieu:	Salle B107
Résumé:	A probing-enhanced stochastic programming approach for the capacitated multi-item lot-sizing problem.
Description:	Franco Quezada In traditional stochastic programming, decisions are made based on known probabilities or distributions of uncertain parameters. However, in real-world scenarios, decision-makers often have opportunities to gather additional information about these uncertainties through a process known as probing. Probing allows for observation of certain random variables, which can provide valuable insights into the behavior of related uncertainties. However, probing is not free—it involves a cost that must be taken into account in the decision-making process. This cost could represent financial expenditure, time, or resource allocation necessary to gather data or perform exploratory actions. Thus, probing involves taking actions or gathering data to learn more about the uncertain variables before making the final decision. In two-stage stochastic programs, this can mean performing certain preliminary actions (probing decisions) that help to reveal more information about future states (first and second-stage decisions). We investigate a probing-enhanced stochastic programming approach for the two-stage stochastic multi-item capacitated lot-sizing problem, which is a classic inventory management problem where decisions are made in two stages to minimize costs while considering uncertain future demand. Two-stage problems, except for very simple models, are generally intractable to solve exactly. Even with complete knowledge of the demand distribution, explicitly integrating the second-stage costs is computationally prohibitive. A common approach to address this complexity is the Sample Average Approximation (SAA) method, which approximates the expectation by sampling from the original distribution to create a finite set of scenarios. Then we adopt a non-anticipative formulation that enables us to ensure that decisions are consistent with the information available at the time of decision-making. The critical aspect of this approach is that the enforcement of non-anticipativity conditions depends on the decisions themselves. Thus, the resulting model includes a vast number of conditional non-anticipativity constraints, proportional to the square of the number of scenarios. This leads to a mixed-integer linear programming (MILP) formulation characterized by a large number of big-M constraints, which can be challenging to solve efficiently. We propose a decomposition approach to solve the resulting non-anticipative formulation, exploiting the structure of the problem by breaking it into smaller, more manageable sub-problems that can be solved efficiently, providing a more practical and scalable solution approach. Preliminary computational results demonstrate that the proposed decomposition algorithm significantly outperforms the other approaches in terms of both solution quality and computation time, achieving improvements by several orders of magnitude. Joint work with Céline Gicquel, Safia Kedad-Sidhoum and Bernardo Pagnoncelli.

Heure:	10:30 - 11:30
Lieu:	Salle C212
Résumé:	Designing sustainable diet plans by solving tri-objective 0-1 programs
Description:	Marianna De Santis We present an algorithm for triobjective nonlinear integer programs that combines the eps-constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then used to determine the nondominated solutions of triobjective 0-1 models, built to design nutritionally adequate and healthy diet plans, minimizing their environmental impact. The diet plans refer to menus for school cafeterias and we consider the carbon, water and nitrogen footprints as conflicting objectives to be minimized. Energy and nutrient contents are constrained in suitable ranges suggested by the dietary recommendation of health authorities. Results obtained on two models and on real world data are reported and discussed. Coauthors: Luca Benvenuti, Alberto De Santis, Daniele Patria

Heure:	10:30 - 11:30
Lieu:	Salle B107
Résumé:	Decision-focused learning: theory and applications to contextual stochastic optimization
Description:	Thibault Prunet Real-world industrial applications frequently confront the task of decision-making under uncertainty. The classical paradigm for these complex problems is to use both machine learning (ML) and combinatorial optimization (CO) in a sequential and independent manner. ML learns uncertain quantities based on historical data, which are then used used as an input for a specific CO problem. Decision-focused learning is a recent paradigm, which directly trains the ML model to make predictions that lead to good decisions. This is achieved by integrating a CO layer in a ML pipeline, which raises several theoretical and practical challenges. In this talk, we aim at providing a comprehensive introduction to decision-focused learning. We will first introduce the main challenges raised by hybrid ML/CO pipelines, the theory of Fenchel-Young losses for surrogate differentiation, and the main applications of decision-focused learning. As a second objective, we will present our ongoing works that aim at developing efficient algorithms based on the Bregman geometry to address the minimization of the empirical regret in complex stochastic optimization problems.