1 présentation

• 
  09h00 - 10h00

  Modeling Fairness in Facility Location and Routing

  • Ljubic Ivana, prés., ESSEC Business School

  Most combinatorial optimization problems evaluate solution quality by aggregating individual performance measures into a single metric. In facility location, for instance, allocation costs from clients to their nearest open facility are typically summarized as the average allocation cost. Similarly, in routing problems, optimization focuses on minimizing the total cost across all routes, often disregarding the individual quality of routes for each driver. Even in machine learning—such as supervised classification—the objective is to minimize the average misclassification error across all observations.

  In this talk, we explore alternative quality measures that account for fairness or equity (e.g., min-max, range, Gini deviation, Hurwicz criterion), as well as robustness (e.g., conditional value at risk, k-sum). To address these objectives, we apply the discrete ordered operator, which provides a unified modeling framework capable of capturing all these quality measures and more. This stands in contrast to much of the existing literature, which typically develops specialized models and solution techniques tailored to each specific measure.

  We provide a generic MIP approach to model these diverse objectives and solve them within a common optimization framework. For facility location problems, we show how the discrete ordered objective can be efficiently handled using Benders decomposition, significantly improving the performance of state-of-the-art MIP approaches. For routing problems, we leverage connections to bilevel optimization to incorporate fairness directly into route planning.

  The talk is based on a joint work with M. Pozo, J. Puerto Albandoz and A. Torrejón