2025-2026

Yasmine BECK - Postdoc at ESSEC 

Wednesday, November 12

Title : A Primer on Bilevel Optimization under Uncertainty and Solution Approaches for Robust Bilevel Problems.

Abstract : Bilevel optimization is a rather young but very active sub-field of mathematical optimization. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. However, the nested structure of bilevel problems makes them intrinsically hard to solve—even if all parameters of the problem are exactly known. Further challenges arise if problems under uncertainty are considered.

In this talk, we begin with a brief introduction to bilevel optimization under uncertainty. In particular, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to classic, i.e., single-level, optimization because not only the problem data but also the (observation of the) decisions of the two players can be subject to uncertainty.

We then explore how techniques from robust optimization can be used to tackle bilevel problems under uncertainty and discuss some recent algorithmic advances for solving mixed-integer linear Gamma-robust bilevel problems. Finally, we conclude with a brief look at emerging solution approaches for another class of robust bilevel problems.

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Nandan KUMAR SINGH, FORE School of Management, New Delhi 

Tuesday, October 21

Title : Optimal Strategies for Battery Design for Recyclability under Uncertainty and

Regulation

Abstract : 

Electric Vehicle battery regulations mandate the Original Equipment Manufacturers (OEMs) to use certain proportion of rare earth metals in the design of newer batteries. This requires the OEMs to enter into collaboration with the battery recyclers. In this paper, we consider the strategic interactions between OEMs and the battery recyclers from the perspective of designing batteries for recyclability when there is uncertainty around the recycling value. We model the interaction as a Stochastic Stackelberg–Nash Equilibrium problem, where the recycler is the follower and decides on the recycling capacity, while the OEM as the leader, seeks to maximize expected profit by optimizing its investment in designing batteries suitable for recycling. We obtain the following results. First, in the absence of any regulation, we show that a contract can lead to a win-win-win outcome for the OEM, the recycler, and the environment. The total business value also increases compared to the case of no collaboration. Second, we show that under a regulation mandating minimum recycling threshold, the total business value increases even more when the battery recyclability design cost is low. Conversely, when the battery recyclability design is costly and the used battery transaction price is high, stricter regulation always decreases business value. However, when the battery recyclability design is costly and the used battery transaction price is low, total business value becomes a convex unimodal function of regulation, the impact is driven by the quantum of minimum recycling material target by the government. Finally, our analysis suggests that when the mandatory recycling level exceeds a certain threshold, it always benefits the recycler and hurts the OEM suggesting that the government could consider introducing subsidies for OEMs to support battery design for recyclability.

Keywords: Electric Vehicle Battery, Recycling, Regulation, Uncertainty, Stochastic Stackelberg Nash Equilibrium.

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Javier MARENCO - University Torcuato Di Tella, Argentina 

Wednesday, October 1

Titre : Dynamic parking in unstructured parking lots

Abstract : We consider the following dynamic car parking problem. We have a parking lot, which we assume is divided into a grid of n × m positions. A single car can be placed in each position. We assume that each position corresponds to a rectangle with its longest side parallel to the horizontal axis, so that each car faces either the left or right side of the grid. In the classic scheme, the grid is divided into vertical "lanes," on which a car cannot be placed, such that the remaining positions allow a path to/from the parking lot entrance/exit. In this work, we consider a more general version of the problem, in which a car can park in any position of the grid, as long as there are paths from the entrance/exit to that position when the car enters and exits the parking lot. Once parked, a car cannot move from its position. A priori, this strategy allows for the allocation of a larger number of cars than the classic scheme, making better use of available resources.

We assume we have a list of reservations, each consisting of a day and time of the reservation, a day and time of the car's arrival at the parking lot, and a day and time of the car's departure from the parking lot. Given this reservation list, the offline problem consists in determining the largest number of cars (or, alternatively, the largest revenue) that can be allocated to the parking lot. The online version consists of determining, for each car in the reservation list in order of reservation date, whether the car can be accepted and, if so, in which position it should be allocated. In this work, we propose an integer linear programming model for the offline problem and several integer linear programming-based strategies for the online problem. Using historical reservation data for a parking lot in Santiago, Chile, we show that online schemes are feasible and allow for a better use of the available space.