We consider general aggregation/disaggregation techniques to address optimization problems that are expressed with the help of sequential decision processes. Our main goals are threefold: a generic formalism that encompasses the aforementioned techniques ; more efficient algorithms to control the aggregation procedures ; open-source codes that leverage and integrate these algorithms to efficiently solve hard combinatorial problems in different application fields.
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Many real-life decision-making problems under uncertainty include some form of interaction between the actions of the decision-maker and the realization of uncertain parameters. For instance, in medical appointment scheduling, no-shows of the patients are typically related to the schedules themselves whereas, in long-term medical treatments, the state of a patient evolves depending on past medication (decision-dependent uncertainty). On the other hand, in planning organ transplants, the uncertainty related to the compatibility of donors and patients needs to be investigated via expensive medical tests (information discovery) under a given budget constraint. It is therefore essential to incorporate the interactions of the decision-maker with the uncertain parameters within optimization under uncertainty models. This project proposes the study and solution of robust optimization models formalizing such interactions under a single mathematical framework with decision-dependent uncertainty sets.
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This project aims at proposing theoretical and practical results for hard combinatorial optimization problems in an uncertain environment. These problems have in common the fact that the parameters needed to assess the validity of the solution and compute its cost are unknown. Uncertainty in decision making can be caused by several external factors. The most common are related to stochastic parameters (service demand, time needed for a task, prices, …). Incomplete information can also come from the presence of competitors whose policies are not known to the decision maker.
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Robust optimization has evolved as a key paradigm for handling data uncertainty within mathematical optimization problems: it requires little historical information, can be used without characterizing probability distributions and often leads to tractable optimization problems that can be treated with existing deterministic optimization paradigms. However, the picture is more complex when some of the decisions (referred to as recourse decisions) can be adjusted after the uncertain data is known, to mitigate the effects of uncertainty, leading to adjustable robust optimization problems. Adjustable problems with discrete variables or multiple decision periods are particularly difficult to solve and, up to now, no scalable exact method has emerged. Project DROI proposes to study primal and dual approximations for such problems.
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The aim of the Grip4All project is to make industry more competitive by developing a new palletising cell adapted to the severe constraints imposed on the logistics flow when handling mixed products (of varying dimensions and weight) and arranging them on a pallet, without having to sort them manually upstream. This new type of palletising meets a strong demand from a number of sectors, notably mass distribution and the food industry. It meets the demand for handling heterogeneous products without imposing constraints on their packaging, which significantly improves productivity and eliminates tedious human tasks. No similar solution currently exists on the market. The flexible robotics issues addressed will be transposable to other logistics processes in the factory of the future.
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The project:
Strategic Power Systems Development for the Future (PowerDev), funded by PEPR TASE, studies optimization methods and reliability/resilience engineering applied to large-scale electrical power systems. The project is led by CentraleSupélec at the University of Paris Saclay and is composed of a consortium of higher education institutions across France (CentraleSupelec, UVSQ, University Grenoble Alpes), as well as research organizations (Inria, CNRS).
Research topic and objectives:
Modern power systems are expected to become increasingly complex to design and operate due to the growing number of renewable energy sources (RES). Renewable energy generation is, by nature, intermittent and introduces an amount of uncertainty that severely affects the physical responses of the power system, particularly in terms of voltage control and frequency regulation [1]. Moreover, RES integration within the power system requires the introduction of many new power electronic devices, which add to the system’s complexity and increase its possible failure modes [2,3]. Combined with unexpected initiating events, these two main features can lead to cascading failure risks, triggering disastrous consequences to the power grid and, most notably, large-scale blackouts [4-7]. The economic and societal consequences to the impacted regions are usually massive, with economic loss measured in the tens of billions of dollars [8]. The main objective of this project is to evaluate and optimize the resilience of power systems in the context of a massive insertion of renewable energies. The project aims to elaborate a comprehensive and integrated set of decision support tools by considering extreme events in present and future climates, the complexity of the power grid, and socio-economic scenarios.
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One way to improve delivery efficiency is to allow the supplier to manage customer inventory itself. This makes it possible to deliver at the most relevant times, while ensuring a minimum level of stock. In this case, the supplier makes replenishment decisions for products based on specific inventory and supply chain policies. This practice is often described as a win-win model: suppliers save on distribution and production costs because they can coordinate shipments for their different customers, and buyers benefit from a better service cost, and can outsource its inventory management, which is not necessarily its core business. In such contexts, the supplier must make three simultaneous decisions: (1) when to serve a given customer, (2) how much to deliver to that customer when served, and (3) how to combine customers into vehicle routes. In the operations research literature, we speak of the “Inventory Routing Problem” (IRP).
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