Mathematical programming approaches for lot-sizing under intermittent renewable energy

Abstract

The industrial sector is currently the second largest global carbon emitter, it should urgently and drastically reduce its carbon emissions to meet the 2050 carbon neutrality target set by the COP-21 Paris Agreement. This global context translates into a huge pressure on industrial companies to lower the carbon footprint of their activities. At the same time, energy cost has become a primary concern for them due to the sharp increase in the price of gas and grid electricity. At a company level, a possible way of simultaneously addressing these two challenges consists in building a decentralized energy system based on renewable sources (e.g. wind, sun) directly on the production site and to use the renewable electricity generated on-site to power, at least partially, the industrial processes. This PhD thesis thus considers an industrial production site partially powered by a decentralized energy system based on intermittent renewable energy sources, and seeks to tackle the challenges posed by the management and planning of such a site at the operational short-term level. More precisely, we focus on how to jointly plan the industrial production and the energy supply of this site, over an horizon spanning the next few days, so as to minimize the total production and energy cost. We first consider a deterministic setting and investigate how to model this combinatorial optimization problem as a mixed-integer linear program. We propose a novel modeling approach which relies on the extension of a multi-product single-resource small-bucket lot-sizing model called the proportional lot-sizing and scheduling problem. This extension is particularly delicate when the problem involves sequence-dependent changeovers whose duration may overlap multiple planning periods. We show that the proposed modeling approach leads to a drastic reduction of the size of the mathematical formulation as compared to state-of-the-art modeling approaches and enables us to significantly improve the numerical efficiency of a mathematical programming solver at providing near-optimal solutions of the problem. We then consider an important aspect of the renewable energy generation: it is highly uncertain and can hardly be accurately predicted. To handle this uncertainty, we propose a two-stage scenario-based stochastic programming approach. This modeling approach results in the formulation of a large-size mixed-integer linear program displaying a block-decomposable structure. To solve it, we develop an enhanced branch-and-Benders-cut algorithm which combines several strategies to increase the convergence speed of the algorithm towards an optimal solution. This allows us to solve to near-optimality instances involving a large number of scenarios. We finally extend our previous work in two directions. We thus include uncertainties on both the renewable energy generation and the demands, and refine our modeling of the decision process by considering multiple decision stages. This allows us to account for the fact the uncertain parameters are revealed progressively over time and that some planning decisions can be adjusted accordingly. We introduce a multi-stage stochastic programming model for this problem and develop an hybrid algorithm combining a branch-and-bound search and a stochastic dual dynamic programming approach to solve it.

Rapporteurs

• M. Raf JANS: Department of Logistics and Operations Management, HEC Montréal, CANADA
• M. Vincent LECLERE, Professeur associé, École nationale des ponts et chaussées, FRANCE

Examinateurs

• Mme Dominique QUADRI, Professeure des universités, Université Paris Saclay, FRANCE
• M. Nabil ABSI, Professeur, Mines Saint-Etienne, FRANCE
• Mme Ayse AKBALIK, Maîtresse de conférences (HDR), Université de Lorraine, FRANCE