I will defend my thesis titled ‘Scheduling Optimization Applied to the Oil Industry’ this Friday, May 13th at 2 p.m. The presentation will be in English and will take place in a hybrid mode: at the Universidade Federal Fluminense (Brazil) and via video conference (Google Meet). The video link is: https://meet.google.com/yqy-qsdr-jzb
The jury will be composed of:
- Agostinho Agra, Dep. de Matemática – Universidade de Aveiro, Portugal (Rapporteur)
- Sophie Demassey, CMA – Mines ParisTech, France (Rapporteuse)
- Yuri Abitbol de Menezes Frota, IC-Universidade Federal Fluminense, Brésil (Encadrant)
- Rosa Maria Videira de Figueiredo, Avignon Université, France Encadrante)
- Serigne Abdoulaye Gueye, Avignon Université, France (Directeur)
- Simone de Lima Martins, IC-Universidade Federal Fluminense, Brésil (Examinatrice)
- Igor Machado Coelho, IC-Universidade Federal Fluminense, Brésil (Examinatrice)
- Ayse Nur Arslan, INSA Rennes, France (Examinatrice)
- David Sotelo Pinheiro da Silva, Petrobras, Brésil (Examinatrice)
Abstract: This thesis proposes new solution approaches for two important problems in the areas of energy, oil and gas, which involve uncertain input parameters.In the context of smart grids, the first problem addresses the reality of microgrids which trade energy with the main grid to either sell its production surplus (from renewable energy sources) or buy an additional amount to support local consumers’ demand. In this scenario, smart control devices are important elements, executing real-time energy scheduling according to fluctuations in production and consumption. As we might expect, the main grid’s power generation and supply becomes more unscheduled and risky as energy trading quantities oscillate over time. The first part of the work studies a flexible bilateral energy contract subscription framework, established between electricity suppliers and a client. The framework is coupled with a real-time command strategy (RTCS), suited for energy scheduling of microgrids with uncertainty in both production and consumption.
The main products are an embedded Robust Optimization model, capable of providing solutions for multi-period-ahead trading of energy, while minimizing the microgrid’s worst-case cost, as well as a set of control strategies for real-time energy scheduling.
During the research, the initial robust optimization model was improved to represent budgeted uncertainty, allowing for less conservative solutions that are, at the same time, more flexible and less expensive, while providing protection against worst-case scenarios.
The proposed solution was tested using consumption and production data collected from a real microgrid in a research lab in Tsukuba, Japan.
Relying on a set of real-world-inspired energy purchase contracts, simulation experiments have confirmed the efficacy of different robust-based RTCS strategies, according to scenario types. For specific protection levels, the robust RTCS was able to dominate the naive deterministic RTCS in all operational cost and system reliability metrics. Results obtained with a case study show that the effectiveness of each robust solution will depend on the microgrid’s load profile and renewable production, which vary according to the season of the year. Hence the importance of the budgeted uncertainty set, which provides a pool of robust solutions, with different protection levels, the decision-maker can choose from.
The second research is related to production planning under uncertainty, in particular the scheduling problem known as Robust Permutation Flow Shop Scheduling. We adopt the budgeted uncertainty approach, where operation processing times are expected to vary within a given interval. Therefore the worst-case scenario is bounded by a budget parameter Gamma, which limits the maximum number of operations whose processing times may oscillate to their worst-case values. The great advantage of this variant of the problem consists in adjusting the level of conservatism of the solution, thus obtaining a balance between solution cost and robustness in the worst case. We developed solution methods for two different objective functions: makespan and weighted sum of job completion times.
To our knowledge, this is the first work to obtain optimal robust solutions to both objectives.
Regarding the makespan objective function, we extended two classical MILP formulations for the deterministic case and combined them with a Column-and-Constraint Generation (C&CG) framework. For this purpose, a dynamic programming algorithm was also developed, allowing the identification of worst-case scenarios in polynomial time. Extensive experimental results demonstrated that the proposed algorithm was effective in obtaining optimal robust schedules for small and medium-sized problems (including 50 x 2, 100 x 2 and 10 x 5, 15 x 5 instances). Additionally, based on a case study with two representative instances, we have assessed the trade-off between solution quality and cost, comparing robust solutions to deterministic and stochastic ones. Also, according to simulations based on three probability distributions, such robust schedules presented only a small overhead in the expected solution cost.
We also developed a Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic to obtain efficient solutions for large problem instances (up to 100 x 50). The evaluation of GRASP performance required the adaptation of literature instances, such as the well-known Taillard instances. Experimental results have demonstrated that the GRASP algorithm is efficient in obtaining optimal robust schedules for small and medium-sized problems, when compared to the C&CG exact solution method. The evaluation was based on 4 sets of test problems and GRASP has been shown to produce optimal or near-optimal solutions on all of these instances.
Finally, we explored the robust flow shop with the weighted sum of job completion times objective, where the processing times of operations are subject to uncertainty. In the context of the oil and gas industry, this variant of the flow shop is associated with the maintenance schedule for oil rigs. When each piece of equipment is subject to maintenance, certain assistance operations must have their order of execution respected. Additionally, to complete this defined set of tasks, oil wells must be shut down only to reopen to production at the end of the schedule. The objective, in this case, is to find a schedule that minimizes the loss of oil production caused by the time that each oil well has remained closed for maintenance. Based on the Column-and-Constraint Generation framework, we were able to obtain exact solutions to instances of size up to 15 x 5. In addition, we proposed a case study applied to the oil and gas industry, using real data, obtained from the history of Brazilian oil platforms.
Keywords: Robust Optimization. Smart grid. Energy. Scheduling. Permutation Flow Shop.