Fabricio Oliveira

Contingency-Constrained Unit Commitment With

This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions.

n - K

This article presents a methodology for conceiving and planning the development of an optimized supply chain of a biodiesel plant sourced from family farms and taking into consideration agricultural, logistic, industrial, and social aspects. This model was successfully applied to the production chain of biodiesel fuel from castor oil in the semi-arid region of Brazil. Results suggest important insights related to the optimal configuration of the crushing units, regarding its location, technology, and when it should be available, as well as the configuration of the production zones along the planning horizon considered. Moreover, a sensitivity analysis is performed in order to measure how possible variations in the considered conjecture can affect the robustness of the solutions.

Security Criterion: A Robust Optimization Approach

We present a scenario decomposition framework based on Lagrangean decomposition for the multi-product, multi-period, supply investment planning problem considering network design and discrete capacity expansion under demand uncertainty. We also consider a risk measure that allows us to reduce the probability of incurring in high costs while preserving the decomposable structure of the problem. To solve the resulting large-scale two-stage mixed-integer stochastic linear programming problem, we propose a novel Lagrangean decomposition scheme. In this context, we compare dierent formulations for the non-anticipativity conditions. In addition to that, we present a new hybrid algorithm for updating the Lagrangean multiplier set, based on the combination of cutting-plane, subgradient and trust-region strategies. Numerical results suggests that dierent formulations of the non-anticipativity conditions have a signicant eect on the performance of the algorithm. Moreover, we observe that the proposed hybrid approach has superior performance when compared with the traditional subgradient algorithm in terms of faster computational times for the problem addressed in this work.

Optimization of biodiesel supply chains based on small farmers: A case study in Brazil

This paper addresses the solution of a two-stage stochastic programming model for a supply chain investment planning problem applied to the petroleum products supply chain. In this context, we present the development of acceleration techniques for the stochastic Benders decomposition that aim to strengthen the cuts generated, as well as to improve the quality of the solutions obtained during the execution of the algorithm. Computational experiments are presented for assessing the eciency of the proposed framework. We compare the performance of the proposed algorithm with two other acceleration techniques. Results suggest that the proposed approach is able to eciently solve the problem under consideration, achieving better performance better in terms of computational times when compared to other two techniques.

A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations

Operational decisions for crude oil scheduling activities are determined on a daily basis and have a strong impact on the overall supply chain cost. The challenge is to develop a feasible schedule at a low cost that has a high level of confidence. This paper presents a framework to support decision making in terminal-refinery systems under supply uncertainty. The proposed framework comprises a stochastic optimization model based on mixed-integer linear programming for scheduling a crude oil pipeline connecting a marine terminal to an oil refinery and a method for representing oil supply uncertainty. The scenario generation method aims at generating a minimal number of scenarios while preserving as much as possible of the uncertainty characteristics. The proposed framework was evaluated considering real-world data. The numerical results suggest the efficiency of the framework in providing resilient solutions in terms of feasibility in the face of the inherent uncertainty.

Accelerating Benders Stochastic Decomposition for the Optimization under Uncertainty of the Petroleum Product Supply Chain

The Brazilian oil industry has gained new momentum after the discovery of large oil reserves in deep under-water. Numerous investments in the oil production chain are expected to support the scale of this operation. Given this context, the use of a decision support system (DSS), which encompasses the complexity of the oil supply chain to support investment decisions, becomes crucial. This paper proposes a DSS that is based on a mixed-integer linear programming (MILP) model that allows the evaluation of different investment alternatives in logistics networks, such as expanding the capacity for transport, handling, and/or storage. Additionally, the DSS is composed of a database structure, business intelligence environment, and graphical visualization tool. The features of the proposed system were evaluated in two case studies. The first case study assesses the synergies between two projects: specifically the expansion of the berthing capacity of vessels in a marine terminal, and the increase in the transport capacity of the pipeline that connects the marine terminal to a distribution base. The second case study evaluates the dependency of the investment in sections of a pipeline that connects a refinery to several distribution bases. These case studies demonstrate the potential use of a DSS that currently optimizes investments in the Brazilian petroleum supply chain.

A framework for crude oil scheduling in an integrated terminal-refinery system under supply uncertainty

This paper presents the application of a stochastic Benders decomposition algorithm for the problem of supply chain investment planning under uncertainty applied to the petroleum byproducts supply chain. The uncertainty considered is related with the unknown demand levels for oil products. For this purpose, a model was developed based on two-stage stochastic programming. It is proposed two different solution methodologies, one based on the classical cutting plane approach presented by Van Slyke & Wets (1969), and other, based on a multi cut extension of it, firstly introduced by Birge & Louveaux (1988). The methods were evaluated on a real sized case study. Preliminary numerical results obtained from computational experiments are encouraging.

Investment planning in the petroleum downstream infrastructure

We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. This dual is widely used in decomposition methods for the solution of SMIPs. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual value. The key improvement in the new algorithm is an inner loop of optimized linearization steps, similar to those taken in the classical Frank--Wolfe method. Numerical results demonstrate that our new algorithm empirically outperforms the standard implementation of progressive hedging for obtaining bounds in SMIP.

Stochastic Benders decomposition for the supply chain investment planning problem under demand uncertainty

This article addresses the problem of scheduling in oil refineries. The problem consists of a multi-product plant scheduling, with two serial machine stages—a mixer and a set of tanks—which have resource constraints and operate on a continuous flow basis. Two models were developed: the first using mixed-integer linear programming (MILP) and the second using genetic algorithms (GA). Their main objective was to meet the whole forecast demand, observing the operating constraints of the refinery and minimizing the number of operational changes. A real-life data-set related to the production of fuel oil and asphalt in a large refinery was used. The MILP and GA models proved to be good solutions for both primary objectives, but the GA model resulted in a smaller number of operational changes. The reason for this is that GA incorporates a multi-criteria approach, which is capable of adaptively updating the weights of the objective throughout the evolutionary process.

Combining Progressive Hedging with a Frank--Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

ABSTRACT The crude oil offloading and supply problem (COSP) is a type of operation maritime inventory routing (MIR) problem encountered by petroleum companies. In COSP, the company not only is responsible for the ship scheduling to carry the crude oil from production sites to discharge ports but also must maintain inventory levels at both ports (production and consumption) between safety operational bounds to avoid disruptions in its crude oil production and/or refining processes. We show how to improve significantly the decision-making process in a Brazilian petroleum company using a mixed-integer linear programming (MILP) model to represent COSP. Comparison tests with a current ship-scheduling method adopted in the company indicated that the use of the MILP model increased the transportation efficiency and reduced costs by 20% on average. In addition to the quantitative gains, the use of a MILP model to solve COSP has succeeded when encountering real-life events, such as variation in production or consumption rates, berth unavailability, and changes in the storage capacities at ports.